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13 pages, 3705 KiB  
Article
Multi-Agent Reinforcement Learning-Based Control Method for Pedestrian Guidance Using the Mojiko Fireworks Festival Dataset
by Masato Kiyama, Motoki Amagasaki and Toshiaki Okamoto
Electronics 2025, 14(6), 1062; https://doi.org/10.3390/electronics14061062 - 7 Mar 2025
Viewed by 80
Abstract
With increasing incidents due to congestion at events, effective pedestrian guidance has become a critical safety concern. Recent research has explored the application of reinforcement learning to crowd simulation, where agents learn optimal actions through trial and error to maximize rewards based on [...] Read more.
With increasing incidents due to congestion at events, effective pedestrian guidance has become a critical safety concern. Recent research has explored the application of reinforcement learning to crowd simulation, where agents learn optimal actions through trial and error to maximize rewards based on environmental states. This study investigates the use of reinforcement learning and simulation techniques to mitigate pedestrian congestion through improved guidance systems. We employ the Multi-Agent Deep Deterministic Policy Gradient (MA-DDPG), a multi-agent reinforcement learning approach, and propose an enhanced method for learning the Q-function for actors within the MA-DDPG framework. Using the Mojiko Fireworks Festival dataset as a case study, we evaluated the effectiveness of our proposed method by comparing congestion levels with existing approaches. The results demonstrate that our method successfully reduces congestion, with agents exhibiting superior cooperation in managing crowd flow. This improvement in agent coordination suggests the potential for practical applications in real-world crowd management scenarios. Full article
(This article belongs to the Special Issue AI-Based Pervasive Application Services)
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<p>Relationship between the agent and the simulator. The simulator sends <math display="inline"><semantics> <msup> <mi>S</mi> <mi>t</mi> </msup> </semantics></math> and <math display="inline"><semantics> <msup> <mi>R</mi> <mi>t</mi> </msup> </semantics></math> to the agent. The agent then outputs the guidance and Q-function.</p>
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<p>Diagram of the actor and critic in MA-DDPG. The actor receives local information and outputs actions. The critic receives global information and outputs a Q-function.</p>
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<p>Overview of the decision-making process in MAT. An agent determines its action based on the current observed state and the previously determined actions of other agents.</p>
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<p>Diagram of how MAT functions [<a href="#B21-electronics-14-01062" class="html-bibr">21</a>]. The agent makes a guidance decision with reference to guidance from <math display="inline"><semantics> <msup> <mi>a</mi> <msub> <mi>i</mi> <mn>0</mn> </msub> </msup> </semantics></math> to <math display="inline"><semantics> <msup> <mi>a</mi> <msub> <mi>i</mi> <mi>m</mi> </msub> </msup> </semantics></math>.</p>
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<p>The actor–critic model structure used in our method. This is the same actor–critic structure used in MA-DDPG. However, it differs in that the actor outputs a Q-function for each action.</p>
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<p>Topographic information of Mojiko, Fukuoka Prefecture. Pedestrians take one of three routes to the end point, and guidance is administered at nine locations.</p>
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<p>Classification of LOS. The area is divided into 12 spatial divisions called Sections. The area numbered 1 is referred to as Section 1.</p>
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<p>Roads observed by each agent. Agent 1 is shown as A1.</p>
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25 pages, 2408 KiB  
Article
Enhancing Spatial Ability Assessment: Integrating Problem-Solving Strategies in Object Assembly Tasks Using Multimodal Joint-Hierarchical Cognitive Diagnosis Modeling
by Jujia Li, Kaiwen Man and Joni M. Lakin
J. Intell. 2025, 13(3), 30; https://doi.org/10.3390/jintelligence13030030 - 5 Mar 2025
Viewed by 182
Abstract
We proposed a novel approach to investigate how problem-solving strategies, identified using response time and eye-tracking data, can impact individuals’ performance on the Object Assembly (OA) task. To conduct an integrated assessment of spatial reasoning ability and problem-solving strategy, we applied the Multimodal [...] Read more.
We proposed a novel approach to investigate how problem-solving strategies, identified using response time and eye-tracking data, can impact individuals’ performance on the Object Assembly (OA) task. To conduct an integrated assessment of spatial reasoning ability and problem-solving strategy, we applied the Multimodal Joint-Hierarchical Cognitive Diagnosis Model (MJ-DINA) to analyze the performance of young students (aged 6 to 14) on 17 OA items. The MJ-DINA model consists of three sub-models: a Deterministic Inputs, Noisy “and” Gate (DINA) model for estimating spatial ability, a lognormal RT model for response time, and a Bayesian Negative Binomial (BNF) model for fixation counts. In the DINA model, we estimated five spatial cognitive attributes aligned with problem-solving processes: encoding, falsification, mental rotation, mental displacement, and intractability recognition. Our model fits the data adequately, with Gelman–Rubin convergence statistics near 1.00 and posterior predictive p-values between 0.05 and 0.95 for the DINA, Log RT, and BNF sub-models, indicating reliable parameter estimation. Our findings indicate that individuals with faster processing speeds and fewer fixation counts, which we label Reflective-Scanner, outperformed the other three identified problem-solving strategy groups. Specifically, sufficient eye movement was a key factor contributing to better performance on spatial reasoning tasks. Additionally, the most effective method for improving individuals’ spatial task performance was training them to master the falsification attribute. This research offers valuable implications for developing tailored teaching methods to improve individuals’ spatial ability, depending on various problem-solving strategies. Full article
(This article belongs to the Special Issue Intelligence Testing and Assessment)
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<p>Example of An Object Assembly Item with Test Procedure.</p>
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<p>A graphical structure of Multimodal Joint-Hierarchical DINA (MJ-DINA) Model. In the higher-order DINA model, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>β</mi> </mrow> <mrow> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>δ</mi> </mrow> <mrow> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> are item parameters, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>θ</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> is person n’s latent ability, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>α</mi> </mrow> <mrow> <mi>n</mi> <mi>k</mi> </mrow> </msub> </mrow> </semantics></math> represents attributes, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Y</mi> </mrow> <mrow> <mi>n</mi> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> is accuracy. In the lognormal RT model, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> is the reciprocal of the error standard deviation, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ξ</mi> </mrow> <mrow> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> is time-intensity, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>τ</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> is processing speed, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>T</mi> </mrow> <mrow> <mi>n</mi> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> is response time. In the NBF model, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>m</mi> </mrow> <mrow> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> is visual intensity, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>d</mi> </mrow> <mrow> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> is visual discrimination, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ϵ</mi> </mrow> <mrow> <mi>n</mi> </mrow> </msub> </mrow> </semantics></math> is visual engagement, and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>V</mi> </mrow> <mrow> <mi>n</mi> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math> is fixation count. Means are <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mi>β</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mi>δ</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mi>ξ</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> (item parameters) and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mi>θ</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mi>τ</mi> </mrow> </msub> <mo>,</mo> <msub> <mrow> <mi>μ</mi> </mrow> <mrow> <mi>ε</mi> </mrow> </msub> </mrow> </semantics></math> (person parameters).</p>
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<p>Descriptive Statistics Summary for Response Accuracy, Response Time, and Fixation Counts.</p>
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<p>Posterior predictive <span class="html-italic">p</span>-values for DINA model (RA), Log RT model (LogT), and negative binomial visual fixation counts model (FCs) over 17 items. The dots represent the statistic-based item-level posterior predictive probability (PPP) values.</p>
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<p>Scatter Plot with Latent Ability, Processing Speed, and Visual Engagement. Proceeding Speed <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>τ</mi> <mo>)</mo> </mrow> </semantics></math> is the x-axis; Visual Engagement <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>ε</mi> <mo>)</mo> </mrow> </semantics></math> is the y-axis; Latent Ability <math display="inline"><semantics> <mrow> <mo>(</mo> <mi>θ</mi> <mo>)</mo> </mrow> </semantics></math> is the z-axis.</p>
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<p>Mastery Probability of Attributes across Problem-Solving Strategy Categories.</p>
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<p>Spatial Reasoning Ability Across Different Strategies and Attributes Mastery Patterns. Higher-order latent spatial ability is plotted on the y-axis, with dashed line at <span class="html-italic">y</span> = 0 indicating the median for latent ability. Attribute mastery patterns in the DINA model is on the x-axis. Four columns are problem-solving strategies: Impulsive-Focuser, Impulsive-Scanner, Reflective-Focuser, and Reflective-Scanner. The pattern “11111” is represented by black dots, while all other patterns are shown as grey dots.</p>
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23 pages, 7131 KiB  
Article
Dynamic Path Planning for Vehicles Based on Causal State-Masking Deep Reinforcement Learning
by Xia Hua, Tengteng Zhang and Jun Cao
Algorithms 2025, 18(3), 146; https://doi.org/10.3390/a18030146 - 5 Mar 2025
Viewed by 110
Abstract
Dynamic path planning enables vehicles to autonomously navigate in unknown or continuously changing environments, thereby reducing reliance on fixed maps. Deep reinforcement learning (DRL), with its superior performance in handling high-dimensional state spaces and complex dynamic environments, has been widely applied to dynamic [...] Read more.
Dynamic path planning enables vehicles to autonomously navigate in unknown or continuously changing environments, thereby reducing reliance on fixed maps. Deep reinforcement learning (DRL), with its superior performance in handling high-dimensional state spaces and complex dynamic environments, has been widely applied to dynamic path planning. Traditional DRL methods are prone to capturing unnecessary noise information and irrelevant features during the training process, leading to instability and decreased adaptability of models in complex dynamic environments. To address this challenge, we propose a dynamic path-planning method based on our Causal State-Masking Twin-delayed Deep Deterministic Policy Gradient (CSM-TD3) algorithm. CSM-TD3 integrates a causal inference mechanism by introducing dynamic state masks and intervention mechanisms, allowing the policy network to focus on genuine causal features for decision optimization and thereby enhancing the convergence speed and generalization capabilities of the agent. Furthermore, causal state-masking DRL allows the system to learn the optimal mask configurations through backpropagation, enabling the model to adaptively adjust the causal features of interest. Extensive experimental results demonstrate that this method significantly enhances the convergence of the TD3 algorithm and effectively improves its performance in dynamic path planning. Full article
(This article belongs to the Section Combinatorial Optimization, Graph, and Network Algorithms)
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<p>Vehicle dynamic model and path-planning environment.</p>
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<p>Agent and environment interactions according to the Markov model.</p>
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<p>Causal graph model of the DAG.</p>
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<p>A diagram of the proposed path-planning control framework for vehicles based on CSM-TD3.</p>
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<p>Comparisons of the average return obtained from the DQN, TD3, and the proposed CSM-TD3 when the obstacle is stationary.</p>
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<p>Comparisons of the average return obtained from the DQN, TD3, and the proposed CSM-TD3 when the obstacle is moving.</p>
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<p>Comparison of the path-planning diagrams of the DQN, TD3, and the proposed GER-TD3 when the obstacle is stationary and the endpoint is <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Comparison of the path-planning diagrams of the DQN, TD3, and the proposed GER-TD3 when the obstacle is stationary and the endpoint is <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mn>4</mn> <mo>,</mo> <mn>3</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Comparison of the path-planning diagrams of the DQN, TD3, and proposed GER-TD3 when the obstacle is stationary and the endpoint is <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>4</mn> <mo>,</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Comparison of the path-planning diagrams of the DQN, TD3, and the proposed GER-TD3 when the obstacle is moving and the endpoint is <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>0</mn> <mo>,</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Comparison of the path-planning diagrams of the DQN, TD3, and the proposed GER-TD3 when the obstacle is moving and the endpoint is <math display="inline"><semantics> <mrow> <mo>(</mo> <mo>−</mo> <mn>4</mn> <mo>,</mo> <mn>3</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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<p>Comparison of the path-planning diagrams of the DQN, TD3, and the proposed GER-TD3 when the obstacle is moving and the endpoint is <math display="inline"><semantics> <mrow> <mo>(</mo> <mn>4</mn> <mo>,</mo> <mn>4</mn> <mo>)</mo> </mrow> </semantics></math>.</p>
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21 pages, 567 KiB  
Review
Review of Deterministic and AI-Based Methods for Fluid Motion Modelling and Sloshing Analysis
by Grzegorz Filo, Paweł Lempa and Konrad Wisowski
Energies 2025, 18(5), 1263; https://doi.org/10.3390/en18051263 - 4 Mar 2025
Viewed by 179
Abstract
Contemporary fluid motion modelling techniques, including the phenomenon of liquid sloshing in tanks, are increasingly associated with the use of artificial intelligence methods. In addition to the still frequently used traditional analysis methods and techniques, such as FEM, CFD, VOF and FSI, there [...] Read more.
Contemporary fluid motion modelling techniques, including the phenomenon of liquid sloshing in tanks, are increasingly associated with the use of artificial intelligence methods. In addition to the still frequently used traditional analysis methods and techniques, such as FEM, CFD, VOF and FSI, there is an increasing number of publications that use elements of artificial intelligence. Among others, artificial neural networks and deep learning techniques are used here in the field of prediction and approximation, as well as genetic and other multi-agent algorithms for optimization. This article analyses of the current state of research using the above techniques and the possibilities and main directions of their further development. Full article
(This article belongs to the Section B: Energy and Environment)
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<p>Number of publications on liquid sloshing modelling: 1—traditional methods; 2—neural network usage; 3—genetic algorithm applications.</p>
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<p>A diagram of CFD method usage for liquid slosh modelling.</p>
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<p>Diagram representing the CFD method with FSI approach for liquid sloshing simulation.</p>
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<p>Machine learning model diagram for liquid sloshing simulation based on ANNs.</p>
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22 pages, 5335 KiB  
Article
Tuning of PID Controllers Using Reinforcement Learning for Nonlinear System Control
by Gheorghe Bujgoi and Dorin Sendrescu
Processes 2025, 13(3), 735; https://doi.org/10.3390/pr13030735 - 3 Mar 2025
Viewed by 184
Abstract
This paper presents the application of reinforcement learning algorithms in the tuning of PID controllers for the control of some classes of continuous nonlinear systems. Tuning the parameters of the PID controllers is performed with the help of the Twin Delayed Deep Deterministic [...] Read more.
This paper presents the application of reinforcement learning algorithms in the tuning of PID controllers for the control of some classes of continuous nonlinear systems. Tuning the parameters of the PID controllers is performed with the help of the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm, which presents a series of advantages compared to other similar methods from machine learning dedicated to continuous state and action spaces. The TD3 algorithm is an off-policy actor–critic-based method and is used as it does not require a system model. Double Q-learning, delayed policy updates and target policy smoothing make TD3 robust against overestimation, increase its stability, and improve its exploration. These enhancements make TD3 one of the state-of-the-art algorithms for continuous control tasks. The presented technique is applied for the control of a biotechnological system that has strongly nonlinear dynamics. The proposed tuning method is compared to the classical tuning methods of PID controllers. The performance of the tuning method based on the TD3 algorithm is demonstrated through a simulation, illustrating the effectiveness of the proposed methodology. Full article
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<p>General scheme of reinforcement learning.</p>
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<p>Actor and critic networks.</p>
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<p>General structure of TD3 algorithm.</p>
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<p>Flow of data through the target network to calculate the TD target using the clipped double Q-learning approach.</p>
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<p>Illustration of TD3-based PID tuning approach.</p>
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<p>Matlab/Simulink implementation of bacterial growth bioprocess.</p>
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<p>Matlab/Simulink implementation block diagram of the proposed control system using the RL-TD3 agent.</p>
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<p>Matlab/Simulink implementation of observation vector.</p>
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<p>Matlab/Simulink implementation of reward function.</p>
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<p>Training of TD3 neural networks.</p>
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<p>Step response of biotechnological system (RL approach).</p>
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<p>Time evolution of command signal and biomass concentration (RL approach).</p>
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<p>Tuning the controller using the PID Tuner app.</p>
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<p>Step response of system output (PID Tuner app).</p>
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<p>Time evolution of command signal and biomass concentration (PID Tuner app).</p>
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24 pages, 5942 KiB  
Article
Nonstationary Stochastic Responses of Transmission Tower-Line System with Viscoelastic Material Dampers Under Seismic Excitations
by Mingjing Chang, Bo Chen, Xiang Xiao and Yanzhou Chen
Materials 2025, 18(5), 1138; https://doi.org/10.3390/ma18051138 - 3 Mar 2025
Viewed by 197
Abstract
The excessive vibration or collapse of a transmission tower-line (TTL) system under seismic excitation can result in significant losses. Viscoelastic material dampers (VMDs) have been recognized as an effective method for structural vibration mitigation. Most existing studies have focused solely on the dynamic [...] Read more.
The excessive vibration or collapse of a transmission tower-line (TTL) system under seismic excitation can result in significant losses. Viscoelastic material dampers (VMDs) have been recognized as an effective method for structural vibration mitigation. Most existing studies have focused solely on the dynamic analysis of TTL systems with control devices under deterministic seismic excitations. Studies focusing on the nonstationary stochastic control of TTL systems with VMDs have not been reported. To this end, this study proposes a comprehensive analytical framework for the nonstationary stochastic responses of TTL systems with VMDs under stochastic seismic excitations. The analytical model of the TTL system is formulated using the Lagrange equation. The six-parameter model of VMDs and the vibration control method are established. Following this, the pseudo-excitation method (PEM) is applied to compute the stochastic response of the controlled TTL system under nonstationary seismic excitations, and a probabilistic framework for analyzing extreme value responses is developed. A real TTL system in China is selected to verify the validity of the proposed method. The accuracy of the proposed framework is validated based on the Monte Carlo method (MCM). A detailed parametric investigation is conducted to determine the optimal damper installation scheme and examine the effects of the service temperature and site type on stochastic seismic responses. The nonstationary stochastic seismic responses of the TTL system are consistent with those based on MCM, validating the accuracy of the proposed analytical framework. VMDs can effectively suppress the structural dynamic responses, with particularly stable control over displacement. The temperature and site type have a notable influence on the stochastic seismic responses of the TTL system. The research findings provide important references for improving the seismic performance of VMDs in TTL systems. Full article
(This article belongs to the Special Issue From Materials to Applications: High-Performance Steel Structures)
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<p>Model of a transmission line for different horizontal directions: (<b>a</b>) in-plane vibration; (<b>b</b>) out-of-plane vibration.</p>
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<p>Mechanical model of the tower: (<b>a</b>) 3D finite element model; (<b>b</b>) lumped model.</p>
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<p>Analytical model of a TTL system: (<b>a</b>) 3D finite element model; (<b>b</b>) lumped model.</p>
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<p>Six-parameter model of VMD: (<b>a</b>) Kelvin element; (<b>b</b>) two Maxwell elements; (<b>c</b>) six-parameter model.</p>
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<p>Damper installation scheme of the TTL system: (<b>a</b>) location of VMDs; (<b>b</b>) damper installation scheme.</p>
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<p>Control efficacy of different schemes: (<b>a</b>) extreme displacement; (<b>b</b>) extreme displacement; (<b>c</b>) extreme velocity; (<b>d</b>) extreme velocity; (<b>e</b>) extreme acceleration; and (<b>f</b>) extreme acceleration.</p>
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<p>Control efficacy of different schemes: (<b>a</b>) extreme displacement; (<b>b</b>) extreme displacement; (<b>c</b>) extreme velocity; (<b>d</b>) extreme velocity; (<b>e</b>) extreme acceleration; and (<b>f</b>) extreme acceleration.</p>
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<p>Nonstationary stochastic seismic responses of TTL system: (<b>a</b>) displacement RMS; (<b>b</b>) displacement RMS; (<b>c</b>) velocity RMS; (<b>d</b>) velocity RMS; (<b>e</b>) acceleration RMS; (<b>f</b>) acceleration RMS.</p>
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<p>Nonstationary stochastic seismic responses of TTL system: (<b>a</b>) displacement RMS; (<b>b</b>) displacement RMS; (<b>c</b>) velocity RMS; (<b>d</b>) velocity RMS; (<b>e</b>) acceleration RMS; (<b>f</b>) acceleration RMS.</p>
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<p>EPSD of structural responses for in-plane vibration: (<b>a</b>) displacement EPSD (original tower); (<b>b</b>) velocity EPSD (original tower); (<b>c</b>) acceleration EPSD (original tower); (<b>d</b>) displacement EPSD (with control); (<b>e</b>) velocity EPSD (with control); (<b>f</b>) acceleration EPSD (with control).</p>
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<p>EPSD of structural responses for in-plane vibration: (<b>a</b>) displacement EPSD (original tower); (<b>b</b>) velocity EPSD (original tower); (<b>c</b>) acceleration EPSD (original tower); (<b>d</b>) displacement EPSD (with control); (<b>e</b>) velocity EPSD (with control); (<b>f</b>) acceleration EPSD (with control).</p>
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<p>EPSD of structural responses for out-of-plane vibration: (<b>a</b>) displacement EPSD (original tower); (<b>b</b>) velocity EPSD (original tower); (<b>c</b>) acceleration EPSD (original tower); (<b>d</b>) displacement EPSD (with control); (<b>e</b>) velocity EPSD (with control); (<b>f</b>) acceleration EPSD (with control).</p>
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<p>Extreme responses of the tower under different service temperatures: (<b>a</b>) extreme displacement; (<b>b</b>) extreme displacement; (<b>c</b>) extreme velocity; (<b>d</b>) extreme velocity; (<b>e</b>) extreme acceleration; (<b>f</b>) extreme acceleration.</p>
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<p>Extreme responses of the tower under different service temperatures: (<b>a</b>) extreme displacement; (<b>b</b>) extreme displacement; (<b>c</b>) extreme velocity; (<b>d</b>) extreme velocity; (<b>e</b>) extreme acceleration; (<b>f</b>) extreme acceleration.</p>
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<p>Extreme responses of the tower with different site types: (<b>a</b>) extreme displacement; (<b>b</b>) extreme displacement; (<b>c</b>) extreme velocity; (<b>d</b>) extreme velocity; (<b>e</b>) extreme acceleration; (<b>f</b>) extreme acceleration.</p>
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24 pages, 1929 KiB  
Article
Robust Optimization for Cooperative Task Assignment of Heterogeneous Unmanned Aerial Vehicles with Time Window Constraints
by Zhichao Gao, Mingfa Zheng, Haitao Zhong and Yu Mei
Axioms 2025, 14(3), 184; https://doi.org/10.3390/axioms14030184 - 2 Mar 2025
Viewed by 239
Abstract
The cooperative task assignment problem with time windows for heterogeneous multiple unmanned aerial vehicles is an attractive complex combinatorial optimization problem. In reality, unmanned aerial vehicles’ fuel consumption exhibits uncertainty due to environmental factors or operational maneuvers, and accurately determining the probability distributions [...] Read more.
The cooperative task assignment problem with time windows for heterogeneous multiple unmanned aerial vehicles is an attractive complex combinatorial optimization problem. In reality, unmanned aerial vehicles’ fuel consumption exhibits uncertainty due to environmental factors or operational maneuvers, and accurately determining the probability distributions for these uncertainties remains challenging. This paper investigates the heterogeneous multiple unmanned aerial vehicle cooperative task assignment model that incorporates time window constraints under uncertain environments. To model the time window constraints, we employ the big-M method. To address the uncertainty in fuel consumption, we apply an adjustable robust optimization approach combined with duality theory, which allows us to derive the robust equivalent form and transform the model into a deterministic mixed-integer linear programming problem. We conduct a series of numerical experiments to compare the optimization results across different objectives, including maximizing task profit, minimizing total distance, minimizing makespan, and incorporating three different time window constraints. The numerical results demonstrate that the robust optimization-based heterogeneous multiple unmanned aerial vehicle cooperative task assignment model effectively mitigates the impact of parameter uncertainty, while achieving a balanced trade-off between robustness and the optimality of task assignment objectives. Full article
(This article belongs to the Special Issue Mathematical Optimizations and Operations Research)
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<p>(<b>a</b>) The optimal task path with the objective of maximizing task profit. (<b>b</b>) The optimal cooperative assignment scheme with the objective of maximizing task profit. (<b>c</b>) The optimal task path with the objective of minimizing total distance. (<b>d</b>) The optimal task path with the objective of minimizing total distance. (<b>e</b>) The optimal task path with the objective of minimizing makespan. (<b>f</b>) The optimal task path with the objective of minimizing makespan. <b>Notation:</b> In (<b>a</b>,<b>c</b>,<b>e</b>), the orientation of the “yellow aircraft” indicates the direction of the corresponding path.</p>
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<p>(<b>a</b>) The optimal task path under no time window. (<b>b</b>) The optimal cooperative assignment scheme under no time window. (<b>c</b>) The optimal task path under a loose time window. (<b>d</b>) The optimal cooperative assignment scheme under a loose time window. (<b>e</b>) The optimal task path under a tight time window. (<b>f</b>) The optimal cooperative assignment scheme under a tight time window.</p>
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<p>(<b>a</b>) Influence of conservative degree with the objective of maximizing task profit. (<b>b</b>) Influence of conservative degree with the objective of minimizing total distance. (<b>c</b>) Influence of conservative degree with the objective of minimizing makespan.</p>
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<p>(<b>a</b>) Comparison of objective values between robust and non-robust solutions with the objective of maximizing task profit. (<b>b</b>) Comparison of objective values between robust and non-robust solutions with the objective of minimizing total distance. (<b>c</b>) Comparison of objective values between robust and non-robust solutions with the objective of minimizing makespan.</p>
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<p>(<b>a</b>) The sub-optimal task path with the objective of maximizing task profit. (<b>b</b>) The sub-optimal cooperative assignment scheme with the objective of maximizing task profit. (<b>c</b>) The sub-optimal task path with the objective of minimizing total distance. (<b>d</b>) The sub-optimal task path with the objective of minimizing total distance. (<b>e</b>) The sub-optimal task path with the objective of minimizing makespan. (<b>f</b>) The sub-optimal task path with the objective of minimizing makespan.</p>
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<p>(<b>a</b>) Influence of fuel consumption deviation disturbance with the objective of maximizing task profit. (<b>b</b>) Influence of fuel consumption deviation disturbance with the objective of minimizing total distance. (<b>c</b>) Influence of fuel consumption deviation disturbance with the objective of minimizing makespan.</p>
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18 pages, 9803 KiB  
Article
Probabilistic Small-Signal Modeling and Stability Analysis of the DC Distribution System
by Wenlong Liu, Bo Zhang, Zimeng Lu, Yuming Liao and Heng Nian
Energies 2025, 18(5), 1196; https://doi.org/10.3390/en18051196 - 28 Feb 2025
Viewed by 203
Abstract
With the advent of large-scale electronic transportation, the construction of electric vehicle charging stations (EVCSs) has increased. The stochastic characteristic of the charging power of EVCSs leads to a risk of destabilization of the DC distribution network when there is a high degree [...] Read more.
With the advent of large-scale electronic transportation, the construction of electric vehicle charging stations (EVCSs) has increased. The stochastic characteristic of the charging power of EVCSs leads to a risk of destabilization of the DC distribution network when there is a high degree of power electronification. Current deterministic stability analysis methods are too complicated to allow for brief descriptions of the effect of probabilistic characteristics of EVCSs on stability. This paper develops a probabilistic small-signal stability analysis method. Firstly, the probabilistic information of the system is obtained by combining the s-domain nodal impedance matrix based on the point estimation method. Then, the probability function of stability is fitted using the Cornish–Fisher expansion method. Finally, a comparison experiment using Monte Carlo simulation demonstrates that this method performs well in balancing accuracy and computational efficiency. The effects of line parameters and system control parameters on stability are investigated in the framework of probabilistic stability. This will provide a probabilistic perspective on the design of more complex power systems in the future. Full article
(This article belongs to the Section F1: Electrical Power System)
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<p>The typical structure of DC distribution system containing EVCSs.</p>
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<p>Schematic diagram of the DC distribution system containing EVCSs.</p>
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<p>Trend of oscillatory mode in the complex coordinate system.</p>
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<p>Verification of s-domain nodal impedance matrix model.</p>
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<p>Comparison of the PDF of the real part of oscillation modes obtained by the proposed analytical method and Monte Carlo simulation.</p>
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<p>PDFs of real part of oscillation modes for different correlations.</p>
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<p>PDFs of the real part of the oscillation modes for different AC grid-line impedances.</p>
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<p>PDFs of real part of oscillation modes for different DC line impedance.</p>
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<p>PDFs of real part of oscillation modes for different <span class="html-italic">K</span><sub>ii</sub>.</p>
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<p>PDFs of real part of oscillation modes for different <span class="html-italic">K</span><sub>pi</sub>.</p>
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<p>PDFs of real part of oscillation modes for different <span class="html-italic">K</span><sub>iv</sub>.</p>
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<p>PDFs of real part of oscillation modes for different <span class="html-italic">K</span><sub>pv</sub>.</p>
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<p>Circuit diagram of VSC.</p>
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<p>Control diagram of VSC.</p>
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<p>Circuit diagram of EVCS.</p>
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<p>Control diagram of EVCS.</p>
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<p>Sensitivity analysis on different sample sizes in Monte Carlo simulations.</p>
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12 pages, 1640 KiB  
Article
Probabilistic Approach for Best Estimate of Fuel Rod Fracture During Loss-of-Coolant Accident
by Hiroki Tanaka, Takafumi Narukawa and Takashi Takata
J. Nucl. Eng. 2025, 6(1), 6; https://doi.org/10.3390/jne6010006 - 28 Feb 2025
Viewed by 144
Abstract
Nuclear power plant risk assessments rely on conservative deterministic criteria for core-damage determination despite significant advancements in plant response and system analyses. This study proposes a probabilistic approach to determine fuel rod fracture during loss-of-coolant accidents (LOCAs) in light-water reactors, addressing the need [...] Read more.
Nuclear power plant risk assessments rely on conservative deterministic criteria for core-damage determination despite significant advancements in plant response and system analyses. This study proposes a probabilistic approach to determine fuel rod fracture during loss-of-coolant accidents (LOCAs) in light-water reactors, addressing the need for more rational and realistic assessments. The methodology integrates a fuel rod fracture probability estimation model with best-estimate-plus-uncertainty analysis of plant response, utilizing the stress–strength model and Monte Carlo simulations. Both stress and strength distributions are estimated through Bayesian statistical modeling, with numerical integration techniques implemented to enhance accuracy for low-frequency events. The application of this approach to a virtual dataset demonstrated that while conventional deterministic methods indicated definitive rod fracture, our probabilistic analysis revealed a more realistic fracture probability of 15.1%. This significant finding highlights the potential reduction in assessment conservatism. The proposed methodology enables a transition from conservative binary evaluations to more realistic probabilistic assessments of core damage, providing more accurate risk insights for decision-making. Full article
(This article belongs to the Special Issue Probabilistic Safety Assessment and Management of Nuclear Facilities)
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<p>Imbalance between stress-side and strength-side estimations in safety assessments.</p>
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<p>The probability density distribution of ECR was estimated using log-normal distribution. The blue histogram represents the histogram of the original data [<a href="#B5-jne-06-00006" class="html-bibr">5</a>], the black solid line indicates the median, the dark gray shaded region shows the 50% credible interval, and the light gray shaded region represents the 95% credible interval.</p>
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<p>The fracture probability curve is estimated using the log-probit model. The red points represent data obtained from LOCA simulation tests (1 indicates fracture, 0 indicates non-fracture) [<a href="#B3-jne-06-00006" class="html-bibr">3</a>], the black solid line shows the median, the dark gray shaded region represents the 50% credible interval, and the light gray shaded region indicates the 95% credible interval.</p>
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<p>Variability of fracture probability estimated by Monte Carlo simulation. In the box plot, the red line within the box represents the mean, and the black line represents the median. The length of the box indicates the Interquartile Range (IQR), while the whiskers extend to either 1.5 × IQR or the maximum/minimum values. Values outside 1.5 × IQR are plotted as individual points. The violin plot shows the mirrored probability density distribution. The colors represent different numbers of trials: green for 10<sup>3</sup> trials, orange for 10<sup>4</sup> trials, and blue for 10<sup>5</sup> trials.</p>
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33 pages, 2224 KiB  
Article
Enhanced Hybrid Algorithms for Inverse Problem Solutions in Computed Tomography
by Rafał Brociek, Mariusz Pleszczyński, Jakub Miarka and Mateusz Goik
Appl. Syst. Innov. 2025, 8(2), 31; https://doi.org/10.3390/asi8020031 - 28 Feb 2025
Viewed by 144
Abstract
This article presents a method for solving the inverse problem of computed tomography using an incomplete dataset. The problem focuses on reconstructing spatial objects based on the data collected from transmitters and receivers (referred to as projection vectors). The novelty of the proposed [...] Read more.
This article presents a method for solving the inverse problem of computed tomography using an incomplete dataset. The problem focuses on reconstructing spatial objects based on the data collected from transmitters and receivers (referred to as projection vectors). The novelty of the proposed approach lies in combining two types of algorithms, namely heuristic and deterministic. Specifically, Artificial Bee Colony (ABC) and Jellyfish Search (JS) algorithms were utilized and compared as heuristic methods, while the deterministic methods were based on the Hooke–Jeeves (HJ) and Nelder–Mead (NM) approaches. By merging these techniques, a hybrid algorithm was developed, integrating the strengths of both heuristic and deterministic algorithms. The proposed hybrid algorithm proved to be approximately five to six times faster than an approach relying solely on metaheuristics while also providing more accurate results. In the worst-case test, the fitness function value for the hybrid algorithm was approximately 22% lower than that of the purely metaheuristic-based approach. Experimental tests further demonstrated that the hybrid algorithm, whether based on Hooke–Jeeves or Nelder–Mead, was stable and well suited for solving the considered problem. The article includes experimental results that confirm the effectiveness, accuracy, and efficiency of the proposed method. Full article
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<p>ABC algorithm’s block scheme.</p>
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<p>JS algorithm’s block scheme.</p>
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<p>Nelder–Mead algorithm’s block scheme.</p>
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<p>Hooke–Jeeves algorithm’s block scheme.</p>
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<p>Shape of the polygon used in Example 1.</p>
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<p>Comparison of fitness function values using 1 circle for ABC and JS algorithms.</p>
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<p>Recreation of the polygon using 1 circle.</p>
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<p>Comparison of the energy absorption values of the polygon and its respective recreations.</p>
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<p>Comparison of fitness functions values using 2 circles for ABC and JS algorithms.</p>
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<p>Recreation of the polygon using 2 circles.</p>
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<p>Comparison of the energy absorption values of the polygon and its respective recreations.</p>
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<p>Comparison of fitness function values using 3 circles for ABC and JS algorithms.</p>
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<p>Recreation of the polygon using 3 circles.</p>
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<p>Comparison of the energy absorption values of the polygon and its respective recreations.</p>
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<p>Comparison of fitness function values using 4 circles for ABC and JS algorithms.</p>
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<p>Recreation of the polygon using 4 circles.</p>
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<p>Comparison of the energy absorption values of the polygon and its respective recreations.</p>
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<p>Comparison of fitness function values using 5 circles for ABC and JS algorithms.</p>
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<p>Recreation of the polygon using 5 circles.</p>
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<p>Comparison of the energy absorption values of the polygon and its respective recreations.</p>
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<p>Recreation of the polygon by hybrid algorithm using 1 circle.</p>
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<p>Comparison of the energy absorption values of the polygon and its respective recreations.</p>
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<p>Recreation of the polygon by hybrid algorithm using 2 circles.</p>
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<p>Comparison of the energy absorption values of the polygon and its respective recreations.</p>
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<p>Recreation of the polygon by hybrid algorithm using 3 circles.</p>
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<p>Comparison of the energy absorption values of the polygon and its respective recreations.</p>
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<p>Recreation of the polygon by hybrid algorithm using 4 circles.</p>
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<p>Comparison of the energy absorption values of the polygon and its respective recreations.</p>
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<p>Recreation of the polygon by hybrid algorithm using 5 circles.</p>
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<p>Comparison of the energy absorption values of the polygon and its respective recreations.</p>
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<p>Comparison of the fitness function values achieved by the ABC algorithm and the hybrid approach.</p>
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<p>Comparison of the calculation time for the ABC algorithm and the hybrid approach.</p>
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<p>The shapes and arrangement of the polygons in the domain.</p>
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<p>Recreation of the polygons by hybrid algorithm using 1 circle.</p>
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<p>Comparison of the energy absorption values of the polygons and their respective recreations.</p>
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<p>Recreation of the polygons by hybrid algorithm using 2 circles.</p>
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<p>Comparison of the energy absorption values of the polygons and their respective recreations.</p>
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<p>Recreation of the polygons by hybrid algorithm using 3 circles.</p>
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<p>Comparison of the energy absorption values of the polygons and their respective recreations.</p>
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<p>Recreation of the polygons by hybrid algorithm using 4 circles.</p>
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<p>Comparison of the energy absorption values of the polygons and their respective recreations.</p>
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<p>Recreation of the polygons by hybrid algorithm using 5 circles.</p>
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<p>Comparison of the energy absorption values of the polygons and their respective recreations.</p>
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<p>Comparison of the fitness function values achieved by the Nelder–Mead and Hooke–Jeeves hybrid approaches.</p>
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<p>Comparison of the calculation times for Nelder–Mead and Hooke–Jeeves hybrid approaches.</p>
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<p>Recreation of the polygons by the hybrid algorithm using 5 circles (after increasing the number of iterations).</p>
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<p>Comparison of the energy absorption values of the polygons and their recreations (after increasing the number of iterations).</p>
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<p>Comparison of the fitness function values achieved by the Nelder–Mead and Hooke–Jeeves algorithms with the hybrid approaches (after increasing number of iterations).</p>
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<p>Comparison of the calculation times for the Nelder–Mead and Hooke–Jeeves algorithms with the hybrid approaches (after increasing the number of iterations).</p>
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17 pages, 7862 KiB  
Article
Two-Dimensional Simulation on the Critical Diameter of Particles in Asymmetric I-Shaped DLD Arrays
by Jiangbo Wu, Zihan Yan, Yongqing He, Jie Liu and Yao Lv
Micromachines 2025, 16(3), 270; https://doi.org/10.3390/mi16030270 - 27 Feb 2025
Viewed by 194
Abstract
Deterministic lateral displacement (DLD) is a passive particle separation method based on microfluidic technology, with its separation mechanism primarily relying on particle size differences. Therefore, the critical separation size is of great significance in the design of DLD devices. The geometric asymmetry of [...] Read more.
Deterministic lateral displacement (DLD) is a passive particle separation method based on microfluidic technology, with its separation mechanism primarily relying on particle size differences. Therefore, the critical separation size is of great significance in the design of DLD devices. The geometric asymmetry of the pillar array design significantly influences fluid behavior and critical particle size variations. This study first analyzed particle motion characteristics through particle trajectory observation experiments within asymmetric microfluidic chips. Subsequently, a two-dimensional numerical simulation method was employed to investigate the effects of three different ratios of lateral gap size to downstream gap size (Gx:Gy) on particle trajectories and flow field distribution. The results indicate that as Gx:Gy decreases, the upward flow rate gradually reduces, accompanied by changes in the flow field velocity distribution, causing particles to favor displacement mode. This study provides new theoretical foundations for the precise regulation of particle motion behavior and introduces novel insights for optimizing DLD device design. Full article
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<p>Design parameters of the pillar arrays. The lateral gap size (G<sub>x</sub>) and the downstream gap size (G<sub>y</sub>) can have different values. The offset angle of the array is θ, every row is shifted laterally Δλ compared to the previous row.</p>
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<p>Device schematics. (<b>a</b>) The structural design of the device; (<b>b</b>) Schematic layout of rectifier array; (<b>c</b>) Geometric parameters of pillar arrays; (<b>d</b>) Schematic diagram of high-speed camera acquisition position.</p>
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<p>Plot of particle trajectories under 20 μL/min. (<b>a</b>) 1 μm particles in zigzag mode; (<b>b</b>) 3 μm particles in zigzag mode; (<b>c</b>) 3 μm particles in displacement mode; (<b>d</b>) 5 μm particles in displacement mode. (The red boxes indicate the position changes of the tracked particle at different time points).</p>
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<p>Diagram of the trajectory of a particle in one cycle: (<b>a</b>) 1 μm particle; (<b>b</b>) 3 μm particle; (<b>c</b>) 5 μm particle. (The dashed lines represent the trajectory of the particle in the flow field).</p>
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<p>Diagram of particle coordinate and streamline in the array: (<b>a</b>) particle coordinate; (<b>b</b>) streamline.</p>
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<p>Three different array configurations: (<b>a</b>) G<sub>x</sub>:G<sub>y</sub> &gt; 1; (<b>b</b>) G<sub>x</sub>:G<sub>y</sub> = 1; (<b>c</b>) G<sub>x</sub>:G<sub>y</sub> &lt; 1.</p>
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<p>Diagram of Pressure distribution in the array: (<b>a</b>) G<sub>x</sub>:G<sub>y</sub> &gt; 1; (<b>b</b>) G<sub>x</sub>:G<sub>y</sub> = 1; (<b>c</b>) G<sub>x</sub>:G<sub>y</sub> &lt; 1; (<b>d</b>) Differential pressure in three arrays.</p>
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<p>G<sub>x</sub>:G<sub>y</sub> &gt; 1 Array Particle Trajectory Diagram: (<b>a</b>) 1.5 μm; (<b>b</b>) 2 μm; (<b>c</b>) 2.5 μm; (<b>d</b>) 3 μm; (<b>e</b>) 3.5 μm.</p>
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<p>G<sub>x</sub>:G<sub>y</sub> = 1 Array Particle Trajectory Diagram: (<b>a</b>) 1.5 μm; (<b>b</b>) 2 μm; (<b>c</b>) 2.5 μm; (<b>d</b>) 3 μm; (<b>e</b>) 3.5 μm.</p>
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<p>G<sub>x</sub>:G<sub>y</sub> &lt; 1 Array Particle Trajectory Diagram: (<b>a</b>) 1.5 μm; (<b>b</b>) 2 μm; (<b>c</b>) 2.5 μm; (<b>d</b>) 3 μm; (<b>e</b>) 3.5 μm.</p>
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<p>Diagram of particle coordinates in the array: (<b>a</b>) G<sub>x</sub>:G<sub>y</sub> &gt; 1; (<b>b</b>) G<sub>x</sub>:G<sub>y</sub> = 1; (<b>c</b>) G<sub>x</sub>:G<sub>y</sub> &lt; 1.</p>
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<p>2 μm particle motion trajectory diagrams, flow line diagrams, and relative displacement diagrams within three arrays: (<b>a</b>) G<sub>x</sub>:G<sub>y</sub> &gt; 1; (<b>b</b>) G<sub>x</sub>:G<sub>y</sub> = 1; (<b>c</b>) G<sub>x</sub>:G<sub>y</sub> &lt; 1; (<b>d</b>) 2 μm particle relative displacement diagram within three arrays.</p>
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<p>2 μm particle motion trajectory diagrams, flow line diagrams, and relative displacement diagrams within three arrays: (<b>a</b>) G<sub>x</sub>:G<sub>y</sub> &gt; 1; (<b>b</b>) G<sub>x</sub>:G<sub>y</sub> = 1; (<b>c</b>) G<sub>x</sub>:G<sub>y</sub> &lt; 1; (<b>d</b>) 2 μm particle relative displacement diagram within three arrays.</p>
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<p>Diagram of relative displacement and particle velocity within three arrays: (<b>a</b>) Relative displacement; (<b>b</b>) Particle velocity.</p>
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19 pages, 7657 KiB  
Article
Subspace-Based Two-Step Iterative Shrinkage/Thresholding Algorithm for Microwave Tomography Breast Imaging
by Ji Wu, Fan Yang, Jinchuan Zheng, Hung T. Nguyen and Rifai Chai
Sensors 2025, 25(5), 1429; https://doi.org/10.3390/s25051429 - 26 Feb 2025
Viewed by 133
Abstract
Microwave tomography serves as a promising non-invasive technique for breast imaging, yet accurate reconstruction in noisy environments remains challenging. We propose an adaptive subspace-based two-step iterative shrinkage/thresholding (S-TwIST) algorithm that enhances reconstruction accuracy through two key innovations: a singular value decomposition (SVD) approach [...] Read more.
Microwave tomography serves as a promising non-invasive technique for breast imaging, yet accurate reconstruction in noisy environments remains challenging. We propose an adaptive subspace-based two-step iterative shrinkage/thresholding (S-TwIST) algorithm that enhances reconstruction accuracy through two key innovations: a singular value decomposition (SVD) approach for extracting deterministic contrast sources, and an adaptive strategy for optimal singular value selection. Unlike conventional DBIM methods that rely solely on secondary incident fields, S-TwIST incorporates deterministic induced currents to achieve more accurate total field approximation. The algorithm’s performance is validated using both synthetic “Austria” profiles and 45 digital breast phantoms derived from the UWCEM repository. The results demonstrate robust reconstruction capabilities across varying noise levels (0–20 dB SNR), achieving average relative errors of 0.4847% in breast tissue reconstruction without requiring prior noise level knowledge. The algorithm successfully recovers complex tissue structures and density distributions, showing potential for clinical breast imaging applications. Full article
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<p>Two-dimensional configuration of the EM scattering problem. The circular sensors array is located outside the domain of interest <span class="html-italic">D</span>. Tx and Rx represent the transmitter and receiver.</p>
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<p>Flowchart of the proposed adaptive S-TwIST algorithm. The algorithm consists of a forward solver for field calculation, an SVD-based inverse solver for induced current retrieval, adaptive L-value selection (L = 5, 10, 15, and 20), and cost function minimization for optimal solution selection.</p>
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<p>The dielectric distribution of “Austria” profile.</p>
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<p>The dielectric properties of the 2D cross-section from the selected digital breast model (breast ID: 070604PA2).</p>
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<p>Linear relationship of (2), shown by the black dash line, compared to the dielectric properties that correspond to the 25th, 50th, and 75th percentile values of measured dielectric properties. (<b>a</b>) conductivity versus permittivity of adipose tissue. (<b>b</b>) Conductivity versus permittivity of fibroglandular tissue.</p>
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<p>Convergence and relative error curves for different values of L of S-TwIST algorithms when SNR is 10 dB. (<b>a</b>) Pixels relative error. (<b>b</b>) Base 10 logarithm of cost function values.</p>
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<p>Reconstructed results for Austria profile when SNR is 10 dB. (<b>a</b>) L = 0, (<b>b</b>) L = 15, (<b>c</b>) L = 30, and (<b>d</b>) adaptive method.</p>
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<p>Convergence and relative error curves for different values of L of S-TwIST algorithms when SNR is 0 dB. (<b>a</b>) Pixels relative error. (<b>b</b>) Base 10 logarithm of cost function values.</p>
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<p>Reconstructed results for Austria profile when SNR is 0 dB. (<b>a</b>) L = 0, (<b>b</b>) L = 15, (<b>c</b>) L = 30, and (<b>d</b>) adaptive method.</p>
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<p>Reconstructed images for three phantoms using two different algorithms when SNR is 20 dB. (<b>a</b>–<b>c</b>) Reconstructions with original TwIST. (<b>d</b>–<b>f</b>) Reconstructions with S-TwIST. (<b>g</b>–<b>i</b>) Original 2-D images of three breast phantoms (mostly fatty, scattered fibro glandular, and heterogeneously dense from left to right).</p>
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<p>The reconstruction results without prior knowledge of breast boundary: (<b>a</b>) the actual permittivity distribution; (<b>b</b>) the reconstructed result using adaptive S-TwIST algorithm. While the density and location of fibroglandular tissues are well reconstructed, the skin boundary is not clearly defined due to lack of prior information.</p>
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26 pages, 12751 KiB  
Article
A Hybrid Model for Risk-Based Strategic Planning in Open-Pit Mining: Integrating Deterministic, Stochastic, and ISO 31000 Approaches
by Petar Markovic, Dejan Stevanovic, Bozo Kolonja, Dragana Slavkovic and Daniel Krzanovic
Appl. Sci. 2025, 15(5), 2500; https://doi.org/10.3390/app15052500 - 26 Feb 2025
Viewed by 312
Abstract
The strategic planning of open-pit mining projects is highly influenced by geological variability, economic fluctuations, and operational uncertainties. Traditional deterministic optimization models often fail to account for these uncertainties, leading to potentially misleading economic evaluations. This paper proposes a hybrid model that integrates [...] Read more.
The strategic planning of open-pit mining projects is highly influenced by geological variability, economic fluctuations, and operational uncertainties. Traditional deterministic optimization models often fail to account for these uncertainties, leading to potentially misleading economic evaluations. This paper proposes a hybrid model that integrates deterministic and stochastic optimization methods, following the principles of the ISO 31000 risk management framework, to comprehensively quantify uncertainty through key parameters affecting strategic mine planning. Monte Carlo simulations were applied to generate probability distributions of input parameters, including metal prices, mining and processing costs, and ore grade variability, allowing for a more robust financial assessment. The results demonstrate that while the deterministic approach estimates an NPV of USD 130.8 million, the stochastic model yields an average NPV of USD 155.5 million with a standard deviation of USD 76.5 million, highlighting the significant variability in financial outcomes. Risk assessment using Value at Risk (VaR) and Conditional Value at Risk (CVaR) further quantifies potential financial losses, revealing a 3% probability of project unprofitability. The developed methodology provides a structured approach to integrating uncertainty into mine planning, enabling more reliable economic evaluations and improving decision-making in strategic mining operations. Full article
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<p>Paper structure.</p>
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<p>The VaR and CVaR for a 95% confidence level.</p>
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<p>The structure of the methodological approach.</p>
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<p>Block model of the deposit with constrained ore block.</p>
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<p>The spatial position of the railway line and ore body.</p>
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<p>Optimal pit shell with ore block representation—deterministic approach.</p>
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<p>Distributions for key economic indicators of the mining project: (<b>a</b>) NPV; (<b>b</b>) IRR; (<b>c</b>) payback period.</p>
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<p>Cash flow for different scenarios.</p>
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<p>Probability of block extraction—plan view.</p>
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<p>Probability of block extraction—cross-section view.</p>
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<p>Cumulative distribution function of project NPV for various confidence intervals: (<b>a</b>) 90%; (<b>b</b>) 95%; (<b>c</b>) 97%.</p>
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25 pages, 2173 KiB  
Article
Generic Patterns in HIV Transmission Dynamics: Insights from a Phenomenological Risk-Stratified Modeling Approach
by Susanne F. Awad and Diego F. Cuadros
BioMedInformatics 2025, 5(1), 11; https://doi.org/10.3390/biomedinformatics5010011 - 26 Feb 2025
Viewed by 155
Abstract
Background: Understanding the dynamics of HIV transmission in heterogeneous populations is crucial for effective prevention strategies. This study introduces the Risk Modulation Point (RMP), a novel threshold identifying where HIV transmission transitions from unsustainable spread to self-sustaining epidemic dynamics. Methods: Using a deterministic, [...] Read more.
Background: Understanding the dynamics of HIV transmission in heterogeneous populations is crucial for effective prevention strategies. This study introduces the Risk Modulation Point (RMP), a novel threshold identifying where HIV transmission transitions from unsustainable spread to self-sustaining epidemic dynamics. Methods: Using a deterministic, risk-stratified compartmental model, we examined HIV transmission across populations stratified into 100–200 risk groups, each characterized by behavioral heterogeneity modeled through a power-law distribution. The model captures key features of HIV progression, with simulations conducted across high- (~20%), moderate- (~5%), and low (~0.2%)-prevalence regimes. Results: Our findings reveal universal patterns in HIV dynamics. The RMP marks a consistent threshold across scenarios, separating low-risk groups where transmission is minimal from higher-risk groups sustaining the epidemic. Logistic growth in HIV prevalence across risk groups, with sharp transitions near the RMP, was observed universally. The force of infection follows power-law scaling, directly reflecting the level and nature of risk behavior within each group. Importantly, the location of the RMP remains largely invariant to the underlying sexual risk distribution, population resolution, and mixing patterns, making it applicable across both generalized and concentrated epidemics. Conclusion: The RMP framework offers actionable public health insights. It identifies key populations and transition regions for targeted interventions such as antiretroviral therapy and pre-exposure prophylaxis. By tracking shifts in the RMP, it also serves as an early warning indicator for epidemic transitions, guiding resource allocation and monitoring. The focus of the model on intrinsic epidemic dynamics, excluding external interventions, highlights its utility in uncovering fundamental transmission patterns. This study bridges theoretical modeling and practical application, providing a flexible framework for understanding HIV and other stratified epidemics. The findings advance HIV modeling by revealing generic patterns that transcend specific contexts, supporting data-driven public health strategies. Full article
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<p>Force of infection (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Λ</mi> </mrow> <mrow> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math>) and HIV prevalence (<span class="html-italic">y<sub>i</sub></span>) across risk groups under different prevalence regimes. Left panels show the force of infection and right panels show the corresponding HIV prevalence distributions across 100 risk groups, with different curves representing varying heterogeneity parameters (<span class="html-italic">α</span><sub>1</sub> to <span class="html-italic">α</span><sub>5</sub>). Top row: High-prevalence scenario (~20%) showing a strong force of infection (reaching ~450) and prevalence saturation near 1.0 in high-risk groups. Middle row: Moderate-prevalence scenario (~5%) demonstrating an intermediate force of infection (~1.0) and more gradual prevalence increases. Bottom row: Low-prevalence scenario (~0.2%) showing a weak force of infection (~0.025) and concentrated prevalence in highest risk groups. The red vertical lines in the prevalence panels indicate Risk Modulation Points (RMPs) where prevalence transitions from negligible to high levels. Higher <span class="html-italic">α</span> values lead to sharper transitions and more concentrated epidemics in high-risk groups across all prevalence regimes.</p>
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<p>(<b>A</b>) Force of infection (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Λ</mi> </mrow> <mrow> <mi>i</mi> </mrow> </msub> </mrow> </semantics></math>) and (<b>B</b>) HIV prevalence (<span class="html-italic">y<sub>i</sub></span>) across 200 risk groups with high prevalence. Panel A shows the force of infection (Y axis) exhibiting exponential growth with increasing risk group index (X-axis), reaching values up to ~2000 for the highest risk groups. Panel B shows the corresponding HIV prevalence distribution (Y axis) with increasing risk group index (X-axis), with red vertical lines indicating Risk Modulation Points (RMPs). Different curves represent varying heterogeneity parameters (<span class="html-italic">α</span><sub>1</sub> to <span class="html-italic">α</span><sub>5</sub>). Higher <span class="html-italic">α</span> values lead to sharper transitions in prevalence and stronger concentration of force of infection in high-risk groups, while maintaining consistent RMP locations. The doubled resolution (200 vs. 100 risk groups) preserves the core patterns while providing finer granularity in the transition regions.</p>
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<p>(<b>A</b>) RMP locations across prevalence levels and (<b>B</b>) Resolution scaling of transition widths. (<b>A</b>) Shows the observed Risk Modulation Point (RMP) locations shifting systematically as prevalence decreases from 20% (RMP ≈ 20) to 0.2% (RMP ≈ 70), reflecting delayed epidemic transitions at lower prevalence levels. (<b>B</b>) Demonstrates how transition widths (Δ<span class="html-italic"><sub>i</sub></span>) scale with risk group resolution, comparing 100 groups (blue) versus 200 groups (green) across different prevalence regimes. The doubling of resolution leads to proportional increases in transition widths while maintaining the relative patterns across prevalence levels.</p>
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<p>RMP Locations and Transition Widths Across Prevalence Regimes. Comparison of Risk Modulation Point (RMP) locations (left panels) and transition widths (Δ<span class="html-italic"><sub>i</sub></span>, right panels) across high- (20%), medium- (5%), and low (0.2%)-prevalence regimes, stratified by heterogeneity parameter (<span class="html-italic">α</span> = 1,3,5). Left panels: RMP locations shift systematically with prevalence levels. At high prevalence, RMP remains constant at iRMP ≈ 20 regardless of <span class="html-italic">α</span>, while at medium and low prevalence, RMP shifts to higher risk groups, reaching iRMP = 50,55,60 (medium) and iRMP = 70,75,80 (low) for <span class="html-italic">α</span> = 1,3,5, respectively. Right panels: Transition widths (Δ<span class="html-italic"><sub>i</sub></span>) narrow with increasing <span class="html-italic">α</span> and decrease as prevalence increases. High prevalence exhibits consistently narrow transitions (Δ<span class="html-italic"><sub>i</sub></span> = 5 across all <span class="html-italic">α</span>), while at medium prevalence, Δ<span class="html-italic"><sub>i</sub></span> reduces from 25 (<span class="html-italic">α</span> = 1) to 10 (<span class="html-italic">α</span> = 5). At low prevalence, broader transitions (Δ<span class="html-italic"><sub>i</sub></span> = 35,30,25) reflect stronger stratification effects.</p>
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Article
Deep Reinforcement Learning in Non-Markov Market-Making
by Luca Lalor and Anatoliy Swishchuk
Risks 2025, 13(3), 40; https://doi.org/10.3390/risks13030040 - 24 Feb 2025
Viewed by 215
Abstract
We develop a deep reinforcement learning (RL) framework for an optimal market-making (MM) trading problem, specifically focusing on price processes with semi-Markov and Hawkes Jump-Diffusion dynamics. We begin by discussing the basics of RL and the deep RL framework used; we deployed the [...] Read more.
We develop a deep reinforcement learning (RL) framework for an optimal market-making (MM) trading problem, specifically focusing on price processes with semi-Markov and Hawkes Jump-Diffusion dynamics. We begin by discussing the basics of RL and the deep RL framework used; we deployed the state-of-the-art Soft Actor–Critic (SAC) algorithm for the deep learning part. The SAC algorithm is an off-policy entropy maximization algorithm more suitable for tackling complex, high-dimensional problems with continuous state and action spaces, like those in optimal market-making (MM). We introduce the optimal MM problem considered, where we detail all the deterministic and stochastic processes that go into setting up an environment to simulate this strategy. Here, we also provide an in-depth overview of the jump-diffusion pricing dynamics used and our method for dealing with adverse selection within the limit order book, and we highlight the working parts of our optimization problem. Next, we discuss the training and testing results, where we provide visuals of how important deterministic and stochastic processes such as the bid/ask prices, trade executions, inventory, and the reward function evolved. Our study includes an analysis of simulated and real data. We include a discussion on the limitations of these results, which are important points for most diffusion style models in this setting. Full article
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<p>A snapshot of the LOB data on 24 April 2024 for the ES futures contract, which expired in June 2024. The x-axis shows the size of the LOs and the y-axis represents the price.</p>
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<p>A general MDP model portraying the interaction between the agent and its environment (env).</p>
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<p>Training results from the first training episode, excluding adverse fills.</p>
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<p>Training results from the first training episode, including adverse fills.</p>
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<p>Histogram of cumulative rewards over all 1000 training episodes, excluding adverse fills.</p>
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<p>Histogram of cumulative rewards over all 1000 training episodes, including adverse fills.</p>
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<p>Testing results from the last testing episode, excluding adverse fills.</p>
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<p>Testing results from the last testing episode, including adverse fills.</p>
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<p>Histogram of cumulative rewards over all 400 testing episodes, excluding adverse fills.</p>
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<p>Histogram of cumulative rewards over all 400 testing episodes, including adverse fills.</p>
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<p>Training results from the first training episode in ES.</p>
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<p>Histogram of cumulative rewards over all 203 training episodes in ES.</p>
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<p>Testing results from the last testing episode in ES.</p>
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<p>Histogram of cumulative rewards over all 139 testing episodes in ES.</p>
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