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Volume 16
Issue 6
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Algorithms, Volume 16, Issue 6 (June 2023) – 48 articles

Cover Story (view full-size image): This study focuses on the design and real-time applications of an Interval Type-2 Fuzzy PID (IT2-FPID) control system for a UAV with a flexible cable-connected payload, comparing it to the PID and Type-1 Fuzzy PID (T1-FPID) counterparts. The primary objective of this work is to address the adverse effects caused by unknown payloads and disturbances which are inherent in the system dynamics. This means the controllers have been tuned without payload and disturbances.
Instead of rewriting the equations of the UAV dynamics and redesigning the controllers to incorporate the additional dynamics of the swinging payload, this study designs the controllers by considering the known dynamics of the UAV itself, without accounting for the payload and disturbance effects. View this paper
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17 pages, 928 KiB  
Article
Enhancing Heart Disease Prediction through Ensemble Learning Techniques with Hyperparameter Optimization
by Daniyal Asif, Mairaj Bibi, Muhammad Shoaib Arif and Aiman Mukheimer
Algorithms 2023, 16(6), 308; https://doi.org/10.3390/a16060308 - 20 Jun 2023
Cited by 33 | Viewed by 8715
Abstract
Heart disease is a significant global health issue, contributing to high morbidity and mortality rates. Early and accurate heart disease prediction is crucial for effectively preventing and managing the condition. However, this remains a challenging task to achieve. This study proposes a machine [...] Read more.
Heart disease is a significant global health issue, contributing to high morbidity and mortality rates. Early and accurate heart disease prediction is crucial for effectively preventing and managing the condition. However, this remains a challenging task to achieve. This study proposes a machine learning model that leverages various preprocessing steps, hyperparameter optimization techniques, and ensemble learning algorithms to predict heart disease. To evaluate the performance of our model, we merged three datasets from Kaggle that have similar features, creating a comprehensive dataset for analysis. By employing the extra tree classifier, normalizing the data, utilizing grid search cross-validation (CV) for hyperparameter optimization, and splitting the dataset with an 80:20 ratio for training and testing, our proposed approach achieved an impressive accuracy of 98.15%. These findings demonstrated the potential of our model for accurately predicting the presence or absence of heart disease. Such accurate predictions could significantly aid in early prevention, detection, and treatment, ultimately reducing the mortality and morbidity associated with heart disease. Full article
(This article belongs to the Special Issue Artificial Intelligence Algorithms for Medicine)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>The proposed model developed to predict the heart disease.</p> Full article ">Figure 2
<p>The ensemble learning procedure.</p> Full article ">Figure 3
<p>The area under the ROC curve and the PR curve of the algorithms using the default hyperparameter settings.</p> Full article ">Figure 4
<p>The area under the ROC curve and PR curve of the algorithms using the optimal hyperparameters according to the randomized search CV.</p> Full article ">Figure 5
<p>The area under the ROC curve and PR curve of the algorithms using the optimal hyperparameters according to the grid search CV.</p> Full article ">Figure 6
<p>A comparison of the models’ performance.</p> Full article ">
20 pages, 1684 KiB  
Article
Multi-Objective PSO with Variable Number of Dimensions for Space Robot Path Optimization
by Petr Kadlec
Algorithms 2023, 16(6), 307; https://doi.org/10.3390/a16060307 - 20 Jun 2023
Cited by 1 | Viewed by 1567
Abstract
This paper aims to solve the space robot pathfinding problem, formulated as a multi-objective (MO) optimization problem with a variable number of dimensions (VND). This formulation enables the search and comparison of potential solutions with different model complexities within a single optimization run. [...] Read more.
This paper aims to solve the space robot pathfinding problem, formulated as a multi-objective (MO) optimization problem with a variable number of dimensions (VND). This formulation enables the search and comparison of potential solutions with different model complexities within a single optimization run. A novel VND MO algorithm based on the well-known particle swarm optimization (PSO) algorithm is introduced and thoroughly described in this paper. The novel VNDMOPSO algorithm is validated on a set of 21 benchmark problems with different dimensionality settings and compared with two other state-of-the-art VND MO algorithms. Then, it is applied to solve five different instances of the space robot pathfinding problem formulated as a VND MO problem where two objectives are considered: (1) the minimal distance of the selected path, and (2) the minimal energy cost (expressed as the number of turning points). VNDMOPSO shows at least comparable or better convergence on the benchmark problems and significantly better convergence properties on the VND pathfinding problems compared with other VND MO algorithms. Full article
(This article belongs to the Special Issue Applications of Evolutionary and Swarm Systems)
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Figure 1

Figure 1
<p>The illustration of the space robot path problem. Three feasible paths from the starting point, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">r</mi> <mi mathvariant="normal">S</mi> </msub> </semantics></math>, to the target point, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">r</mi> <mi mathvariant="normal">T</mi> </msub> </semantics></math>, form the Pareto front of the multi-objective SRPP.</p> Full article ">Figure 2
<p>The VNDMOPSO DSVs manipulation for the velocity update formula: (<b>a</b>) the selection of new dimension, <math display="inline"><semantics> <msub> <mi>N</mi> <mi>p</mi> </msub> </semantics></math>, of the <span class="html-italic">p</span>-th particle, (<b>b</b>) corresponding update of vectors global best, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">g</mi> <mi>p</mi> </msub> </semantics></math>, personal best, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">b</mi> <mi>p</mi> </msub> </semantics></math>, and previous position, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">u</mi> <mi>p</mi> </msub> </semantics></math>.</p> Full article ">Figure 3
<p>Results of <math display="inline"><semantics> <mi>dHV</mi> </semantics></math> metric for algorithms VNDMOPSO, VLMOPSO, and VNDGDE3 for dimensionality settings <math display="inline"><semantics> <mrow> <mi mathvariant="script">S</mi> <mn>1</mn> </mrow> </semantics></math>: <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi mathvariant="normal">d</mi> </msub> <mo>∈</mo> <mfenced separators="" open="{" close="}"> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mn>12</mn> </mfenced> </mrow> </semantics></math>.</p> Full article ">Figure 4
<p>Results of <math display="inline"><semantics> <mi>dHV</mi> </semantics></math> metric for algorithms VNDMOPSO, VLMOPSO, and VNDGDE3 for dimensionality settings <math display="inline"><semantics> <mrow> <mi mathvariant="script">S</mi> <mn>2</mn> </mrow> </semantics></math>: <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi mathvariant="normal">d</mi> </msub> <mo>∈</mo> <mfenced separators="" open="{" close="}"> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mn>22</mn> </mfenced> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>Results of <math display="inline"><semantics> <mi>dHV</mi> </semantics></math> metric for algorithms VNDMOPSO, VLMOPSO, and VNDGDE3 for dimensionality settings <math display="inline"><semantics> <mrow> <mi mathvariant="script">S</mi> <mn>3</mn> </mrow> </semantics></math>: <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mi mathvariant="normal">d</mi> </msub> <mo>∈</mo> <mfenced separators="" open="{" close="}"> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mn>52</mn> </mfenced> </mrow> </semantics></math>.</p> Full article ">Figure 6
<p>Percentage of agents with different dimensions expressed in terms of the number of turning points, <math display="inline"><semantics> <msub> <mi>N</mi> <mi mathvariant="normal">T</mi> </msub> </semantics></math>, against the number of iterations on <math display="inline"><semantics> <mrow> <mi mathvariant="script">P</mi> <mn>4</mn> </mrow> </semantics></math> problem instance for two settings of parameters, <math display="inline"><semantics> <msub> <mi>p</mi> <mi mathvariant="normal">g</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>p</mi> <mi mathvariant="normal">b</mi> </msub> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>0.05</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi mathvariant="normal">b</mi> </msub> <mo>=</mo> <mn>0.10</mn> </mrow> </semantics></math>; and (<b>b</b>) <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi mathvariant="normal">g</mi> </msub> <mo>=</mo> <mn>0.20</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mi mathvariant="normal">b</mi> </msub> <mo>=</mo> <mn>0.40</mn> </mrow> </semantics></math>.</p> Full article ">Figure 7
<p>Median values of <math display="inline"><semantics> <mi>dHV</mi> </semantics></math> metric versus parameter <math display="inline"><semantics> <msub> <mi>p</mi> <mi mathvariant="normal">g</mi> </msub> </semantics></math>. The median is selected from 100 independent runs of the VNDMOPSO algorithm for 21 benchmark problems with dimensional settings <math display="inline"><semantics> <mrow> <mi mathvariant="script">S</mi> <mn>1</mn> </mrow> </semantics></math>.</p> Full article ">Figure 8
<p>Maps of obstacles for: (<b>a</b>–<b>d</b>) artificial problem instances <math display="inline"><semantics> <mrow> <mi mathvariant="script">P</mi> <mn>1</mn> </mrow> </semantics></math>–<math display="inline"><semantics> <mrow> <mi mathvariant="script">P</mi> <mn>4</mn> </mrow> </semantics></math>, (<b>e</b>) real-life photograph of Apollo 11 landing area [<a href="#B46-algorithms-16-00307" class="html-bibr">46</a>], and (<b>f</b>) instance <math display="inline"><semantics> <mrow> <mi mathvariant="script">P</mi> <mn>5</mn> </mrow> </semantics></math> based on (<b>e</b>). Markers ’×’ show locations of the robot’s starting point, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">r</mi> <mi mathvariant="script">S</mi> </msub> </semantics></math> (red color), and target point, <math display="inline"><semantics> <msub> <mi mathvariant="bold-italic">r</mi> <mi mathvariant="script">T</mi> </msub> </semantics></math> (blue).</p> Full article ">Figure 9
<p>The true solution of the <math display="inline"><semantics> <mrow> <mi mathvariant="script">P</mi> <mn>4</mn> </mrow> </semantics></math> problem instance found by an exhaustive search: (<b>a</b>) the Pareto front formed by three discrete points (marked by symbols “×”); and (<b>b</b>) the found paths for corresponding members of the Pareto front.</p> Full article ">Figure 10
<p>The standard boxplots (min, 1st quartile, median, 3rd quartile, max value) of the <math display="inline"><semantics> <mi>dHV</mi> </semantics></math> metric for algorithms VNDMOPSO, VNDGDE3, VLMOPSO, and SCMOPSO on five pathfinding problem instances <math display="inline"><semantics> <mrow> <mi mathvariant="script">P</mi> <mn>1</mn> </mrow> </semantics></math>–<math display="inline"><semantics> <mrow> <mi mathvariant="script">P</mi> <mn>5</mn> </mrow> </semantics></math>.</p> Full article ">Figure 11
<p>Selected Pareto-optimal solutions found by VNDMOPSO algorithm with maximal value of the <math display="inline"><semantics> <mi>HV</mi> </semantics></math> metric for pathfinding problem instances <math display="inline"><semantics> <mrow> <mi mathvariant="script">P</mi> <mn>1</mn> </mrow> </semantics></math>–<math display="inline"><semantics> <mrow> <mi mathvariant="script">P</mi> <mn>5</mn> </mrow> </semantics></math> (<b>a</b>–<b>e</b>).</p> Full article ">
16 pages, 6941 KiB  
Article
An Alternative Multi-Physics-Based Methodology for Strongly Coupled Electro-Magneto-Mechanical Problems
by Federico Maria Reato, Claudio Ricci, Jan Misfatto, Matteo Calzaferri and Simone Cinquemani
Algorithms 2023, 16(6), 306; https://doi.org/10.3390/a16060306 - 19 Jun 2023
Viewed by 1444
Abstract
The analysis of complex systems tends to be approached through a separation and a simplification of the main macro phenomena and, thus, addressed through dedicated techniques, tools, and algorithms. A smart and interesting possibility, instead, is represented by the so-called model-based design analysis, [...] Read more.
The analysis of complex systems tends to be approached through a separation and a simplification of the main macro phenomena and, thus, addressed through dedicated techniques, tools, and algorithms. A smart and interesting possibility, instead, is represented by the so-called model-based design analysis, which allows one to interface phenomena coming from interactions of different physical natures. This paper aims to propose a multi-physics Matlab/Simulink®-based architecture that allows one to integrate general and strongly non-linear coupling phenomena, taking efforts from two novel implemented bi-directional co-simulation routines based on Spice® and ESRF Radia® engines. Emphasis is dedicated to the discussion and description of the co-simulation algorithms and processes characteristic of these routines, which allow the analog electronic and the magneto dynamic domain’s integration under a single simulation environment. To highlight the reliability of the multi-domain architecture and to validate the reported co-simulation results, a comparison with the experimental measures obtained on an innovative MEMS electromagnetic actuator are proposed. Full article
(This article belongs to the Collection Feature Papers in Algorithms)
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Figure 1
<p>Proposed multi-domain co-simulation architecture and time discretization logic.</p> Full article ">Figure 2
<p>PySpice-Matlab/Simulink co-simulation algorithm.</p> Full article ">Figure 3
<p>Co-simulation initialized NETLIST.</p> Full article ">Figure 4
<p>ESRF Radia-Matlab/Simulink co-simulation algorithm.</p> Full article ">Figure 5
<p>Three-dimensional graphical representation of the MEMS electromagnetic actuator.</p> Full article ">Figure 6
<p>MEMS electromagnetic actuator schematic model.</p> Full article ">Figure 7
<p>MEMS multi-domain co-simulation model.</p> Full article ">Figure 8
<p>Three-dimensional magneto-static Finite Volume Model.</p> Full article ">Figure 9
<p>GUI schematic representation of the Spice-based circuit.</p> Full article ">Figure 10
<p>Sectional view of the multibody model.</p> Full article ">Figure 11
<p>(<b>a</b>) Co-simulation numerical results; (<b>b</b>) referred experimental measurements.</p> Full article ">Figure 12
<p>MOSFET gate PWM signal.</p> Full article ">Figure 13
<p>MEMS diaphragm estimated deflection.</p> Full article ">Figure 14
<p>MEMS magnetic actuation force.</p> Full article ">Figure 15
<p>MOSFET drain voltage.</p> Full article ">
36 pages, 6469 KiB  
Article
Physics-Informed Deep Learning for Traffic State Estimation: A Survey and the Outlook
by Xuan Di, Rongye Shi, Zhaobin Mo and Yongjie Fu
Algorithms 2023, 16(6), 305; https://doi.org/10.3390/a16060305 - 17 Jun 2023
Cited by 11 | Viewed by 5137
Abstract
For its robust predictive power (compared to pure physics-based models) and sample-efficient training (compared to pure deep learning models), physics-informed deep learning (PIDL), a paradigm hybridizing physics-based models and deep neural networks (DNNs), has been booming in science and engineering fields. One key [...] Read more.
For its robust predictive power (compared to pure physics-based models) and sample-efficient training (compared to pure deep learning models), physics-informed deep learning (PIDL), a paradigm hybridizing physics-based models and deep neural networks (DNNs), has been booming in science and engineering fields. One key challenge of applying PIDL to various domains and problems lies in the design of a computational graph that integrates physics and DNNs. In other words, how the physics is encoded into DNNs and how the physics and data components are represented. In this paper, we offer an overview of a variety of architecture designs of PIDL computational graphs and how these structures are customized to traffic state estimation (TSE), a central problem in transportation engineering. When observation data, problem type, and goal vary, we demonstrate potential architectures of PIDL computational graphs and compare these variants using the same real-world dataset. Full article
(This article belongs to the Collection Feature Papers on Artificial Intelligence Algorithms and Their Applications)
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Figure 1

Figure 1
<p>Comparison of pure physics-based, data-driven, and hybrid paradigms (adapted from [<a href="#B2-algorithms-16-00305" class="html-bibr">2</a>]).</p> Full article ">Figure 2
<p>Schematic of PDE solution approximation.</p> Full article ">Figure 3
<p>Data types for TSE (adapted from [<a href="#B12-algorithms-16-00305" class="html-bibr">12</a>], including fixed location sensors (blue hexagons), roadside camera, and collocation points (black crosses)).</p> Full article ">Figure 4
<p>Fundamental diagram (red line) with data (blue dots).</p> Full article ">Figure 5
<p>Flowchart of joint training of PIDL.</p> Full article ">Figure 6
<p>PIDL flowchart for three-parameter-based LWR, consisting of a PUNN for traffic density estimation and a PICG for calculating the residual, where <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mo>(</mo> <mi>δ</mi> <mo>,</mo> <mi>p</mi> <mo>,</mo> <mi>σ</mi> <mo>,</mo> <msub> <mi>ρ</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msub> <mo>,</mo> <mi>ϵ</mi> <mo>)</mo> </mrow> </semantics></math>.</p> Full article ">Figure 7
<p>Estimated traffic density <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> (<b>left</b>) and traffic velocity <span class="html-italic">u</span> (<b>right</b>) of the PIDL when the number of loop detectors is 3, where the horizontal black lines in the heatmap represent the sensor positions. In each half, the prediction heatmap and snapshots at certain time points are presented. Note that the PUNN does not predict <span class="html-italic">u</span> directly, and instead, it is calculated by <math display="inline"><semantics> <mrow> <mi>Q</mi> <mo>(</mo> <mi>ρ</mi> <mo>)</mo> <mo>/</mo> <mi>ρ</mi> </mrow> </semantics></math> in the post-processing.</p> Full article ">Figure 8
<p>Average traffic density and speed on US 101 highway. Heatmap for the traffic density (<b>left</b>) and velocity (<b>right</b>).</p> Full article ">Figure 9
<p>Results of the deterministic PIDL models for the NGSIM dataset. “#loop” stands for the number of loop detectors. (<b>a</b>) RE of the traffic density; (<b>b</b>) RE of the traffic velocity.</p> Full article ">Figure 10
<p>Ratios of the contributions made by the physics-based component and the data-driven component to the optimal performance of PIDL.</p> Full article ">Figure 11
<p>PIDL architecture for UQ-TSE. The PhysGAN (<b>a</b>) consists of a generator, a discriminator, and a PICG. The PhysFlow (<b>b</b>) consists of a normalizing flow and a PICG. The PhysFlowGAN (<b>c</b>) consists of a normalizing flow, a discriminator, and a PICG. In each subfigure, the top blue box encloses the data-driven component, and the bottom red box encloses the physics component. (<b>a</b>) PhysGAN architecture. In the data-driven component, the observation is used to calculate the discriminator loss function <math display="inline"><semantics> <mrow> <mi>L</mi> <mi>o</mi> <mi>s</mi> <msub> <mi>s</mi> <mi>ϕ</mi> </msub> </mrow> </semantics></math> using Equation (<a href="#FD12-algorithms-16-00305" class="html-disp-formula">12</a>) and the data loss of the generator <math display="inline"><semantics> <msub> <mi>L</mi> <mi>O</mi> </msub> </semantics></math> using Equation (<a href="#FD13-algorithms-16-00305" class="html-disp-formula">13</a>). In the physics-based component, the collocation points are used to calculate the residual <math display="inline"><semantics> <msub> <mi>r</mi> <mi>C</mi> </msub> </semantics></math> using Equation (<a href="#FD10-algorithms-16-00305" class="html-disp-formula">10</a>), which is then used to calculate the physics loss of the generator <math display="inline"><semantics> <msub> <mi>L</mi> <mi>C</mi> </msub> </semantics></math> with two different ways of incorporating the residuals. (<b>b</b>) PhysFlow architecture. In the data-driven component, the inverse flow function <math display="inline"><semantics> <msubsup> <mi>G</mi> <mrow> <mi>θ</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> </semantics></math> aims to map the observation to a prior that follows a Gaussian distribution. In the physics-based component, the flow function maps a Gaussian prior to the collocation points, and a PICG is used to calculate the physics loss <math display="inline"><semantics> <msub> <mi>L</mi> <mi>C</mi> </msub> </semantics></math> as in PhysGAN. (<b>c</b>) PhysFlowGAN architecture. This combines the architectures of PhysGAN and PhysFlow.</p> Full article ">Figure 12
<p>Estimated traffic density <math display="inline"><semantics> <mi>ρ</mi> </semantics></math> (<b>left</b>) and traffic velocity (<b>right</b>) of the PI-GAN when the number of loop detectors is equal to 3, where the horizontal black lines in the heatmap represent the positions of the loop detectors. In each half, the prediction heatmap and snapshots at certain time points are presented.</p> Full article ">Figure 13
<p>Results of the PIDL-UQ models for the NGSIM dataset. (<b>a</b>) RE of the traffic density; (<b>b</b>) RE of the traffic velocity; (<b>c</b>) KL of the traffic density; (<b>d</b>) KL of the traffic velocity; (<b>e</b>) summary of RE and KL of the traffic density and velocity of all data sizes.</p> Full article ">Figure 14
<p>Ratios of the contributions made by the physics-based component and the data-driven component to the optimal training of TrafficFlowGAN. <math display="inline"><semantics> <mi>β</mi> </semantics></math> and <math display="inline"><semantics> <mi>α</mi> </semantics></math> are hyperparameters in Equation (<a href="#FD10-algorithms-16-00305" class="html-disp-formula">10</a>) which control the contribution of the physics-based and data-driven components, respectively.</p> Full article ">Figure A1
<p>Error heatmaps of the NN and PIDL-LWR-FDL models. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>S</mi> <msub> <mi>E</mi> <mi>ρ</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> of the PIDL-LWR-FDL; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>S</mi> <msub> <mi>E</mi> <mi>ρ</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> of the NN.</p> Full article ">Figure A2
<p>Error heatmaps of the EKF and TrafficFlowGAN. (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>S</mi> <msub> <mi>E</mi> <mi>ρ</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> of the TrafficFlowGAN; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>S</mi> <msub> <mi>E</mi> <mi>ρ</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> of the EKF; (<b>c</b>) prediction’s standard deviation of the traffic density of the TrafficFlowGAN; (<b>d</b>) prediction’s standard deviation of the traffic density of the EKF.</p> Full article ">
18 pages, 6442 KiB  
Article
Fault-Diagnosis Method for Rotating Machinery Based on SVMD Entropy and Machine Learning
by Lijun Zhang, Yuejian Zhang and Guangfeng Li
Algorithms 2023, 16(6), 304; https://doi.org/10.3390/a16060304 - 17 Jun 2023
Cited by 8 | Viewed by 1917
Abstract
Rolling bearings and gears are important components of rotating machinery. Their operating condition affects the operation of the equipment. Fault in the accessory directly leads to equipment downtime or a series of adverse reactions in the system, which brings enormous pecuniary loss to [...] Read more.
Rolling bearings and gears are important components of rotating machinery. Their operating condition affects the operation of the equipment. Fault in the accessory directly leads to equipment downtime or a series of adverse reactions in the system, which brings enormous pecuniary loss to the institution. Hence, it is of great significance to detect the operating status of rolling bearings and gears for fault diagnosis. At present, the vibration method is considered to be the most common method for fault diagnosis, a method that analyzes the equipment by collecting vibration signals. However, rotating-machinery fault diagnosis is challenging due to the need to select effective fault feature vectors, use appropriate machine-learning classification methods, and achieve accurate fault diagnosis. To solve this problem, this paper illustrates a new fault-diagnosis method combining successive variational-mode decomposition (SVMD) entropy values and machine learning. First, the simulation signal and the real fault signal are used to analyze and compare the variational-mode decomposition (VMD) and SVMD methods. The comparison results prove that SVMD can be a useful method for fault diagnosis. Then, these two methods are utilized to extract the energy entropy and fuzzy entropy of the gearbox dataset of Southeast University (SEU), respectively. The feature vector and multiple machine-learning classification models are constructed for failure-mode identification. The experimental-analysis results successfully verify the effectiveness of the combined SVMD entropy and machine-learning approach for rotating-machinery fault diagnosis. Full article
(This article belongs to the Special Issue Machine Learning and Deep Learning Applications for Anomaly and Fault Detection)
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Figure 1

Figure 1
<p>Time-domain–frequency-domain diagram of the simulated signal: (<b>a</b>) signal time-domain waveform; (<b>b</b>) signal frequency-domain diagram.</p> Full article ">Figure 2
<p>VMD signal-decomposition-component time-domain–frequency-domain diagram: (<b>a</b>) time-domain diagram of each component; (<b>b</b>) frequency-domain diagram of each component.</p> Full article ">Figure 3
<p>SVMD signal-decomposition-component time-domain–frequency-domain diagram: (<b>a</b>) time-domain diagram of each component; (<b>b</b>) frequency-domain diagram of each component.</p> Full article ">Figure 4
<p>Time-domain–frequency-domain diagram of the simulated signal with superimposed random signal: (<b>a</b>) time-domain diagram of the random signal; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>X</mi> <mfenced separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math> signal time-domain frequency-domain diagram.</p> Full article ">Figure 5
<p>VMD signal-decomposition-component time-domain–frequency-domain diagram: (<b>a</b>) time-domain diagram of each component; (<b>b</b>) frequency-domain diagram of each component.</p> Full article ">Figure 6
<p>SVMD signal-decomposition-component time-domain–frequency-domain plots: (<b>a</b>) time-domain plots of each component; (<b>b</b>) frequency-domain plots of each component.</p> Full article ">Figure 7
<p>Simulated signal-component energy entropy: (<b>a</b>) component energy entropy of <math display="inline"><semantics> <mrow> <mi>x</mi> <mfenced separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>; (<b>b</b>) component energy entropy of <math display="inline"><semantics> <mrow> <mi>X</mi> <mfenced separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>.</p> Full article ">Figure 8
<p>Correlation-confusion matrix of <math display="inline"><semantics> <mrow> <mi>x</mi> <mfenced separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>: (<b>a</b>) VMD decomposition correlation of <math display="inline"><semantics> <mrow> <mi>x</mi> <mfenced separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>; (<b>b</b>) SVMD decomposition correlation of <math display="inline"><semantics> <mrow> <mi>x</mi> <mfenced separators="|"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </semantics></math>.</p> Full article ">Figure 9
<p>Correlation-confusion matrix of <span class="html-italic">X</span>(<span class="html-italic">t</span>): (<b>a</b>) VMD decomposition correlation of <span class="html-italic">X</span>(<span class="html-italic">t</span>); (<b>b</b>) SVMD decomposition correlation of <span class="html-italic">X</span>(<span class="html-italic">t</span>).</p> Full article ">Figure 10
<p>Simulated signal-component fuzzy entropy: (<b>a</b>) component fuzzy entropy of <span class="html-italic">x</span>(<span class="html-italic">t</span>); (<b>b</b>) component fuzzy entropy of <span class="html-italic">X</span>(<span class="html-italic">t</span>).</p> Full article ">Figure 11
<p>Experimental flowchart.</p> Full article ">Figure 12
<p>Confusion matrix of SVM classification of gearbox working condition I energy entropy in the SEU dataset: (<b>a</b>) VMD; (<b>b</b>) SVMD.</p> Full article ">Figure 13
<p>Confusion matrix of fuzzy-entropy SVM classification of gearbox working condition I in the SEU dataset: (<b>a</b>) VMD; (<b>b</b>) SVMD.</p> Full article ">Figure 14
<p>GDS3000 experimental platform.</p> Full article ">
28 pages, 9566 KiB  
Article
Optimized Workflow Framework in Construction Projects to Control the Environmental Properties of Soil
by Per Lindh and Polina Lemenkova
Algorithms 2023, 16(6), 303; https://doi.org/10.3390/a16060303 - 17 Jun 2023
Cited by 1 | Viewed by 1798
Abstract
To optimize the workflow of civil engineering construction in a harbour, this paper developed a framework of the contaminant leaching assessment carried out on the stabilized/solidified dredged soil material. The specimens included the sampled sediments collected from the in situ fieldwork in Arendal [...] Read more.
To optimize the workflow of civil engineering construction in a harbour, this paper developed a framework of the contaminant leaching assessment carried out on the stabilized/solidified dredged soil material. The specimens included the sampled sediments collected from the in situ fieldwork in Arendal and Kongshavn. The background levels of the concentration of pollutants were evaluated to assess the cumulative surface leaching of substances from samples over two months. The contamination of soil was assessed using a structured workflow scheme on the following toxic substances, heavy metals—As, Pb, Cd, Cr, Hg, Ni, and Zn; organic compounds—PAH-16 and PCB; and organotin compounds—TBT. The numerical computation and data analysis were applied to the results of geochemical testing creating computerised solutions to soil quality evaluation in civil engineering. Data modelling enabled the estimation of leaching of the contaminants in one year. The estimated leaching of As is 0.9153 mg/m2, for Ni—2.8178 mg/m2, for total PAH-16 as 0.0507 mg/m2, and for TBT—0.00061 mg/m2 per year. The performance of the sediments was examined with regard to permeability through a series of the controlled experiments. The environmental engineering tests were implemented in the Swedish Geotechnical Institute (SGI) in a triplicate mode over 64 days. The results were compared for several sites and showed that the amount of As is slightly higher in Kongshavn than for Arendal, while the content of Cd, Cr, and Ni is lower. For TBT, the levels are significantly lower than for those at Arendal. The algorithm of permeability tests evaluated the safety of foundation soil for construction of embankments and structures. The optimized assessment methods were applied for monitoring coastal areas through the evaluated permeability of soil and estimated leaching rates of heavy metals, PHB, PACs, and TBT in selected test sites in harbours of southern Norway. Full article
(This article belongs to the Collection Feature Papers in Algorithms for Multidisciplinary Applications)
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<p>Containers in which dredged soil materials were stored after transportation. Photo source: Per Lindh.</p> Full article ">Figure 2
<p>Process of surface leaching test on soil specimens. Photo source: Per Lindh.</p> Full article ">Figure 3
<p>Permeability of soil in relation to the ratio between cement (c) and slag (s) for dredged soil. The best results with the lowest permeability of soil show the combination of binders for 30% cement and 70% slag. The abbreviation <math display="inline"><semantics> <mrow> <msub> <mi>H</mi> <mi>W</mi> </msub> <msub> <mi>L</mi> <mi>B</mi> </msub> </mrow> </semantics></math> stands for “high water–low binder” level in a mixture.</p> Full article ">Figure 4
<p>Permeability of soil samples changing over time of experiment (in hours), Specimen IDs: (<b>a</b>) <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>_</mo> <mn>5</mn> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mn>4</mn> <mo>_</mo> <mn>1</mn> </mrow> </semantics></math>, (<b>c</b>) <math display="inline"><semantics> <mrow> <mn>5</mn> <mo>_</mo> <mn>4</mn> </mrow> </semantics></math>, (<b>d</b>) <math display="inline"><semantics> <mrow> <mn>3</mn> <mo>_</mo> <mn>5</mn> </mrow> </semantics></math>, (<b>e</b>) <math display="inline"><semantics> <mrow> <mn>6</mn> <mo>_</mo> <mn>5</mn> </mrow> </semantics></math>, and (<b>f</b>) <math display="inline"><semantics> <mrow> <mn>8</mn> <mo>_</mo> <mn>5</mn> </mrow> </semantics></math>.</p> Full article ">Figure 5
<p>Cumulative leaching of arsenic (As) against time in tested specimen samples.</p> Full article ">Figure 6
<p>Cumulative leaching of nickel (Ni) over time in tested soil specimens.</p> Full article ">Figure 7
<p>Cumulative leaching of PAH-16 in tested soil samples.</p> Full article ">Figure 8
<p>Developed leaching of TBT from the soil samples over time. Blue area represents the significant level of cumulative leaching.</p> Full article ">
14 pages, 4156 KiB  
Article
Identification of Highlighted Cells in Low-Variance Raster Data Application to Digital Elevation Models
by Manuel Antonio Ureña-Cámara and Antonio Tomás Mozas-Calvache
Algorithms 2023, 16(6), 302; https://doi.org/10.3390/a16060302 - 16 Jun 2023
Cited by 1 | Viewed by 1240
Abstract
This study describes a new algorithm developed to detect local cells of minimum or maximum heights in grid Digital Elevation Models (DEMs). DEMs have a low variance in digital levels due to the spatial continuity of the data. Traditional algorithms, such as SIFT, [...] Read more.
This study describes a new algorithm developed to detect local cells of minimum or maximum heights in grid Digital Elevation Models (DEMs). DEMs have a low variance in digital levels due to the spatial continuity of the data. Traditional algorithms, such as SIFT, are based on statistical variance, which present issues to determine these highlighted cells. However, one of the main purposes of this identification is the use of these points (cells) to assess the positional accuracy of these products by comparing those extracted from the DEM with those obtained from a more accurate source. In this sense, we developed an algorithm based on a moveable window composed of variable sizes, which is displaced along the image to characterize each set of cells. The determination of highlighted cells is based on the absolute differences of digital levels in the same DEM and compared to those obtained from other DEMs. The application has been carried out using a great number of data, considering four zones, two spatial resolutions, and different definitions of height surfaces. The results have demonstrated the feasibility of the algorithm for the identification of these cells. Thus, this approach expects an improvement in traditional procedures. The algorithm can be used to contrast DEMs obtained from different sources or DEMs from the same source that have been affected by generalization procedures. Full article
(This article belongs to the Collection Feature Papers in Algorithms)
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<p>Statistics of datasets IMC-PT and DEMs: (<b>a</b>) mean values; (<b>b</b>) standard deviations.</p> Full article ">Figure 2
<p>Methodology proposed in this study: (<b>a</b>) workflow; (<b>b</b>) example of the procedure for obtaining two sets of pixels to correlate. The acronyms are as follows: DV: Digital value of pixel; n: number of cells in the ring; d: distance in pixels from the center of the ring in the reference image; D: distance of the search window in pixels in the search image; n: number of pixels of the ring of distance d; n’: number of pixels of the ring of distance d’; f: relation between approximate pixel spatial resolution from reference image and search image.</p> Full article ">Figure 3
<p>DEMs used in the application of the proposed methodology.</p> Full article ">Figure 4
<p>Frequency of correlation coefficient values for all the zones and all comparisons.</p> Full article ">Figure 5
<p>Distances in rows and columns of the matched keypoints (red: vertical; blue: horizontal).</p> Full article ">Figure 6
<p>Total distance of matched keypoints.</p> Full article ">Figure 7
<p>Examples of correlation coefficients greater than 0.99 (red colored zones) for the four tested zones. The DEMs were DTM05 compared with DSM05. The background is the orthophoto map of Spain (IGN of Spain) [<a href="#B24-algorithms-16-00302" class="html-bibr">24</a>].</p> Full article ">
20 pages, 9775 KiB  
Article
Quantifying Uncertainties in OC-SMART Ocean Color Retrievals: A Bayesian Inversion Algorithm
by Elliot Pachniak, Yongzhen Fan, Wei Li and Knut Stamnes
Algorithms 2023, 16(6), 301; https://doi.org/10.3390/a16060301 - 16 Jun 2023
Cited by 1 | Viewed by 1782
Abstract
The Ocean Color—Simultaneous Marine and Aerosol Retrieval Tool (OC-SMART) is a robust data processing platform utilizing scientific machine learning (SciML) in conjunction with comprehensive radiative transfer computations to provide accurate remote sensing reflectances (Rrs estimates), aerosol optical depths, and inherent optical [...] Read more.
The Ocean Color—Simultaneous Marine and Aerosol Retrieval Tool (OC-SMART) is a robust data processing platform utilizing scientific machine learning (SciML) in conjunction with comprehensive radiative transfer computations to provide accurate remote sensing reflectances (Rrs estimates), aerosol optical depths, and inherent optical properties. This paper expands the capability of OC-SMART by quantifying uncertainties in ocean color retrievals. Bayesian inversion is used to relate measured top of atmosphere radiances and a priori data to estimate posterior probability density functions and associated uncertainties. A framework of the methodology and implementation strategy is presented and uncertainty estimates for Rrs retrievals are provided to demonstrate the approach by applying it to MODIS, OLCI Sentinel-3, and VIIRS sensor data. Full article
(This article belongs to the Section Algorithms for Multidisciplinary Applications)
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<p>Framework for formulation of the uncertainty estimations applied to OC-SMART.</p> Full article ">Figure 2
<p>The difference between simulated Rayleigh-corrected TOA radiances and measured Rayleigh-corrected TOA radiances from MODIS represented as a percentage for (<b>Top Left</b>) 412 nm, (<b>Top Right</b>) 531 nm, and (<b>Bottom Left</b>) 667 nm. (<b>Bottom Right</b>) A convergence map of OC-SMART output <math display="inline"><semantics> <msub> <mi>R</mi> <mi>rs</mi> </msub> </semantics></math>. In this image, over 95% of the retrieved <math display="inline"><semantics> <msub> <mi>R</mi> <mi>rs</mi> </msub> </semantics></math> are converged (shown in blue color). Zones of non-convergence, shown in red, are primarily located in coastal bays and near areas of heavy cloud cover.</p> Full article ">Figure 3
<p>Verification of the remote sensing reflectance (<math display="inline"><semantics> <msub> <mi>R</mi> <mi>rs</mi> </msub> </semantics></math>) at 412, 443, 488, 531, 547, 667, 678, and 748 nm retrieved by the MLNN algorithm against a synthetic testing dataset (<span class="html-italic">N</span> = 10,000).</p> Full article ">Figure 4
<p>(<b>Left panel</b>) Locations of interest off the east coast of the United States on 9 March 2016 (MODIS). ST1 (Red) is located in the optically complex Chesapeake bay region, ST2 (Blue) is located in near coastal waters, and ST3 (Black) is located in the open ocean. (<b>Right panel</b>) <math display="inline"><semantics> <msub> <mi>R</mi> <mi>rs</mi> </msub> </semantics></math> with uncertainties for three locations of interest and for several wavelengths.</p> Full article ">Figure 5
<p>Remote sensing reflectance data from MODIS sensor (<b>Left</b>), corresponding standard uncertainties (<b>Center</b>), and relative uncertainty (<b>Right</b>) for several wavelengths off the east coast of the United States on 9 March 2016. Relative uncertainty tends to be consistent for all pixels in a wavelength.</p> Full article ">Figure 6
<p>(<b>Left panel</b>) Locations of interest in the Gulf of Mexico on 4 March 2020 (MODIS). ST4 (Red) is located in the central gulf region while ST5 (Blue) is located in the coastal waters of southwest Florida. (<b>Right panel</b>) <math display="inline"><semantics> <msub> <mi>R</mi> <mi>rs</mi> </msub> </semantics></math> with uncertainties for two locations of interest for several wavelengths.</p> Full article ">Figure 7
<p>Remote sensing reflectance data from MODIS sensor (<b>Left</b>), corresponding standard uncertainties (<b>Center</b>), and relative uncertainty (<b>Right</b>) for several wavelengths over the gulf of Mexico on 4 March 2020. Elevated values near Cuba and the Bahamas are due to shallow waters where reflection from the ocean bottom should be included (ignored in the current version of OC-SMART).</p> Full article ">Figure 8
<p>(<b>Left panel</b>) Locations of interest off the east coast of China on 19 March 2016 (MODIS). ST6 (red) is located between Korea and western Japan in the Sea of Japan, ST7 (blue) is located in the East China Sea near the Korean peninsula. (<b>Right panel</b>) <math display="inline"><semantics> <msub> <mi>R</mi> <mi>rs</mi> </msub> </semantics></math> with uncertainties for two locations of interest for several wavelengths.</p> Full article ">Figure 9
<p>Remote sensing reflectance data from MODIS sensor (<b>Left</b>), corresponding standard uncertainties (<b>Center</b>), and relative uncertainty (<b>Right</b>) for several wavelengths near the Korean peninsula and sea of Japan on 19 March 2016.</p> Full article ">Figure 10
<p><math display="inline"><semantics> <msub> <mi>R</mi> <mi>rs</mi> </msub> </semantics></math> uncertainties for the three locations identified in <a href="#algorithms-16-00301-f004" class="html-fig">Figure 4</a> for several wavelengths. Panel (<b>A</b>) shows the actual calculated uncertainty. Panel (<b>B</b>) shows the same uncertainty calculation but with the measurement term considered to be zero for all values. Panel (<b>C</b>) shows the uncertainty calculation if the APEs of all wavelengths were set to 10%.</p> Full article ">Figure 11
<p>(<b>Left panel</b>) Locations of interest near the Iberian peninsula on 21 January 2022. ST8 (red) is located in the Golfo de Cadiz near the delta of two prominent rivers, ST9 (black) is located west of Lisbon. (<b>Right panel</b>) <math display="inline"><semantics> <msub> <mi>R</mi> <mi>rs</mi> </msub> </semantics></math> from OLCI Sentinel-3 sensor data with uncertainties for two locations of interest for several wavelengths.</p> Full article ">Figure 12
<p>Remote sensing reflectance data from OLCI Sentinel-3 sensor (<b>Left</b>), corresponding standard uncertainties (<b>Center</b>), and relative uncertainty (<b>Right</b>) for several wavelengths near the Iberian peninsula on 21 January 2022.</p> Full article ">Figure 13
<p>(<b>Left panel</b>) Locations of interest off Northeast coast of the United States on 2 May 2021. ST10 (red) is located south of Nova Scotia in optically complex waters, ST11 (black) is located in an open region of the Atlantic ocean. (<b>Right panel</b>) <math display="inline"><semantics> <msub> <mi>R</mi> <mi>rs</mi> </msub> </semantics></math> from VIIRS sensor data with uncertainties for two locations of interest for several wavelengths.</p> Full article ">Figure 14
<p>Remote sensing reflectance data from VIIRS sensor (<b>Left</b>), corresponding standard uncertainties (<b>Center</b>), and relative uncertainty (<b>Right</b>) for several wavelengths off the Northeast coast of the United States of America on 2 May 2021.</p> Full article ">
12 pages, 482 KiB  
Article
Classification of CO Environmental Parameter for Air Pollution Monitoring with Grammatical Evolution
by Evangelos D. Spyrou, Chrysostomos Stylios and Ioannis Tsoulos
Algorithms 2023, 16(6), 300; https://doi.org/10.3390/a16060300 - 15 Jun 2023
Cited by 1 | Viewed by 1794
Abstract
Air pollution is a pressing concern in urban areas, necessitating the critical monitoring of air quality to understand its implications for public health. Internet of Things (IoT) devices are widely utilized in air pollution monitoring due to their sensor capabilities and seamless data [...] Read more.
Air pollution is a pressing concern in urban areas, necessitating the critical monitoring of air quality to understand its implications for public health. Internet of Things (IoT) devices are widely utilized in air pollution monitoring due to their sensor capabilities and seamless data transmission over the Internet. Artificial intelligence (AI) and machine learning techniques play a crucial role in classifying patterns derived from sensor data. Environmental stations offer a multitude of parameters that can be obtained to uncover hidden patterns showcasing the impact of pollution on the surrounding environment. This paper focuses on utilizing the CO parameter as an indicator of pollution in two datasets collected from wireless environmental monitoring devices in the greater Port area and the Town Hall of Igoumenitsa City in Greece. The datasets are normalized to facilitate their utilization in classification algorithms. The k-means algorithm is applied, and the elbow method is used to determine the optimal number of clusters. Subsequently, the datasets are introduced to the grammatical evolution algorithm to calculate the percentage fault. This method constructs classification programs in a human-readable format, making it suitable for analysis. Finally, the proposed method is compared against four state-of-the-art models: the Adam optimizer for optimizing artificial neural network parameters, a genetic algorithm for training an artificial neural network, the Bayes model, and the limited-memory BFGS method applied to a neural network. The comparison reveals that the GenClass method outperforms the other approaches in terms of classification error. Full article
(This article belongs to the Special Issue Machine Learning Algorithms in Prediction Model)
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<p>Environmental monitoring wireless communication.</p> Full article ">Figure 2
<p>Optimal number of clusters using elbow.</p> Full article ">Figure 3
<p>The used grammar in BNF notation.</p> Full article ">Figure 4
<p>Example of one-point crossover.</p> Full article ">Figure 5
<p>Average classification error measured on Port dataset.</p> Full article ">Figure 6
<p>Average classification error on Town Hall dataset.</p> Full article ">
10 pages, 327 KiB  
Article
A Multithreaded Algorithm for the Computation of Sample Entropy
by George Manis, Dimitrios Bakalis and Roberto Sassi
Algorithms 2023, 16(6), 299; https://doi.org/10.3390/a16060299 - 15 Jun 2023
Cited by 2 | Viewed by 1392
Abstract
Many popular entropy definitions for signals, including approximate and sample entropy, are based on the idea of embedding the time series into an m-dimensional space, aiming to detect complex, deeper and more informative relationships among samples. However, for both approximate and sample [...] Read more.
Many popular entropy definitions for signals, including approximate and sample entropy, are based on the idea of embedding the time series into an m-dimensional space, aiming to detect complex, deeper and more informative relationships among samples. However, for both approximate and sample entropy, the high computational cost is a severe limitation. Especially when large amounts of data are processed, or when parameter tuning is employed premising a large number of executions, the necessity of fast computation algorithms becomes urgent. In the past, our research team proposed fast algorithms for sample, approximate and bubble entropy. In the general case, the bucket-assisted algorithm was the one presenting the lowest execution times. In this paper, we exploit the opportunities given by the multithreading technology to further reduce the computation time. Without special requirements in hardware, since today even our cost-effective home computers support multithreading, the computation of entropy definitions can be significantly accelerated. The aim of this paper is threefold: (a) to extend the bucket-assisted algorithm for multithreaded processors, (b) to present updated execution times for the bucket-assisted algorithm since the achievements in hardware and compiler technology affect both execution times and gain, and (c) to provide a Python library which wraps fast C implementations capable of running in parallel on multithreaded processors. Full article
(This article belongs to the Collection Parallel and Distributed Computing: Algorithms and Applications)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Example of the bucket-assisted algorithm. An example of an integrated signal is depicted. The value of <span class="html-italic">m</span> is 2 and the distance between the lines is <span class="html-italic">r</span>. Points between the solid lines B and C can be similar only to points between the dashed lines A and D. Similarity checks for points between lines B and C should be limited only to points between lines A and C to avoid double checking. Figure from [<a href="#B13-algorithms-16-00299" class="html-bibr">13</a>].</p> Full article ">Figure 2
<p><b>Left panel</b>: speedups for randomly generated time series. <b>Right panel</b>: speedups for a set of 54 Holter recordings in sinus rhythm.</p> Full article ">
12 pages, 2004 KiB  
Article
Prediction of Freeway Traffic Breakdown Using Artificial Neural Networks
by Yiming Zhao and Jing Dong-O’Brien
Algorithms 2023, 16(6), 298; https://doi.org/10.3390/a16060298 - 15 Jun 2023
Cited by 1 | Viewed by 1638
Abstract
Traffic breakdown is the transition of traffic flow from an uncongested state to a congested state. During peak hours, when a large number of on-ramp vehicles merge with mainline traffic, it can cause a significant drop in speed and subsequently lead to traffic [...] Read more.
Traffic breakdown is the transition of traffic flow from an uncongested state to a congested state. During peak hours, when a large number of on-ramp vehicles merge with mainline traffic, it can cause a significant drop in speed and subsequently lead to traffic breakdown. Therefore, ramp meters have been used to regulate the traffic flow from the ramps to maintain stable traffic flow on the mainline. However, existing traffic breakdown prediction models do not consider on-ramp traffic flow. In this paper, an algorithm based on artificial neural networks (ANN) is developed to predict the probability of a traffic breakdown occurrence on freeway segments with merging traffic, considering temporal and spatial correlations of the traffic conditions from the location of interest, the ramp, and the upstream and downstream segments. The feature selection analysis reveals that the traffic condition of the ramps has a significant impact on the occurrence of traffic breakdown on the mainline. Therefore, the traffic flow characteristics of the on-ramp, along with other significant features, are used to build the ANN model. The proposed ANN algorithm can predict the occurrence of traffic breakdowns on freeway segments with merging traffic with an accuracy of 96%. Furthermore, the model has been deployed at a different location, which yields a predictive accuracy of 97%. In traffic operations, the high probability of the occurrence of a traffic breakdown can be used as a trigger for the ramp meters. Full article
(This article belongs to the Special Issue Neural Network for Traffic Forecasting)
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<p>Study site and sensor location.</p> Full article ">Figure 2
<p>Traffic breakdown example (data collected at I-235 WB mile maker 7, on 5 February 2022).</p> Full article ">Figure 3
<p>Flow chart of the research process.</p> Full article ">Figure 4
<p>ANN model design.</p> Full article ">
13 pages, 958 KiB  
Communication
On a Class of Orthogonal Polynomials as Corrections in Lienard Differential System: Applications
by Vesselin Kyurkchiev, Anton Iliev, Asen Rahnev and Nikolay Kyurkchiev
Algorithms 2023, 16(6), 297; https://doi.org/10.3390/a16060297 - 12 Jun 2023
Cited by 13 | Viewed by 1422
Abstract
In this paper we demonstrate some specialized modules for investigating the dynamics of differential models, an integral part of a planned much more general Web-based application for scientific computing. As “corrections” in the Lienard differential system is presented a class of orthogonal polynomials [...] Read more.
In this paper we demonstrate some specialized modules for investigating the dynamics of differential models, an integral part of a planned much more general Web-based application for scientific computing. As “corrections” in the Lienard differential system is presented a class of orthogonal polynomials (also known as “shell polynomials”). We will note that some specifics of the amplitudes of these polynomials open up the possibility of modeling signals from the field of antenna-feeder techniques. Algorithms and modules have been consistently used for: automatic generation of a theorem on the number and type of limit cycles (in the light of Melnikov’s considerations); study of the Hamiltonian of the system and “level curves”; for the study of catastrophic surfaces (in the light of Zeeman’s considerations), etc. Similar studies have been carried out for associated polynomials. Numerical examples, illustrating our results using CAS MATHEMATICA are given. Full article
(This article belongs to the Collection Feature Papers in Algorithms)
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<p>The polynomials <math display="inline"><semantics> <mrow> <msub> <mi>P</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for fixed <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>7</mn> <mo>,</mo> <mn>9</mn> </mrow> </semantics></math>.</p> Full article ">Figure 2
<p>Level curves (the case 1).</p> Full article ">Figure 3
<p>Level curves (the case 2).</p> Full article ">Figure 4
<p>(<b>a</b>) The Melnikov polynomial <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>(</mo> <msup> <mi>r</mi> <mn>2</mn> </msup> <mo>,</mo> <mn>3</mn> <mo>)</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>16</mn> </mfrac> <mo>=</mo> <mn>0.0625</mn> </mrow> </semantics></math> (three limit cycles); (<b>b</b>) The Melnikov polynomial <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>(</mo> <msup> <mi>r</mi> <mn>2</mn> </msup> <mo>,</mo> <mn>3</mn> <mo>)</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>7</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.0735880318901</mn> </mrow> </semantics></math> (simple limit cycle <math display="inline"><semantics> <mrow> <mn>1.06318</mn> </mrow> </semantics></math> and limit cycle <math display="inline"><semantics> <mrow> <mn>0.587389</mn> </mrow> </semantics></math> with multiplicity two).</p> Full article ">Figure 5
<p>(<b>a</b>) The Melnikov polynomial <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>(</mo> <msup> <mi>r</mi> <mn>2</mn> </msup> <mo>,</mo> <mn>5</mn> <mo>)</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>11</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mfrac> <mn>13</mn> <mrow> <mn>11</mn> <mo>,</mo> <mn>520</mn> </mrow> </mfrac> </mrow> </semantics></math> (five limit cycles); (<b>b</b>) The Melnikov polynomial <math display="inline"><semantics> <mrow> <mi>M</mi> <mo>(</mo> <msup> <mi>r</mi> <mn>2</mn> </msup> <mo>,</mo> <mn>5</mn> <mo>)</mo> </mrow> </semantics></math> for <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>11</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>μ</mi> <mo>=</mo> <mn>0.0012953041893</mn> </mrow> </semantics></math> (simple limit cycles <math display="inline"><semantics> <mrow> <mn>0.639205</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>0.706901</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mn>1.03221</mn> </mrow> </semantics></math> and limit cycle <math display="inline"><semantics> <mrow> <mn>0.338942</mn> </mrow> </semantics></math> with multiplicity two).</p> Full article ">Figure 6
<p>The simulations (system (6)) for <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>c</mi> <mo>=</mo> <mn>0.995</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>=</mo> <mn>0.0001</mn> </mrow> </semantics></math>: (<b>a</b>) the solution of the system; (<b>b</b>) <span class="html-italic">y</span>-component of the solution; (<b>c</b>) the portrait; (<b>d</b>) emitting chart.</p> Full article ">Figure 7
<p>The simulations (system (6)) for <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.08</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>c</mi> <mo>=</mo> <mn>0.001</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>=</mo> <mn>0.0001</mn> </mrow> </semantics></math>: (<b>a</b>) the solution of the system; (<b>b</b>) <span class="html-italic">y</span>-component of the solution; (<b>c</b>) the portrait; (<b>d</b>) emitting chart.</p> Full article ">Figure 8
<p>The catastrophe surfaces in the light of Zeeman considerations.</p> Full article ">Figure 9
<p>The catastrophe surfaces in the light of Zeeman considerations.</p> Full article ">Figure 10
<p>The polynomials <math display="inline"><semantics> <mrow> <msubsup> <mi>P</mi> <mi>n</mi> <mo>∗</mo> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> for fixed <math display="inline"><semantics> <mrow> <mi>a</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>c</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>7</mn> <mo>,</mo> <mn>9</mn> </mrow> </semantics></math>.</p> Full article ">Figure 11
<p>The simulations (system (8)) for <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.8</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>y</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.6</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>b</mi> <mo>=</mo> <mn>0.9</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>c</mi> <mo>=</mo> <mn>0.7809</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <mi>ϵ</mi> <mo>=</mo> <mn>0.0001</mn> </mrow> </semantics></math>: (<b>a</b>) the solution of the system; (<b>b</b>) <span class="html-italic">y</span>-component of the solution; (<b>c</b>) the portrait; (<b>d</b>) emitting chart.</p> Full article ">
14 pages, 5723 KiB  
Article
Noise Cancellation Method Based on TVF-EMD with Bayesian Parameter Optimization
by Miaomiao Yu, Hongyong Yuan, Kaiyuan Li and Lizheng Deng
Algorithms 2023, 16(6), 296; https://doi.org/10.3390/a16060296 - 12 Jun 2023
Cited by 3 | Viewed by 1521
Abstract
To separate the noise and important signal features of the indoor carbon dioxide (CO2) concentration signal, we proposed a noise cancellation method, based on time-varying, filtering-based empirical mode decomposition (TVF-EMD) with Bayesian optimization (BO). The adaptive parameters of TVF-EMD, that is, [...] Read more.
To separate the noise and important signal features of the indoor carbon dioxide (CO2) concentration signal, we proposed a noise cancellation method, based on time-varying, filtering-based empirical mode decomposition (TVF-EMD) with Bayesian optimization (BO). The adaptive parameters of TVF-EMD, that is, bandwidth threshold ξ and B-spline order n, were determined by the BO algorithm, and the correlation coefficient for the kurtosis index (CCKur) constituted the objective function. Initially, the objective function CCKur was introduced to systematically identify anomalous signals while preserving signal feature extraction between the modes and the input signal. Subsequently, the proposed signal noise cancellation model based on TVF-EMD and the BO algorithm were employed, along with the Hurst exponent, to extract the sensitive mode. An examination of the optimization indices of the decomposed intrinsic mode functions (IMFs), namely CC, Kur, MI, EE, EEMI, and CCKur, revealed that the synthetic measurement index CCKur and objective function fitness were reasonable and effective. The proposed method exhibited better signal cancellation performance, compared to that of TVF-EMD with the default values, EMD, the moving average method, and the exponential smoothing method. Full article
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<p>Flowchart of Bayesian optimization.</p> Full article ">Figure 2
<p>Flowchart for the noise-cancellation model.</p> Full article ">Figure 3
<p>Office CO<sub>2</sub> concentrations throughout the day.</p> Full article ">Figure 4
<p>Decomposition results of the CO<sub>2</sub> signal obtained by (<b>a</b>) EMD and (<b>b</b>) TVF-EMD.</p> Full article ">Figure 5
<p>Hurst exponent values in different modes.</p> Full article ">Figure 6
<p>Comparison of signal noise cancellation and the simulated CO<sub>2</sub>-concentration signal.</p> Full article ">Figure 7
<p>Relationship between IMF and the optimization index.</p> Full article ">Figure 7 Cont.
<p>Relationship between IMF and the optimization index.</p> Full article ">Figure 8
<p>Hyperparameter importance in the decomposition result.</p> Full article ">Figure 9
<p>Relationship between IMF indices and the bandwidth threshold.</p> Full article ">Figure 9 Cont.
<p>Relationship between IMF indices and the bandwidth threshold.</p> Full article ">
60 pages, 11060 KiB  
Article
An Experimental Outlook on Quality Metrics for Process Modelling: A Systematic Review and Meta Analysis
by Ashish T. S. Ireddy and Sergey V. Kovalchuk
Algorithms 2023, 16(6), 295; https://doi.org/10.3390/a16060295 - 10 Jun 2023
Viewed by 2516
Abstract
The ideology behind process modelling is to visualise lengthy event logs into simple representations interpretable to the end user. Classifying process models as simple or complex is based on criteria that evaluate attributes of models and quantify them on a scale. These metrics [...] Read more.
The ideology behind process modelling is to visualise lengthy event logs into simple representations interpretable to the end user. Classifying process models as simple or complex is based on criteria that evaluate attributes of models and quantify them on a scale. These metrics measure various characteristics of process models and describe their qualities. Over the years, vast amounts of metrics have been proposed in the community, making it difficult to find and select the appropriate ones for implementation. This paper presents a state-of-the-art meta-review that lists and summarises all the evaluation metrics proposed to date. We have studied the behaviour of the four most widely used metrics in process mining with an experiment. Further, we have used seven healthcare domain datasets of varying natures to analyse the behaviour of these metrics under different threshold conditions. Our work aims to propose and demonstrate the capabilities to use our selected metrics as a standard of measurement for the process mining domain. Full article
(This article belongs to the Special Issue Process Mining and Its Applications)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Selection procedure for broad-spectrum study.</p> Full article ">Figure 2
<p>The selection procedure for the meta-review.</p> Full article ">Figure 3
<p>Branching of evaluation in process modelling.</p> Full article ">Figure 4
<p>The taxonomy of metrics (1997–2023), (* indicates metrics that are repeating in more than one characteristic quality).</p> Full article ">Figure 5
<p>The variation patterns of process control features (R1 and R2).</p> Full article ">Figure 6
<p>Fitness ratings of datasets 1 to 7 in R1.</p> Full article ">Figure 7
<p>Fitness ratings of datasets 1 to 7 in R2.</p> Full article ">Figure 8
<p>Precision ratings of datasets 1 to 7 in R1.</p> Full article ">Figure 9
<p>Precision ratings of datasets 1 to 7 in R2.</p> Full article ">Figure 10
<p>Generalisation ratings of datasets 1 to 7 in R1.</p> Full article ">Figure 11
<p>Generalisation ratings of datasets 1 to 7 in R2.</p> Full article ">Figure 12
<p>Simplicity ratings of datasets 1 to 7 in R1.</p> Full article ">Figure 13
<p>Simplicity ratings of datasets 1 to 7 in R2.</p> Full article ">Figure 14
<p>An optimal range for a process model in R1.</p> Full article ">Figure 15
<p>Process model to demonstrate the looping threshold.</p> Full article ">Figure A1
<p>Workflow for Fitness.</p> Full article ">Figure A2
<p>Workflow for Precision.</p> Full article ">Figure A3
<p>Workflow for Generalisation.</p> Full article ">Figure A4
<p>Workflow for Simplicity.</p> Full article ">Figure A5
<p>P1: Impact of adding activities on fitness—sample 1.</p> Full article ">Figure A6
<p>P2: Impact of adding activities on fitness—sample 1.</p> Full article ">Figure A7
<p>P1: Impact on generalisation due to addition of activities in R1—sample 1.</p> Full article ">Figure A8
<p>P2: Impact on generalisation due to addition of activities in R1—sample 1.</p> Full article ">Figure A9
<p>Impact on generalisation of the process model when in R2—sample 1–part 1.</p> Full article ">Figure A10
<p>Impact on generalisation of the process model when in R2—sample 1–part 2.</p> Full article ">Figure A11
<p>P1: Impact on simplicity in R1—sample 7.</p> Full article ">Figure A12
<p>P2: Impact on simplicity in R1—sample 7.</p> Full article ">Figure A13
<p>Impact on simplicity in R2—sample 5.</p> Full article ">Figure A14
<p>Process model graphs of dataset 1 in R1 and R2.</p> Full article ">Figure A15
<p>Process model graphs of dataset 1 in R1 and R2.</p> Full article ">Figure A16
<p>Process model graphs of dataset 3 in R1 and R2.</p> Full article ">Figure A17
<p>Process model graphs of dataset 3 in R1 and R2.</p> Full article ">Figure A18
<p>Process model graphs of dataset 5 in R1 and R2.</p> Full article ">Figure A19
<p>Process model graphs of dataset 5 in R1 and R2.</p> Full article ">Figure A20
<p>Process model graphs of dataset 7 in R1 and R2.</p> Full article ">Figure A21
<p>Process model graphs of dataset 7 in R1 and R2.</p> Full article ">
25 pages, 8359 KiB  
Article
Generalized Algorithm Based on Equivalent Circuits for Evaluating Shielding Effectiveness of Electronic Equipment Enclosures
by Anton A. Ivanov, Aleksey A. Kvasnikov, Alexander V. Demakov, Maxim E. Komnatnov, Sergei P. Kuksenko and Talgat R. Gazizov
Algorithms 2023, 16(6), 294; https://doi.org/10.3390/a16060294 - 8 Jun 2023
Cited by 1 | Viewed by 1912
Abstract
The article proposes a generalized algorithm for evaluating the shielding effectiveness (SE) of electronic equipment enclosures. The algorithm is based on a number of analytical models that use equivalent circuits to obtain SE values. The article begins with a brief review and interpretation [...] Read more.
The article proposes a generalized algorithm for evaluating the shielding effectiveness (SE) of electronic equipment enclosures. The algorithm is based on a number of analytical models that use equivalent circuits to obtain SE values. The article begins with a brief review and interpretation of the mathematical formulation used in the algorithm. Then, we describe the proposed algorithm using flowcharts, and we perform its validation. The validation results show that the proposed algorithm has acceptable accuracy and gives SE values comparable to numerical methods or measurements, with much less time costs. The last part of the article presents the software developed to evaluate SE based on analytical models. Full article
(This article belongs to the Collection Feature Papers in Algorithms for Multidisciplinary Applications)
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<p>Rectangular enclosure with aperture excited by a plane wave (<b>a</b>), equivalent circuit for calculating SE (<b>b</b>).</p> Full article ">Figure 2
<p>Equivalent circuits after the first (<b>a</b>) and second (<b>b</b>) transformation steps.</p> Full article ">Figure 3
<p>Front wall with an aperture shifted to the left (<b>a</b>), arbitrarily shaped aperture replaced by a set of coplanar stripline segments (<b>b</b>).</p> Full article ">Figure 4
<p>Enclosure front wall perforated with circular apertures (<b>a</b>), array of staggered apertures (<b>b</b>).</p> Full article ">Figure 5
<p>The aperture populated with wire grid (<b>a</b>) and geometry of this wire grid (<b>b</b>).</p> Full article ">Figure 6
<p>Cylindrical enclosure with the aperture at the base.</p> Full article ">Figure 7
<p>Enclosure populated with dielectric plate (<b>a</b>), equivalent circuit for calculating SE (<b>b</b>).</p> Full article ">Figure 8
<p>Enclosure filled with a conductive post (<b>a</b>), equivalent circuit for calculating SE (<b>b</b>).</p> Full article ">Figure 9
<p>Enclosure filled with a conductive plate (<b>a</b>), equivalent circuit for calculating SE (<b>b</b>).</p> Full article ">Figure 10
<p>Main flowchart of the generalized algorithm for the SE evaluation.</p> Full article ">Figure 11
<p>Algorithm of <span class="html-italic">Z<sub>ap</sub></span> calculation for a single aperture (Flowchart 2).</p> Full article ">Figure 12
<p>Algorithm of <span class="html-italic">Z<sub>ap</sub></span> calculation for an aperture array or a perforated wall (Flowchart 3).</p> Full article ">Figure 13
<p>Algorithm of <span class="html-italic">Z<sub>ap</sub></span> calculation for a group of apertures (Flowchart 4).</p> Full article ">Figure 14
<p>Algorithm of equivalent circuit transformation (Flowchart 5).</p> Full article ">Figure 15
<p>Algorithm of equivalent circuit transformation for a rectangular enclosure with internal filling (Flowchart 6).</p> Full article ">Figure 16
<p>Algorithm of equivalent circuit transformation for a cylindrical enclosure with internal filling (Flowchart 7).</p> Full article ">Figure 17
<p>Empty enclosure with a squared aperture of 80 × 80 mm<sup>2</sup>.</p> Full article ">Figure 18
<p>Enclosure populated with conductive plate (<b>a</b>), enclosure with dielectric filled slot (<b>b</b>). In the left photo, the enclosure has no wall.</p> Full article ">Figure 19
<p>Test setups for measuring SE according to IEEE STD 299.1 (<b>a</b>) and using the indirect method (<b>b</b>).</p> Full article ">Figure 20
<p>Frequency dependencies of the SE for the empty enclosure with a squared aperture.</p> Full article ">Figure 21
<p>Frequency dependencies of the SE for enclosures from cases 2 (<b>a</b>) and 3 (<b>b</b>).</p> Full article ">Figure 22
<p>Shielding enclosure of the Ethernet filter (<b>a</b>) and frequency dependencies of its SE (<b>b</b>).</p> Full article ">Figure 23
<p>Enclosure of the ABB FOX 515 multiplexer (<b>a</b>) and frequency dependencies of its SE (<b>b</b>).</p> Full article ">Figure 24
<p>Frequency dependencies of the SE for the cylindrical enclosure filled with dielectric.</p> Full article ">Figure 25
<p>Software architecture as a UML package diagram.</p> Full article ">Figure 26
<p>GUI of the software prototype: setting the enclosure geometry (<b>a</b>), displaying the three-dimensional pattern of the SE (<b>b</b>).</p> Full article ">
16 pages, 2287 KiB  
Article
Random forest Algorithm for the Classification of Spectral Data of Astronomical Objects
by José-Luis Solorio-Ramírez, Raúl Jiménez-Cruz, Yenny Villuendas-Rey and Cornelio Yáñez-Márquez
Algorithms 2023, 16(6), 293; https://doi.org/10.3390/a16060293 - 8 Jun 2023
Cited by 1 | Viewed by 2944
Abstract
Over time, human beings have built increasingly large astronomical observatories to increase the number of discoveries related to celestial objects. However, the amount of collected elements far exceeds the human capacity to analyze findings without help. For this reason, researchers must now turn [...] Read more.
Over time, human beings have built increasingly large astronomical observatories to increase the number of discoveries related to celestial objects. However, the amount of collected elements far exceeds the human capacity to analyze findings without help. For this reason, researchers must now turn to machine learning to analyze such data, identifying and classifying transient objects or events within extensive observations of the firmament. Algorithms from the family of random forests (an ensemble of decision trees) have become a powerful tool that can be used to classify astronomical events and objects. This work aims to illustrate the versatility of machine learning algorithms, such as decision trees, to facilitate the identification and classification of celestial bodies by manipulating hyperparameters and studying the attributes of celestial body datasets. By applying a random forest algorithm to a well-known dataset that includes three types of celestial bodies, its effectiveness was compared against some supervised classifiers of the most important approaches (Bayes, nearest neighbors, support vector machines, and neural networks). The results show that random forests are a good alternative for data analysis and classification in astronomical observations. Full article
(This article belongs to the Collection Feature Papers in Algorithms for Multidisciplinary Applications)
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<p>Hyperparameter tuning: Randomized vs. Grid Search.</p> Full article ">Figure 2
<p>Schematic illustration of the result of the validation method.</p> Full article ">Figure 3
<p>Schematic illustration of a confusion matrix for two classes.</p> Full article ">Figure 4
<p>Confusion matrix resulting from applying the proposed random forest algorithm on the SDSS DR14 dataset.</p> Full article ">Figure 5
<p>Comparative bar chart of balanced accuracy values resulting from applying the six classification algorithms on the SDSS DR14 dataset. The proposed random forest algorithm is represented in pink.</p> Full article ">Figure 6
<p>Confusion matrix resulting from applying the proposed random forest algorithm on the SDSS DR16 dataset.</p> Full article ">Figure 7
<p>Comparative bar chart of balanced accuracy values resulting from applying the six classification algorithms on the SDSS DR16 dataset. The proposed random forest algorithm is represented in pink.</p> Full article ">Figure 8
<p>Confusion matrix resulting from applying the proposed random forest algorithm on the SDSS DR17 dataset.</p> Full article ">Figure 9
<p>Comparative bar chart of balanced accuracy values resulting from applying the six classification algorithms on the SDSS DR17 dataset. The proposed random forest algorithm is represented in pink.</p> Full article ">
24 pages, 1564 KiB  
Article
Improving Accuracy of Face Recognition in the Era of Mask-Wearing: An Evaluation of a Pareto-Optimized FaceNet Model with Data Preprocessing Techniques
by Damilola Akingbesote, Ying Zhan, Rytis Maskeliūnas and Robertas Damaševičius
Algorithms 2023, 16(6), 292; https://doi.org/10.3390/a16060292 - 5 Jun 2023
Cited by 4 | Viewed by 3185
Abstract
The paper presents an evaluation of a Pareto-optimized FaceNet model with data preprocessing techniques to improve the accuracy of face recognition in the era of mask-wearing. The COVID-19 pandemic has led to an increase in mask-wearing, which poses a challenge for face recognition [...] Read more.
The paper presents an evaluation of a Pareto-optimized FaceNet model with data preprocessing techniques to improve the accuracy of face recognition in the era of mask-wearing. The COVID-19 pandemic has led to an increase in mask-wearing, which poses a challenge for face recognition systems. The proposed model uses Pareto optimization to balance accuracy and computation time, and data preprocessing techniques to address the issue of masked faces. The evaluation results demonstrate that the model achieves high accuracy on both masked and unmasked faces, outperforming existing models in the literature. The findings of this study have implications for improving the performance of face recognition systems in real-world scenarios where mask-wearing is prevalent. The results of this study show that the Pareto optimization allowed improving the overall accuracy over the 94% achieved by the original FaceNet variant, which also performed similarly to the ArcFace model during testing. Furthermore, a Pareto-optimized model no longer has a limitation of the model size and is much smaller and more efficient version than the original FaceNet and derivatives, helping to reduce its inference time and making it more practical for use in real-life applications. Full article
(This article belongs to the Special Issue Machine Learning and Deep Learning in Pattern Recognition)
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<p>CASIA dataset images samples.</p> Full article ">Figure 2
<p>VGG-FACE dataset images samples.</p> Full article ">Figure 3
<p>Combined dataset images samples.</p> Full article ">Figure 4
<p>Sample of training images after augmentation.</p> Full article ">Figure 5
<p>Illustration of Cutmix and MixUp image augmentations.</p> Full article ">Figure 6
<p>Pareto-optimized FaceNet architecture.</p> Full article ">Figure 7
<p>Grad-Cam example.</p> Full article ">Figure 8
<p>Accuracy and loss curves.</p> Full article ">Figure 9
<p>SR-GAN.</p> Full article ">
23 pages, 1351 KiB  
Article
An Effective Local Particle Swarm Optimization-Based Algorithm for Solving the School Timetabling Problem
by Ioannis X. Tassopoulos, Christina A. Iliopoulou, Iosif V. Katsaragakis and Grigorios N. Beligiannis
Algorithms 2023, 16(6), 291; https://doi.org/10.3390/a16060291 - 4 Jun 2023
Cited by 1 | Viewed by 1718
Abstract
This paper deals with the school timetabling problem. The problem was formulated as encountered in a typical Greek high school. A local version of the particle swarm optimization algorithm was developed and applied to the problem at hand. Results on well-established benchmark instances [...] Read more.
This paper deals with the school timetabling problem. The problem was formulated as encountered in a typical Greek high school. A local version of the particle swarm optimization algorithm was developed and applied to the problem at hand. Results on well-established benchmark instances showed that the proposed algorithm achieved the proven optima provided from an integer programming method presented in earlier research. In almost all cases, the current algorithm beat the integer programming method, either concerning the lower bound yielded or the execution time needed. Full article
(This article belongs to the Collection Feature Paper in Metaheuristic Algorithms and Applications)
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<p>The structure of particles.</p> Full article ">Figure 2
<p>Example of replacing a timeslot (column) of a particle (matrix B) by a timeslot of source particle (matrix A), i.e., the global best or personal best or local best. The result is the particle named “produced B”.</p> Full article ">Figure 3
<p>Box plots of total cost values for each input instance (after 30 Monte Carlo runs).</p> Full article ">Figure 4
<p>Box plots of execution times for each input instance (after 30 Monte Carlo runs).</p> Full article ">
21 pages, 2828 KiB  
Article
Integration of Polynomials Times Double Step Function in Quadrilateral Domains for XFEM Analysis
by Sebastiano Fichera, Gregorio Mariggiò, Mauro Corrado and Giulio Ventura
Algorithms 2023, 16(6), 290; https://doi.org/10.3390/a16060290 - 4 Jun 2023
Viewed by 1632
Abstract
The numerical integration of discontinuous functions is an abiding problem addressed by various authors. This subject gained even more attention in the context of the extended finite element method (XFEM), in which the exact integration of discontinuous functions is crucial to obtaining reliable [...] Read more.
The numerical integration of discontinuous functions is an abiding problem addressed by various authors. This subject gained even more attention in the context of the extended finite element method (XFEM), in which the exact integration of discontinuous functions is crucial to obtaining reliable results. In this scope, equivalent polynomials represent an effective method to circumvent the problem while exploiting the standard Gauss quadrature rule to exactly integrate polynomials times step function. Certain scenarios, however, might require the integration of polynomials times two step functions (i.e., problems in which branching cracks, kinking cracks or crack junctions within a single finite element occur). In this context, the use of equivalent polynomials has been investigated by the authors, and an algorithm to exactly integrate arbitrary polynomials times two Heaviside step functions in quadrilateral domains has been developed and is presented in this paper. Moreover, the algorithm has also been implemented into a software library (DD_EQP) to prove its precision and effectiveness and also the proposed method’s ease of implementation into any existing computational software or framework. The presented algorithm is the first step towards the numerical integration of an arbitrary number of discontinuities in quadrilateral domains. Both the algorithm and the library have a wide application range, in addition to fracture mechanics, from mathematical computing of complex geometric regions, to computer graphics and computational mechanics. Full article
(This article belongs to the Special Issue Computational Methods and Optimization for Numerical Analysis)
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<p>A 2D quadrangular domain <math display="inline"><semantics> <mi mathvariant="sans-serif">Ω</mi> </semantics></math> crossed by a discontinuity line <span class="html-italic">d</span>.</p> Full article ">Figure 2
<p>A 2D quadrangular domain <math display="inline"><semantics> <mi mathvariant="sans-serif">Ω</mi> </semantics></math> crossed by two discontinuity lines: <span class="html-italic">q</span> and <span class="html-italic">r</span>.</p> Full article ">Figure 3
<p>Use of the auxiliary integration limit <span class="html-italic">s</span> to evaluate the equivalent polynomials <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>H</mi> <mo stretchy="false">˜</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. In the figure <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>H</mi> <mo stretchy="false">˜</mo> </mover> <mi>B</mi> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mover accent="true"> <mi>H</mi> <mo stretchy="false">˜</mo> </mover> <msup> <mi>q</mi> <mo>+</mo> </msup> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>)</mo> </mrow> <mo>−</mo> <msubsup> <mover accent="true"> <mi>H</mi> <mo stretchy="false">˜</mo> </mover> <msup> <mi>r</mi> <mo>+</mo> </msup> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math>. (<b>a</b>) Integration domain evaluated by means of <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>H</mi> <mo stretchy="false">˜</mo> </mover> <msup> <mi>q</mi> <mo>+</mo> </msup> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> with respect to the discontinuity <span class="html-italic">q</span> and the auxiliary integration limit <span class="html-italic">s</span>. (<b>b</b>) Integration domain evaluated by means of <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>H</mi> <mo stretchy="false">˜</mo> </mover> <msup> <mi>r</mi> <mo>+</mo> </msup> </msub> <mrow> <mo>(</mo> <mi mathvariant="bold-italic">x</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> with respect to the discontinuity <span class="html-italic">r</span> and the auxiliary integration limit <span class="html-italic">s</span>.</p> Full article ">Figure 4
<p>Isoparametric mapping of a quadrangular element. (<b>a</b>) Element configuration in the global coordinate system. (<b>b</b>) Element configuration in the parent coordinate system.</p> Full article ">Figure 5
<p>Software illustrative examples. (<b>a</b>) Example 1: parallelogram domain cut by two discontinuities intersecting inside the domain. (<b>b</b>) Example 2: parallelogram domain cut by two discontinuities intersecting outside the domain.</p> Full article ">
19 pages, 402 KiB  
Article
Adding a Tail in Classes of Perfect Graphs
by Anna Mpanti, Stavros D. Nikolopoulos and Leonidas Palios
Algorithms 2023, 16(6), 289; https://doi.org/10.3390/a16060289 - 3 Jun 2023
Viewed by 1312
Abstract
Consider a graph G which belongs to a graph class C. We are interested in connecting a node w∉V(G) to G by a single edge uw where u∈V(G); we call [...] Read more.
Consider a graph G which belongs to a graph class C. We are interested in connecting a node w∉V(G) to G by a single edge uw where u∈V(G); we call such an edge a tail. As the graph resulting from G after the addition of the tail, denoted G+uw, need not belong to the class C, we want to compute the number of non-edges of G in a minimum C-completion of G+uw, i.e., the minimum number of non-edges (excluding the tail uw) to be added to G+uw so that the resulting graph belongs to C. In this paper, we study this problem for the classes of split, quasi-threshold, threshold and P4-sparse graphs and we present linear-time algorithms by exploiting the structure of split graphs and the tree representation of quasi-threshold, threshold and P4-sparse graphs. Full article
(This article belongs to the Special Issue Graph Theoretic Methods in Scientific Computing & Industrial Applications)
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<p>(<b>left</b>) The structure of the tree representation of a threshold graph [<a href="#B45-algorithms-16-00289" class="html-bibr">45</a>]; (<b>right</b>) Formation for the addition of the tail <math display="inline"><semantics> <mrow> <mi>u</mi> <mi>w</mi> </mrow> </semantics></math>.</p> Full article ">Figure 2
<p>The tree representation of a quasi-threshold graph.</p> Full article ">Figure 3
<p>The forbidden subgraphs for the class of <math display="inline"><semantics> <msub> <mi>P</mi> <mn>4</mn> </msub> </semantics></math>-sparse graphs [<a href="#B38-algorithms-16-00289" class="html-bibr">38</a>].</p> Full article ">Figure 4
<p>(<b>left</b>) A thin spider; (<b>right</b>) a thick spider.</p> Full article ">Figure 5
<p>The path <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mn>0</mn> </msub> <msub> <mi>t</mi> <mn>1</mn> </msub> <mo>⋯</mo> <msub> <mi>t</mi> <mi>h</mi> </msub> <mi>u</mi> </mrow> </semantics></math> from the root <math display="inline"><semantics> <msub> <mi>t</mi> <mn>0</mn> </msub> </semantics></math> of the <math display="inline"><semantics> <msub> <mi>P</mi> <mn>4</mn> </msub> </semantics></math>-sparse tree to the leaf associated with <span class="html-italic">u</span> and the vertex sets <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>V</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>V</mi> <mi>h</mi> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 6
<p>(<b>left</b>) Formation 1; (<b>right</b>) Formation 2 where <span class="html-italic">t</span> is a 1- or a 2-node. Formation 1 is a special case of Formation 2 when <math display="inline"><semantics> <mrow> <mi>Z</mi> <mo>=</mo> <mo>∅</mo> </mrow> </semantics></math>.</p> Full article ">Figure 7
<p>(<b>left</b>) The <math display="inline"><semantics> <msub> <mi>P</mi> <mn>4</mn> </msub> </semantics></math>-sparse tree <math display="inline"><semantics> <msub> <mi>T</mi> <mrow> <mi>O</mi> <mi>P</mi> <mi>T</mi> </mrow> </msub> </semantics></math> in which the leaves for <math display="inline"><semantics> <mrow> <mi>u</mi> <mo>,</mo> <mi>w</mi> </mrow> </semantics></math> do not have the same parent node and have node <span class="html-italic">t</span> as their least common ancestor; (<b>right</b>) The <math display="inline"><semantics> <msub> <mi>P</mi> <mn>4</mn> </msub> </semantics></math>-sparse tree <math display="inline"><semantics> <msub> <mi>T</mi> <mi>R</mi> </msub> </semantics></math> obtained by using Formation 2 just above node <span class="html-italic">t</span> which results in no more fill edges than those in <math display="inline"><semantics> <msub> <mi>G</mi> <mrow> <mi>O</mi> <mi>P</mi> <mi>T</mi> </mrow> </msub> </semantics></math>.</p> Full article ">Figure 8
<p>A transformation that reduces the number of fill edges.</p> Full article ">
18 pages, 651 KiB  
Article
An Adaptive Deep Learning Neural Network Model to Enhance Machine-Learning-Based Classifiers for Intrusion Detection in Smart Grids
by Xue Jun Li, Maode Ma and Yihan Sun
Algorithms 2023, 16(6), 288; https://doi.org/10.3390/a16060288 - 2 Jun 2023
Cited by 7 | Viewed by 2516
Abstract
Modern smart grids are built based on top of advanced computing and networking technologies, where condition monitoring relies on secure cyberphysical connectivity. Over the network infrastructure, transported data containing confidential information, must be protected as smart grids are vulnerable and subject to various [...] Read more.
Modern smart grids are built based on top of advanced computing and networking technologies, where condition monitoring relies on secure cyberphysical connectivity. Over the network infrastructure, transported data containing confidential information, must be protected as smart grids are vulnerable and subject to various cyberattacks. Various machine learning based classifiers were proposed for intrusion detection in smart grids. However, each of them has respective advantage and disadvantages. Aiming to improve the performance of existing machine learning based classifiers, this paper proposes an adaptive deep learning algorithm with a data pre-processing module, a neural network pre-training module and a classifier module, which work together classify intrusion data types using their high-dimensional data features. The proposed Adaptive Deep Learning (ADL) algorithm obtains the number of layers and the number of neurons per layer by determining the characteristic dimension of the network traffic. With transfer learning, the proposed ADL algorithm can extract the original data dimensions and obtain new abstract features. By combining deep learning models with traditional machine learning-based classification models, the performance of classification of network traffic data is significantly improved. By using the Network Security Laboratory-Knowledge Discovery in Databases (NSL-KDD) dataset, experimental results show that the proposed ADL algorithm improves the effectiveness of existing intrusion detection methods and reduces the training time, indicating a promising candidate to enhance network security in smart grids. Full article
(This article belongs to the Special Issue AI for Cybersecurity: Robust models for Authentication, Threat and Anomaly Detection)
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<p>Illustration diagram shows how a Back Propagation Neural Network works.</p> Full article ">Figure 2
<p>Illustration diagram of the adaptive deep learning framework.</p> Full article ">Figure 3
<p>Illustration diagram of the model of transferring learning.</p> Full article ">Figure 4
<p>The confusion matrix results of two-class classification using the existing four classification methods: KNN, Naïve Bayes, BPNN and DT.</p> Full article ">Figure 5
<p>Performance comparison of two-class classifications using the existing four classification methods: KNN, Naïve Bayes, BPNN and DT.</p> Full article ">Figure 6
<p>The confusion matrix results of multi-classification using the existing four classification methods: KNN, Naïve Bayes, BPNN and DT.</p> Full article ">Figure 7
<p>Performance comparison of multi-classification using the existing four classification methods: KNN, Naïve Bayes, BPNN and DT.</p> Full article ">
25 pages, 8154 KiB  
Article
A Fast Hybrid Pressure-Correction Algorithm for Simulating Incompressible Flows by Projection Methods
by Jiannong Fang
Algorithms 2023, 16(6), 287; https://doi.org/10.3390/a16060287 - 2 Jun 2023
Viewed by 1845
Abstract
To enforce the conservation of mass principle, a pressure Poisson equation arises in the numerical solution of incompressible fluid flow using the pressure-based segregated algorithms such as projection methods. For unsteady flows, the pressure Poisson equation is solved at each time step usually [...] Read more.
To enforce the conservation of mass principle, a pressure Poisson equation arises in the numerical solution of incompressible fluid flow using the pressure-based segregated algorithms such as projection methods. For unsteady flows, the pressure Poisson equation is solved at each time step usually in physical space using iterative solvers, and the resulting pressure gradient is then applied to make the velocity field divergence-free. It is generally accepted that this pressure-correction stage is the most time-consuming part of the flow solver and any meaningful acceleration would contribute significantly to the overall computational efficiency. The objective of the present work was to develop a fast hybrid pressure-correction algorithm for numerical simulation of incompressible flows around obstacles in the context of projection methods. The key idea is to adopt different numerical methods/discretisations in the sub-steps of projection methods. Here, a classical second-order time-marching projection method, which consists of two sub-steps, was chosen for the purposes of demonstration. In the first sub-step, the momentum equations were discretised on unstructured grids and solved by conventional numerical methods, here a meshless method. In the second sub-step (pressure-correction), the proposed algorithm adopts a double-discretisation system and combines the weighted least-squares approximation with the essence of immersed boundary methods. Such a design allowed us to develop an FFT-based solver to speed up the solution of the pressure Poisson equation for flow cases with obstacles, while keeping the implementation of the boundary conditions for the momentum equations as easy as conventional numerical methods do with unstructured grids. The numerical experiments of five test cases were performed to verify and validate the proposed hybrid algorithm and evaluate its computational performance. The results showed that the new FFT-based hybrid algorithm works and is robust, and it was significantly faster than the multigrid-based reference method. The hybrid algorithm opens an avenue for the development of next-generation high-performance parallel computational fluid dynamics solvers for incompressible flows. Full article
(This article belongs to the Collection Feature Papers in Algorithms)
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<p>Double-discretisation for the hybrid approach.</p> Full article ">Figure 2
<p>Flow chart of the projection method using the hybrid pressure-correction algorithm.</p> Full article ">Figure 3
<p>Geometry of the flow over a square with periodic lateral boundary conditions. The side length of the square is <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>=</mo> <mn>0.04</mn> </mrow> </semantics></math> m, and the side length of the square lattice is <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> m. The two monitoring points 1 and 2 for comparing the time histories of numerical solutions are located at <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mi>L</mi> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mo>−</mo> <mi>L</mi> <mo>/</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mi>D</mi> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mo>−</mo> <mi>D</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics></math>, respectively.</p> Full article ">Figure 4
<p>Comparison of numerical solutions obtained by the reference method (<b>left</b>) and the hybrid method (<b>right</b>) for the first test case at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>4000</mn> </mrow> </semantics></math> s. Shown from top to bottom are the contours of the horizontal velocity component <span class="html-italic">U</span>, the vertical velocity component <span class="html-italic">V</span>, and the pressure <span class="html-italic">P</span>, respectively.</p> Full article ">Figure 5
<p>Comparison of the time histories of the horizontal and vertical velocity components at Monitoring Point 1 obtained by the reference method and the hybrid method for the first test case.</p> Full article ">Figure 6
<p>Comparison of the time histories of the pressure at the two monitoring points 1 and 2 obtained by the reference method and the hybrid method for the first test case.</p> Full article ">Figure 7
<p>Spatial error convergence for laminar flow over a square simulated by the reference (<b>left</b>) and hybrid (<b>right</b>) methods.</p> Full article ">Figure 8
<p>Temporal error convergence for laminar flow over a square simulated by the reference (<b>left</b>) and hybrid (<b>right</b>) methods.</p> Full article ">Figure 9
<p>Geometry of the flow around a cylinder with periodic lateral boundary conditions. The radius of the cylinder is <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math> m, and the side length of the square lattice is <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> m. The three monitoring points 1, 2, and 3 for comparing the time histories of numerical solutions are located at <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mi>L</mi> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mo>−</mo> <mi>L</mi> <mo>/</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mi>r</mi> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math>, respectively.</p> Full article ">Figure 10
<p>Comparison of numerical solutions obtained by the reference method (<b>left</b>) and the hybrid method (<b>right</b>) for the second test case at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>300</mn> </mrow> </semantics></math> s. Shown from top to bottom are the contours of the horizontal velocity component <span class="html-italic">U</span>, the vertical velocity component <span class="html-italic">V</span>, and the pressure <span class="html-italic">P</span>, respectively.</p> Full article ">Figure 11
<p>Comparison of the time histories of the horizontal and vertical velocity components at Monitoring Point 1 obtained by the reference method and the hybrid method for the second test case.</p> Full article ">Figure 12
<p>Comparison of the time histories of the pressure at Monitoring Point 1 and the pressure difference between the two monitoring points 2 and 3 obtained by the reference method and the hybrid method for the second test case.</p> Full article ">Figure 13
<p>Comparison of numerical solutions obtained by the reference method (<b>left</b>) and the hybrid method (<b>right</b>) for the third test case at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>300</mn> </mrow> </semantics></math> s. Shown from top to bottom are the contours of the horizontal velocity component <span class="html-italic">U</span>, the vertical velocity component <span class="html-italic">V</span>, and the pressure <span class="html-italic">P</span>, respectively.</p> Full article ">Figure 13 Cont.
<p>Comparison of numerical solutions obtained by the reference method (<b>left</b>) and the hybrid method (<b>right</b>) for the third test case at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>300</mn> </mrow> </semantics></math> s. Shown from top to bottom are the contours of the horizontal velocity component <span class="html-italic">U</span>, the vertical velocity component <span class="html-italic">V</span>, and the pressure <span class="html-italic">P</span>, respectively.</p> Full article ">Figure 14
<p>Comparison of the time histories of the horizontal and vertical velocity components at Monitoring Point 1 obtained by the reference method and the hybrid method for the third test case.</p> Full article ">Figure 15
<p>Comparison of the time histories of the pressure at Monitoring Point 1 and the pressure difference between the two monitoring points 2 and 3 obtained by the reference method and the hybrid method for the third test case.</p> Full article ">Figure 16
<p>Geometry of the flow over periodic triangular hills in a channel. The height of the hill is <math display="inline"><semantics> <mrow> <mi>h</mi> <mo>=</mo> <mn>0.02</mn> </mrow> </semantics></math> m, and the width of the hill is <math display="inline"><semantics> <mrow> <mn>0.04</mn> </mrow> </semantics></math> m. The height of the channel is <math display="inline"><semantics> <mrow> <mi>L</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> m. The two monitoring points 1 and 2 for comparing the time histories of numerical solutions are located at <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mi>L</mi> <mo>/</mo> <mn>2</mn> <mo>,</mo> <mo>−</mo> <mi>L</mi> <mo>/</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mo>−</mo> <mi>L</mi> <mo>/</mo> <mn>2</mn> <mo>+</mo> <mi>h</mi> <mo>)</mo> </mrow> </semantics></math>, respectively.</p> Full article ">Figure 17
<p>Comparison of numerical solutions obtained by the reference method (<b>left</b>) and the hybrid method (<b>right</b>) for the fourth test case at the time when the horizontal velocity at Monitoring Point 1 reaches the median in the accelerating phase. Shown from top to down are the contours of the horizontal velocity component <span class="html-italic">U</span>, the vertical velocity component <span class="html-italic">V</span>, and the pressure <span class="html-italic">P</span>, respectively.</p> Full article ">Figure 18
<p>Comparison of time histories of the horizontal and vertical velocity components at Monitoring Point 1 obtained by the reference method and the hybrid method for the fourth test case.</p> Full article ">Figure 19
<p>Comparison of time histories of the pressure at the two monitoring points 1 and 2 obtained by the reference method and the hybrid method for the fourth test case.</p> Full article ">Figure 20
<p>Schematic of the geometry for the lid-driven polar cavity flow. The flow is driven by the moving wall at <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <msub> <mi>R</mi> <mi>i</mi> </msub> </mrow> </semantics></math>, and the polar cavity is defined by <math display="inline"><semantics> <mrow> <msub> <mi>R</mi> <mi>i</mi> </msub> <mo>≤</mo> <mi>r</mi> <mo>≤</mo> <msub> <mi>R</mi> <mi>o</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>−</mo> <mi>α</mi> <mo>/</mo> <mn>2</mn> <mo>≤</mo> <mi>θ</mi> <mo>≤</mo> <mi>α</mi> <mo>/</mo> <mn>2</mn> </mrow> </semantics></math>. The red dashed rectangle indicates the extended computational domain for solving the pressure Poisson equation.</p> Full article ">Figure 21
<p>Comparison of the radial and azimuthal velocity components along four radial lines for the lid-driven polar cavity flow at different Reynolds numbers.</p> Full article ">Figure 21 Cont.
<p>Comparison of the radial and azimuthal velocity components along four radial lines for the lid-driven polar cavity flow at different Reynolds numbers.</p> Full article ">
21 pages, 3991 KiB  
Article
Developing Prediction Model of Travel Times of the Logistics Fleets of Large Convenience Store Chains Using Machine Learning
by Yang-Kuei Lin, Chien-Fu Chen and Tien-Yin Chou
Algorithms 2023, 16(6), 286; https://doi.org/10.3390/a16060286 - 1 Jun 2023
Viewed by 1522
Abstract
Convenience store chains are many people’s top choice for dining and leisure and have logistics procedures that involve each store receiving multiple deliveries because of the varying delivery periods and suitable temperatures for different goods. The estimated arrival time for each delivery has [...] Read more.
Convenience store chains are many people’s top choice for dining and leisure and have logistics procedures that involve each store receiving multiple deliveries because of the varying delivery periods and suitable temperatures for different goods. The estimated arrival time for each delivery has a huge impact on the route arrangement and convenience store preparation for dispatchers to schedule future deliveries. This study collected global positioning system travel data from a fleet of one of the top convenience store chains in Taiwan between April 2021 and March 2022 and proposed machine learning to establish a model to predict travel times. For unavailable data, we proposed the nonlinear regression equation to fill in the missing GPS data. Moreover, the study used the data between April 2022 and September 2022 with mean absolute percentage error to validate the prediction effects exceeding 97%. Therefore, the proposed model based on historical data and the machine learning algorithm in this study can help logistics fleets estimate accurate travel times for their scheduling of future delivery tasks and arranging routes. Full article
(This article belongs to the Special Issue Optimization Algorithms in Logistics, Transportation, and SCM)
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<p>Google Maps’ estimated travel time from the Taichung Industrial Park to Taichung Railway Station for immediate departure (31 min) (Source: Google Maps, accessed on 16 May 2023).</p> Full article ">Figure 2
<p>Google Maps’ estimated travel time from the Taichung Industrial Park to Taichung Railway Station at 08:30 on the next day (20 min to 1 h) (Source: Google Maps, accessed on 16 May 2023).</p> Full article ">Figure 3
<p>Pseudocode of the algorithm.</p> Full article ">Figure 4
<p>Data processing flow.</p> Full article ">Figure 5
<p>Distribution of the travel time records for travel from Kaohsiung Warehouse to Zhutian First Store in period 6 (Time unit: seconds, outliers are marked in red).</p> Full article ">Figure 6
<p>Distribution of the travel time records for travel from Kaohsiung Warehouse to Zhutian First Store in period 7 (Time unit: seconds, outliers are marked in red).</p> Full article ">Figure 7
<p>Distribution of the daily travel time records for travel from Kaohsiung Warehouse to Zhutian First Store (Time unit: seconds, outliers are marked in red).</p> Full article ">Figure 8
<p>Google Maps’ estimated travel time from Kaohsiung Warehouse to Zhutian First Store for departure at 06:30 on the next day (35–55 min) (Source: Google Maps, accessed on 16 May 2023).</p> Full article ">Figure 9
<p>Regression equation.</p> Full article ">Figure 10
<p>Plot of validation result.</p> Full article ">
23 pages, 1093 KiB  
Article
Evolving Dispatching Rules for Dynamic Vehicle Routing with Genetic Programming
by Domagoj Jakobović, Marko Đurasević, Karla Brkić, Juraj Fosin, Tonči Carić and Davor Davidović
Algorithms 2023, 16(6), 285; https://doi.org/10.3390/a16060285 - 1 Jun 2023
Cited by 7 | Viewed by 2041
Abstract
Many real-world applications of the vehicle routing problem (VRP) are arising today, which range from physical resource planning to virtual resource management in the cloud computing domain. A common trait of these applications is usually the large scale size of problem instances, which [...] Read more.
Many real-world applications of the vehicle routing problem (VRP) are arising today, which range from physical resource planning to virtual resource management in the cloud computing domain. A common trait of these applications is usually the large scale size of problem instances, which require fast algorithms to generate solutions of acceptable quality. The basis for many VRP approaches is a heuristic which builds a candidate solution that may subsequently be improved by a local search procedure. Since there are many variants of the basic VRP model, specialised algorithms must be devised that take into account specific constraints and user-defined objective measures. Another factor is that the scheduling process may be carried out in dynamic conditions, where future information may be uncertain or unavailable or may be subject to change. When all of this is considered, there is a need for customised heuristics, devised for a specific problem variant, that could be used in highly dynamic environments. In this paper, we use genetic programming (GP) to evolve a suitable dispatching rule to build solutions for different objectives and classes of VRP problems, applicable in both dynamic and stochastic conditions. The results show great potential, since this method may be used for different problem classes and user-defined performance objectives. Full article
(This article belongs to the Special Issue Algorithms for Natural Computing Models)
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<p>An example GP tree representing a priority function <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>dist</mi> <mo>+</mo> <mi>dist</mi> <mo>)</mo> <mo>∗</mo> <mi>pos</mi> <mo>(</mo> <mi mathvariant="normal">d</mi> <mo>)</mo> </mrow> </semantics></math>.</p> Full article ">Figure 2
<p>Total travelled distance in dynamic CVRP—GP dispatching rules.</p> Full article ">Figure 3
<p>Test results on VRPTW instances with 200 customers.</p> Full article ">Figure 4
<p>Test results on VRPTW instances with different number of customers.</p> Full article ">Figure 5
<p>Total travelled distance in dynamic VRPTW—GP dispatching rules.</p> Full article ">Figure 6
<p>Analysis of stopping criteria—test set performance by number of function evaluations.</p> Full article ">Figure 7
<p>Analysis of learning set size—test set performance.</p> Full article ">
16 pages, 1679 KiB  
Article
Fully Parallel Homological Region Adjacency Graph via Frontier Recognition
by Fernando Díaz-del-Río, Pablo Sanchez-Cuevas, María José Moron-Fernández, Daniel Cascado-Caballero, Helena Molina-Abril and Pedro Real
Algorithms 2023, 16(6), 284; https://doi.org/10.3390/a16060284 - 31 May 2023
Viewed by 1730
Abstract
Relating image contours and regions and their attributes according to connectivity based on incidence or adjacency is a crucial task in numerous applications in the fields of image processing, computer vision and pattern recognition. In this paper, the crucial incidence topological information of [...] Read more.
Relating image contours and regions and their attributes according to connectivity based on incidence or adjacency is a crucial task in numerous applications in the fields of image processing, computer vision and pattern recognition. In this paper, the crucial incidence topological information of 2-dimensional images is extracted in an efficient manner through the computation of a new structure called the HomDuRAG of an image; that is, the dual graph of the HomRAG (a topologically consistent extended version of the classical RAG). These representations are derived from the two traditional self-dual square grids (in which physical pixels play the role of 2-dimensional cells) and encapsulate the whole set of topological features and relations between the three types of objects embedded in a digital image: 2-dimensional (regions), 1-dimensional (contours) and 0-dimensional objects (crosses). Here, a first version of a fully parallel algorithm to compute this new representation is presented, whose timing complexity order (in the worst case and supposing one processing element per 0-cell) is O(log(M×N)) , M and N being the height and width of the image. Efficient implementations of this parallel algorithm would allow images to be processed in real time, as well as permit us to uncover fast algorithms for contour detection and segmentation, opening new perspectives within the image processing field. Full article
(This article belongs to the Collection Parallel and Distributed Computing: Algorithms and Applications)
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<p>(<b>Left</b>): small image representing a double contact between regions K and L and a hole (H). The X region envelops the K and L regions. (<b>Right</b>): the image’s classical <span class="html-italic">RAG</span>.</p> Full article ">Figure 2
<p>(<b>Left</b>): crosses of the image in <a href="#algorithms-16-00284-f001" class="html-fig">Figure 1</a>. (<b>Center</b>): highlighting frontiers with black solid lines. (<b>Right</b>): Complete homological information of the image in <a href="#algorithms-16-00284-f001" class="html-fig">Figure 1</a>. Representative cells are as follows: squares corresponding to four regions (2D); black and white crosses corresponding to seven frontiers (1D); black circles corresponding to four crosses (0D); and, in addition, a pink cross corresponding to the hole of region X, and a white circle corresponding to the hole of the external frontier (which is represented by a white cross).</p> Full article ">Figure 3
<p>(<b>a</b>): Simplified <math display="inline"><semantics> <mrow> <mi>H</mi> <mi>S</mi> <mi>F</mi> </mrow> </semantics></math>. A 2 × 3 image embedded in its <math display="inline"><semantics> <mrow> <mi>A</mi> <mi>C</mi> <mi>C</mi> </mrow> </semantics></math> framework. There are four blue, one red and one green pixels. Circles represent 0-cells comprising three cases: black circles denote crossings between boundaries, gray denotes belonging to a boundary, and voids denote being inside an object neither belonging to a boundary nor crossings. (<b>b</b>): Jump distance matrix. The matrix of jump distances corresponding to the image. Each 0-cell has two distances pointing to its eastern and western neighbors, respectively.</p> Full article ">Figure 4
<p>In order to obtain the jump values of each 0-cell, the 4-adjacent 2-cells are compared, so that a 4-bit code is calculated as shown on the right side of the figure. The left side of the figure shows a table with all possible codes (codes 1, 2, 4 and 8 are not possible) and the calculation of the hopping directions for each 0-cell according to this code. <math display="inline"><semantics> <mrow> <mi>N</mi> <mi>c</mi> <mo>=</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </semantics></math> is the number of columns.</p> Full article ">Figure 5
<p>(<b>Left</b>): homological information representative cells of the image in <a href="#algorithms-16-00284-f001" class="html-fig">Figure 1</a> (uppercase, lowercase letters and numbers are 2-, 1- and 0-cells, respectively). (<b>Center</b>): homological information in the form of adjacencies among crosses and frontier holes expressed as a <span class="html-italic">HomDuRAG</span> graph. (<b>Right</b>): homological information in the form of adjacencies among regions (including adjacencies for region holes) of the same image, meaning the <span class="html-italic">HomRAG</span>.</p> Full article ">Figure 6
<p>Complete pipeline of the algorithm to compute the <span class="html-italic">HomDuRAG</span>. The detailed description of the whole process is depicted in Algorithm 1.</p> Full article ">Figure 7
<p>Three cases showing how the jump distances of each 0-cell increase with each new iteration of the algorithm shown in Algorithm 1. Black circles numbered 1 and 2 represent crosses. Red arrows represent jumps in one direction and blue arrows in the opposite direction. (<b>Left</b>): regular exponential increasing of jump distances. (<b>Center</b>): reaching crosses. (<b>Right</b>): when both jumps go to the same 0-cell, a cycle is detected in a frontier; then, no additional jump increase is required.</p> Full article ">Figure 8
<p>(<b>Left</b>): example values of the image in <a href="#algorithms-16-00284-f001" class="html-fig">Figure 1</a> (K = 2, H = 4, L = 8, X = 9). (<b>Center</b>,<b>Right</b>): initial <math display="inline"><semantics> <mrow> <mi>J</mi> <mi>a</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>J</mi> <mi>b</mi> </mrow> </semantics></math> for the 0-cells of this image (orange cells represent crosses).</p> Full article ">Figure 9
<p>Exponential growth of <math display="inline"><semantics> <mrow> <mi>J</mi> <mi>a</mi> </mrow> </semantics></math> values for the image in <a href="#algorithms-16-00284-f001" class="html-fig">Figure 1</a>. At the end, a new 0-cell representative of the hole is detected and marked in the bottom rightmost element. <math display="inline"><semantics> <mrow> <mi>J</mi> <mi>b</mi> </mrow> </semantics></math> presents values in a similar pattern but in opposite directions. (orange cells represent crosses).</p> Full article ">Figure 10
<p>(<b>Left</b>): Final labels of the frontiers for the image in <a href="#algorithms-16-00284-f001" class="html-fig">Figure 1</a>. Orange cells represent cross/hole representatives; the rest of colored cells correspond to 0-cells inside regions. (<b>Center</b>): Final <span class="html-italic">HomDuRAG</span> expressed as a table for the image in <a href="#algorithms-16-00284-f001" class="html-fig">Figure 1</a>. The first column holds cross addresses. The next four columns hold the adjacencies with other crosses (or with themselves in the case of a hole). The last four columns hold the pixel colors around each cross. (<b>Right</b>): <span class="html-italic">HomDuRAG</span> of this table.</p> Full article ">Figure 11
<p>(<b>a</b>): a <math display="inline"><semantics> <mrow> <mn>13</mn> <mo>×</mo> <mn>13</mn> </mrow> </semantics></math> image containing the longest perimeter zigzag object. (<b>b</b>): <span class="html-italic">M</span> = image width = image length. <span class="html-italic">P</span> = perimeter = <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>(</mo> <mi>M</mi> <mo>−</mo> <mn>1</mn> <mo>)</mo> <mo>×</mo> <mo>(</mo> <mi>M</mi> <mo>−</mo> <mn>2</mn> <mo>)</mo> <mo>)</mo> <mo>+</mo> <mn>4</mn> <mo>×</mo> <mo>(</mo> <mo>(</mo> <mi>M</mi> <mo>−</mo> <mn>1</mn> <mo>)</mo> <mo>/</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mn>2</mn> <mo>(</mo> <mi>P</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> </semantics></math> = theoretical number of iterations to compute jump distances for the 0-cells that represent crosses and cycles. <math display="inline"><semantics> <msub> <mi>n</mi> <mrow> <mi>i</mi> <mi>t</mi> <mi>e</mi> <mi>r</mi> </mrow> </msub> </semantics></math> = number of iterations of Stage 1 of the algorithm.</p> Full article ">
27 pages, 476 KiB  
Article
The Porcupine Measure for Comparing the Performance of Multi-Objective Optimization Algorithms
by Christiaan Scheepers and Andries Engelbrecht
Algorithms 2023, 16(6), 283; https://doi.org/10.3390/a16060283 - 31 May 2023
Cited by 1 | Viewed by 1895
Abstract
In spite of being introduced over twenty-five years ago, Fonseca and Fleming’s attainment surfaces have not been widely used. This article investigates some of the shortcomings that may have led to the lack of adoption of this performance measure. The quantitative measure based [...] Read more.
In spite of being introduced over twenty-five years ago, Fonseca and Fleming’s attainment surfaces have not been widely used. This article investigates some of the shortcomings that may have led to the lack of adoption of this performance measure. The quantitative measure based on attainment surfaces, introduced by Knowles and Corne, is analyzed. The analysis shows that the results obtained by the Knowles and Corne approach are influenced (biased) by the shape of the attainment surface. Improvements to the Knowles and Corne approach for bi-objective Pareto-optimal front (POF) comparisons are proposed. Furthermore, assuming M objective functions, an M-dimensional attainment-surface-based quantitative measure, named the porcupine measure, is proposed for comparing the performance of multi-objective optimization algorithms. A computationally optimized version of the porcupine measure is presented and empirically analyzed. Full article
(This article belongs to the Special Issue Multi-Objective and Multi-Level Optimization: Algorithms and Applications)
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<p>Example Pareto-optimal front and attainment surface. (<b>a</b>) An approximated Pareto-optimal front. (<b>b</b>) Attainment surface.</p> Full article ">Figure 2
<p>Attainment surfaces. (<b>a</b>) Example attainment surfaces with intersection lines. (<b>b</b>) Example attainment surfaces with unequally spread intersection lines. (<b>c</b>) Grand attainment surface.</p> Full article ">Figure 3
<p>Attainment surfaces with rotation-based intersection lines. (<b>a</b>) Concave POF. (<b>b</b>) Convex POF.</p> Full article ">Figure 4
<p>Attainment surfaces with outward/inward intersection lines. (<b>a</b>) Inward. (<b>b</b>) Outward.</p> Full article ">Figure 5
<p>Attainment surface with Manhattan distance calculations.</p> Full article ">Figure 6
<p>Attainment surfaces with unbiased ASSIL. (<b>a</b>) Convex POF. (<b>b</b>) Concave POF.</p> Full article ">Figure 7
<p>Test case Pareto-optimal fronts. Dots represent algorithm <span class="html-italic">A</span>, and triangles represent algorithm <span class="html-italic">B</span>. (<b>a</b>) Case 1. (<b>b</b>) Case 2. (<b>c</b>) Case 3. (<b>d</b>) Case 4. (<b>e</b>) Case 5. (<b>f</b>) Case 6.</p> Full article ">Figure 8
<p>Test case Pareto-optimal front geometries. (<b>a</b>) Concave. (<b>b</b>) Convex. (<b>c</b>) Linear. (<b>d</b>) Mixed. (<b>e</b>) Disconnected.</p> Full article ">Figure 9
<p>Convex POF and attainment surface with WASSILs.</p> Full article ">Figure 10
<p>3-dimensional attainment surface.</p> Full article ">Figure 11
<p>Top, front, and side view of attainment surface with naive subdivisions. (<b>a</b>) Top. (<b>b</b>) Front. (<b>c</b>) Side.</p> Full article ">Figure 12
<p>A 3-dimensional attainment surface with naive subdivisions.</p> Full article ">Figure 13
<p>A 3-dimensional attainment surface with naive subdivisions and intersection vectors.</p> Full article ">Figure 14
<p>A 3-dimensional attainment surface with optimized subdivisions.</p> Full article ">Figure 15
<p>A 3-dimensional attainment surface with optimized subdivisions and intersection vectors.</p> Full article ">
24 pages, 3664 KiB  
Article
Iterative Oblique Decision Trees Deliver Explainable RL Models
by Raphael C. Engelhardt, Marc Oedingen, Moritz Lange, Laurenz Wiskott and Wolfgang Konen
Algorithms 2023, 16(6), 282; https://doi.org/10.3390/a16060282 - 31 May 2023
Cited by 3 | Viewed by 2420
Abstract
The demand for explainable and transparent models increases with the continued success of reinforcement learning. In this article, we explore the potential of generating shallow decision trees (DTs) as simple and transparent surrogate models for opaque deep reinforcement learning (DRL) agents. We investigate [...] Read more.
The demand for explainable and transparent models increases with the continued success of reinforcement learning. In this article, we explore the potential of generating shallow decision trees (DTs) as simple and transparent surrogate models for opaque deep reinforcement learning (DRL) agents. We investigate three algorithms for generating training data for axis-parallel and oblique DTs with the help of DRL agents (“oracles”) and evaluate these methods on classic control problems from OpenAI Gym. The results show that one of our newly developed algorithms, the iterative training, outperforms traditional sampling algorithms, resulting in well-performing DTs that often even surpass the oracle from which they were trained. Even higher dimensional problems can be solved with surprisingly shallow DTs. We discuss the advantages and disadvantages of different sampling methods and insights into the decision-making process made possible by the transparent nature of DTs. Our work contributes to the development of not only powerful but also explainable RL agents and highlights the potential of DTs as a simple and effective alternative to complex DRL models. Full article
(This article belongs to the Special Issue Advancements in Reinforcement Learning Algorithms)
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<p>Flowchart of ITER (Algorithm 1).</p> Full article ">Figure 2
<p>Return <math display="inline"><semantics> <mover> <mi>R</mi> <mo>¯</mo> </mover> </semantics></math> as a function of DT depth <span class="html-italic">d</span> for all environments and all presented algorithms. The <span class="html-italic">solved</span>-threshold is shown as dash-dotted green line, the average oracle performance as dashed orange line, and the DTs performances as solid lines with average and <math display="inline"><semantics> <mrow> <mo>±</mo> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math> of ten repetitions as shaded area. Note: (i) For <span class="html-small-caps">Acrobot</span> we show two plots to include the BB curve. (ii) Good performance in <span class="html-small-caps">CartPole</span> leads to overlapping curves: oracle, BB, and ITER are all constantly at <math display="inline"><semantics> <mrow> <mover> <mi>R</mi> <mo>¯</mo> </mover> <mo>=</mo> <mn>500</mn> </mrow> </semantics></math>.</p> Full article ">Figure 3
<p>Evolution of the training dataset with iterations for OPCT of depth 5 for <span class="html-small-caps">Pendulum</span> (observables mapped back to 2D). The plots show from left to right the observations added to the dataset in each iteration (by the oracle in iteration 0 and by the tree in iterations 1–3).</p> Full article ">Figure 4
<p>Evolution of OPCT performance with iterations. Shown are mean <math display="inline"><semantics> <mrow> <mo>±</mo> <mn>1</mn> <mi>σ</mi> </mrow> </semantics></math> of 10 repetitions. Generally, the return increases notably in the first few iterations. For most environments, a significant improvement after 10 iterations is not observed. (The OPCTs’ depths are chosen according to <a href="#algorithms-16-00282-t002" class="html-table">Table 2</a>a.)</p> Full article ">Figure 5
<p>Decision surfaces for <span class="html-small-caps">MountainCar</span> (MC, discrete actions) and <span class="html-small-caps">MountainCarContinuous</span> (MCC, continuous actions). Column 1 shows the DRL agents. The OPCTs in column 2 (depth 1) and column 3 (depth 2) were trained with algorithm ITER. The number in brackets in each subplot title is the average return <math display="inline"><semantics> <mover> <mi>R</mi> <mo>¯</mo> </mover> </semantics></math>. The black dots represent trajectories of 100 evaluation episodes with same starting conditions across the different agents. They indicate the regions actually visited in the observation space.</p> Full article ">Figure 6
<p>OPCT of depth 1 obtained by ITER solving <span class="html-small-caps">MountainCar</span> with a return of <math display="inline"><semantics> <mrow> <mover> <mi>R</mi> <mo>¯</mo> </mover> <mo>=</mo> <mo>−</mo> <mn>107.47</mn> </mrow> </semantics></math> in 100 evaluation episodes.</p> Full article ">Figure 7
<p>Distance to hyperplanes for <span class="html-small-caps">LunarLander</span>. The diagrams show root node, left child, and right child from top to bottom. Small points: node is “inactive” for this observation (the observation is not routed through this node). Big points: node is “active”.</p> Full article ">Figure 8
<p>Distance plots for <span class="html-small-caps">Pendulum</span>. Three of the diagrams show the distance to the hyperplanes of root node 0, left child node 1, and right child node 2. The lower left plot shows the distance to the equilibrium point <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>0</mn> <mo>)</mo> </mrow> </semantics></math> in observation space. The vertical line at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>64</mn> </mrow> </semantics></math> marks the step where the distance for node 0 approaches zero.</p> Full article ">Figure 9
<p>Distance plot for <span class="html-small-caps">Acrobot</span>. The tree has only one node.</p> Full article ">Figure 10
<p>OPCT sensitivity analysis for <span class="html-small-caps">CartPole</span>: (<b>a</b>) including all weights, (<b>b</b>) with velocity weight <math display="inline"><semantics> <msub> <mi>w</mi> <mi>v</mi> </msub> </semantics></math> set to zero. Parameter <tt>angle</tt> is the most important, <tt>velocity</tt> is least important.</p> Full article ">Figure 11
<p>OPCT sensitivity analysis for <span class="html-small-caps">LunarLander</span>: (<b>a</b>) including all weights, (<b>b</b>) with the weights for the legs set to zero. <math display="inline"><semantics> <msub> <mi>v</mi> <mi>y</mi> </msub> </semantics></math> is most important, the ground-contacts of the legs are least important.</p> Full article ">
13 pages, 305 KiB  
Article
Folding Every Point on a Polygon Boundary to a Point
by Nattawut Phetmak and Jittat Fakcharoenphol
Algorithms 2023, 16(6), 281; https://doi.org/10.3390/a16060281 - 31 May 2023
Viewed by 1661
Abstract
We consider a problem in computational origami. Given a piece of paper as a convex polygon P and a point f located within, we fold every point on a boundary of P to f and compute a region that is safe from folding, [...] Read more.
We consider a problem in computational origami. Given a piece of paper as a convex polygon P and a point f located within, we fold every point on a boundary of P to f and compute a region that is safe from folding, i.e., the region with no creases. This problem is an extended version of a problem by Akitaya, Ballinger, Demaine, Hull, and Schmidt that only folds corners of the polygon. To find the region, we prove structural properties of intersections of parabola-bounded regions and use them to devise a linear-time algorithm. We also prove a structural result regarding the complexity of the safe region as a variable of the location of point f, i.e., the number of arcs of the safe region can be determined using the straight skeleton of the polygon P. Full article
(This article belongs to the Special Issue Machine Learning in Computational Geometry)
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<p>The problem of folding every point on the boundary of a polygon <span class="html-italic">P</span> to a point <span class="html-italic">f</span>. (<b>a</b>) Sample creases from points on edge <math display="inline"><semantics> <mover> <mrow> <msub> <mi>v</mi> <mn>2</mn> </msub> <msub> <mi>v</mi> <mn>3</mn> </msub> </mrow> <mo>¯</mo> </mover> </semantics></math>; (<b>b</b>) The safe region <span class="html-italic">R</span>.</p> Full article ">Figure 2
<p>Comparison of the settings of the problem considered in this paper with that of [<a href="#B4-algorithms-16-00281" class="html-bibr">4</a>]. (<b>a</b>) Corner folding in [<a href="#B4-algorithms-16-00281" class="html-bibr">4</a>]; (<b>b</b>) Boundary folding in our paper.</p> Full article ">Figure 3
<p>Fold-and-unfold points on a line to a fixed point multiple times, creating an envelope of a parabola.</p> Full article ">Figure 4
<p>Interpretation of a parabola as a projection of a conic section. (<b>a</b>) Mapping a tilted parabola to the <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </semantics></math>-plane; (<b>b</b>) Projection of a parabola on the <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>y</mi> </mrow> </semantics></math>-plane; (<b>c</b>) Two cutting planes; (<b>d</b>) Angle bisector and two intersections.</p> Full article ">Figure 5
<p>Arc decomposition of a parabola.</p> Full article ">Figure 6
<p>Three cases of adding parabola <math display="inline"><semantics> <msub> <mi>p</mi> <mi>i</mi> </msub> </semantics></math> to the partial safe region <math display="inline"><semantics> <msub> <mi>R</mi> <mrow> <mi>i</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </semantics></math>. (<b>a</b>) <span class="html-italic">Case 1</span>: <math display="inline"><semantics> <msub> <mi>p</mi> <mi>i</mi> </msub> </semantics></math> does not change the region. (<b>b</b>) <span class="html-italic">Case 2</span>: <math display="inline"><semantics> <msub> <mi>p</mi> <mi>i</mi> </msub> </semantics></math> clips the region. (<b>c</b>) <span class="html-italic">Case 3</span>: <math display="inline"><semantics> <msub> <mi>p</mi> <mi>i</mi> </msub> </semantics></math> eclipses some parabola.</p> Full article ">Figure 7
<p>Proof of Lemma 4.</p> Full article ">Figure 8
<p>Safe regions with 2 and 3 parabola arcs. (<b>a</b>) Safe regions with query points <math display="inline"><semantics> <msub> <mi>f</mi> <mn>2</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>f</mi> <mn>3</mn> </msub> </semantics></math>; (<b>b</b>) An event circle determines the numbers of arcs.</p> Full article ">Figure 9
<p>The straight skeleton of polygon <span class="html-italic">P</span>, with each face colored differently. Points <math display="inline"><semantics> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>c</mi> <mn>6</mn> </msub> </mrow> </semantics></math> are event points.</p> Full article ">Figure 10
<p>Intersections of event circles from the straight skeleton determine <math display="inline"><semantics> <mrow> <mo>|</mo> <mi>A</mi> <mo>(</mo> <msub> <mi>R</mi> <mi>f</mi> </msub> <mo>)</mo> <mo>|</mo> </mrow> </semantics></math>.</p> Full article ">
27 pages, 431 KiB  
Article
Reinforcement Learning in a New Keynesian Model
by Szabolcs Deák, Paul Levine, Joseph Pearlman and Bo Yang
Algorithms 2023, 16(6), 280; https://doi.org/10.3390/a16060280 - 31 May 2023
Cited by 1 | Viewed by 2128
Abstract
We construct a New Keynesian (NK) behavioural macroeconomic model with bounded-rationality (BR) and heterogeneous agents. We solve and simulate the model using a third-order approximation for a given policy and evaluate its properties using this solution. The model is inhabited by fully rational [...] Read more.
We construct a New Keynesian (NK) behavioural macroeconomic model with bounded-rationality (BR) and heterogeneous agents. We solve and simulate the model using a third-order approximation for a given policy and evaluate its properties using this solution. The model is inhabited by fully rational (RE) and BR agents. The latter are anticipated utility learners, given their beliefs of aggregate states, and they use simple heuristic rules to forecast aggregate variables exogenous to their micro-environment. In the most general form of the model, RE and BR agents learn from their forecasting errors by observing and comparing them with each other, making the composition of the two types endogenous. This reinforcement learning is then at the core of the heterogeneous expectations model and leads to the striking result that increasing the volatility of exogenous shocks, by assisting the learning process, increases the proportion of RE agents and is welfare-increasing. Full article
(This article belongs to the Special Issue Advancements in Reinforcement Learning Algorithms)
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<p>RE versus RE-BR composite expectations with <math display="inline"><semantics> <mrow> <msub> <mi>n</mi> <mi>h</mi> </msub> <mo>=</mo> <msub> <mi>n</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>0.25</mn> <mo>,</mo> <mn>1.0</mn> </mrow> </semantics></math>; Taylor rule with <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>π</mi> </msub> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>y</mi> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mrow> <mi>d</mi> <mi>y</mi> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>; monetary policy shock.</p> Full article ">Figure A1
<p>Comparison of stability properties of RE, EL and AU models in <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>ρ</mi> <mi>r</mi> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mi>π</mi> </msub> <mo>)</mo> </mrow> </semantics></math> space; <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mi>r</mi> </msub> <mo>&gt;</mo> <mn>0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; red: determinancy; black: indeterminacy; green: instability. (<b>a</b>) RE: <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>y</mi> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>; (<b>b</b>) EL: <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>y</mi> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>; (<b>c</b>) AU: <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>y</mi> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>.</p> Full article ">Figure A2
<p>Comparisonof stability properties of EL and AU models in <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mi>θ</mi> <mi>y</mi> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mi>π</mi> </msub> <mo>)</mo> </mrow> </semantics></math> space; <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; red: determinancy; black: indeterminacy; green: instability. (<b>a</b>) EL: <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>; (<b>b</b>) AU: <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>.</p> Full article ">Figure A3
<p>RE versus RE-BR composite expectations with <math display="inline"><semantics> <mrow> <msub> <mi>n</mi> <mi>h</mi> </msub> <mo>=</mo> <msub> <mi>n</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>0.25</mn> <mo>,</mo> <mn>1.0</mn> </mrow> </semantics></math>; Taylor rule with <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>π</mi> </msub> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>y</mi> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>; technology shock.</p> Full article ">Figure A4
<p>RE versus RE-BR composite expectations with <math display="inline"><semantics> <mrow> <msub> <mi>n</mi> <mi>h</mi> </msub> <mo>=</mo> <msub> <mi>n</mi> <mi>f</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math>; <math display="inline"><semantics> <mrow> <msub> <mi>λ</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>0.25</mn> <mo>,</mo> <mn>1.0</mn> </mrow> </semantics></math>; Taylor rule with <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mi>r</mi> </msub> <mo>=</mo> <mn>0.7</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>π</mi> </msub> <mo>=</mo> <mn>1.5</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mi>y</mi> </msub> <mo>=</mo> <mn>0.3</mn> </mrow> </semantics></math>; mark-up shock.</p> Full article ">
17 pages, 4102 KiB  
Article
A Shadowed Type-2 Fuzzy Approach for Crossover Parameter Adaptation in Differential Evolution
by Patricia Ochoa, Cinthia Peraza, Oscar Castillo and Zong Woo Geem
Algorithms 2023, 16(6), 279; https://doi.org/10.3390/a16060279 - 31 May 2023
Cited by 2 | Viewed by 1801
Abstract
The shadowed type-2 fuzzy systems are used more frequently today as they provide an alternative to classical fuzzy logic. The primary purpose of fuzzy logic is to simulate reasoning in a computer. This work aims to use shadowed type-2 fuzzy systems (ST2-FS) to [...] Read more.
The shadowed type-2 fuzzy systems are used more frequently today as they provide an alternative to classical fuzzy logic. The primary purpose of fuzzy logic is to simulate reasoning in a computer. This work aims to use shadowed type-2 fuzzy systems (ST2-FS) to dynamically adapt the crossing parameter of differential evolution (DE). To test the performance of the dynamic crossing parameter, the motor position control problem was used, which contains an interval type-2 fuzzy system (IT2-FS) for controlling the motor. A comparison is made between the original DE and the algorithm using shadowed type-2 fuzzy systems (DE-ST2-FS), as well as a comparison with the results of other state-of-the-art metaheuristics. Full article
(This article belongs to the Special Issue Algorithms for PID Controller 2024)
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<p>Illustration of the type-1 and interval type-2 fuzzy sets.</p> Full article ">Figure 2
<p>Illustration of the general type-2 fuzzy set.</p> Full article ">Figure 3
<p>Illustration of the shadowed set.</p> Full article ">Figure 4
<p>Proposal flowchart.</p> Full article ">Figure 5
<p>Shadowed fuzzy system integrated with the DE algorithm (DE-ST2-FS).</p> Full article ">Figure 6
<p>IT2-FLC controller.</p> Full article ">Figure 7
<p>Graphical comparison of experimentation.</p> Full article ">Figure 8
<p>Best result DE-ST2-FS without noise.</p> Full article ">Figure 9
<p>Best result DE-ST2-FS with noise 0.5.</p> Full article ">Figure 10
<p>Best result DE-ST2-FS with noise 0.7.</p> Full article ">Figure 11
<p>Best result DE-ST2-FS with noise 0.9.</p> Full article ">
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