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3 pages, 148 KiB

Open AccessEditorial

Special Issue “Optimisation Models and Applications”

by Siamak Pedrammehr and Mohammad Reza Chalak Qazani

Axioms 2024, 13(1), 45; https://doi.org/10.3390/axioms13010045 - 11 Jan 2024

Viewed by 1227

Abstract

Optimisation models have transcended their origins to become indispensable tools across many fields, including engineering, economics, the environment, health, systems of systems, businesses, and beyond [...] Full article

(This article belongs to the Special Issue Optimization Models and Applications)

Research

Jump to: Editorial

14 pages, 292 KiB

Open AccessArticle

On Mond–Weir-Type Robust Duality for a Class of Uncertain Fractional Optimization Problems

by Xiaole Guo

Axioms 2023, 12(11), 1029; https://doi.org/10.3390/axioms12111029 - 2 Nov 2023

Viewed by 982

Abstract

This article is focused on the investigation of Mond–Weir-type robust duality for a class of semi-infinite multi-objective fractional optimization with uncertainty in the constraint functions. We first establish a Mond–Weir-type robust dual problem for this fractional optimization problem. Then, by combining a new [...] Read more.

This article is focused on the investigation of Mond–Weir-type robust duality for a class of semi-infinite multi-objective fractional optimization with uncertainty in the constraint functions. We first establish a Mond–Weir-type robust dual problem for this fractional optimization problem. Then, by combining a new robust-type subdifferential constraint qualification condition and a generalized convex-inclusion assumption, we present robust

ε

-quasi-weak and strong duality properties between this uncertain fractional optimization and its uncertain Mond–Weir-type robust dual problem. Moreover, we also investigate robust

ε

-quasi converse-like duality properties between them. Full article

(This article belongs to the Special Issue Optimization Models and Applications)

21 pages, 25832 KiB

Open AccessArticle

Designing a Secure Mechanism for Image Transferring System Based on Uncertain Fractional Order Chaotic Systems and NLFPID Sliding Mode Controller

by Mohammad Rasouli, Assef Zare, Hassan Yaghoubi and Roohallah Alizadehsani

Axioms 2023, 12(9), 828; https://doi.org/10.3390/axioms12090828 - 28 Aug 2023

Viewed by 931

Abstract

A control method for the robust synchronization of a class of chaotic systems with unknown time delay, unknown uncertainty, and unknown disturbance is presented. The robust controller was designed using a nonlinear fractional order PID sliding surface. The Lyapunov method was used to [...] Read more.

A control method for the robust synchronization of a class of chaotic systems with unknown time delay, unknown uncertainty, and unknown disturbance is presented. The robust controller was designed using a nonlinear fractional order PID sliding surface. The Lyapunov method was used to determine the update laws, prove the stability of the proposed mechanism, and guarantee the convergence of the synchronization errors to zero. The simulation was performed using MATLAB software to evaluate the performance of the proposed mechanism, and the results showed that it was efficient. Finally, the proposed method was combined with a secure communication application to encrypt images, and the results obtained were favorable regarding the standard criteria of correlation, NPCR, PSNR, and information entropy. Full article

(This article belongs to the Special Issue Optimization Models and Applications)

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16 pages, 532 KiB

Open AccessArticle

Robust Multi-Criteria Traffic Network Equilibrium Problems with Path Capacity Constraints

by Xing-Xing Ma and Yang-Dong Xu

Axioms 2023, 12(7), 662; https://doi.org/10.3390/axioms12070662 - 3 Jul 2023

Cited by 1 | Viewed by 1005

Abstract

With the progress of society and the diversification of transportation modes, people are faced with more and more complicated travel choices, and thus, multi-criteria route choosing optimization problems have drawn increased attention in recent years. A number of multi-criteria traffic network equilibrium problems [...] Read more.

With the progress of society and the diversification of transportation modes, people are faced with more and more complicated travel choices, and thus, multi-criteria route choosing optimization problems have drawn increased attention in recent years. A number of multi-criteria traffic network equilibrium problems have been proposed, but most of them do not involve data uncertainty nor computational methods. This paper focuses on the methods for solving robust multi-criteria traffic network equilibrium problems with path capacity constraints. The concepts of the robust vector equilibrium and the robust vector equilibrium with respect to the worst case are introduced, respectively. For the robust vector equilibrium, an equivalent min–max optimization problem is constructed. A direct search algorithm, in which the step size without derivatives and redundant parameters, is proposed for solving this min–max problem. In addition, we construct a smoothing optimization problem based on a variant version of ReLU activation function to compute the robust weak vector equilibrium flows with respect to the worst case and then find robust vector equilibrium flows with respect to the worst case by using the heaviside step function. Finally, extensive numerical examples are given to illustrate the excellence of our algorithms compared with existing algorithms. It is shown that the proposed min–max algorithm may take less time to find the robust vector equilibrium flows and the smoothing method can more effectively generate a subset of the robust vector equilibrium with respect to the worst case. Full article

(This article belongs to the Special Issue Optimization Models and Applications)

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13 pages, 304 KiB

Open AccessArticle

A Nonconstant Gradient Constrained Problem for Nonlinear Monotone Operators

by Sofia Giuffrè

Axioms 2023, 12(6), 605; https://doi.org/10.3390/axioms12060605 - 18 Jun 2023

Viewed by 1106

Abstract

The purpose of the research is the study of a nonconstant gradient constrained problem for nonlinear monotone operators. In particular, we study a stationary variational inequality, defined by a strongly monotone operator, in a convex set of gradient-type constraints. We investigate the relationship [...] Read more.

The purpose of the research is the study of a nonconstant gradient constrained problem for nonlinear monotone operators. In particular, we study a stationary variational inequality, defined by a strongly monotone operator, in a convex set of gradient-type constraints. We investigate the relationship between the nonconstant gradient constrained problem and a suitable double obstacle problem, where the obstacles are the viscosity solutions to a Hamilton–Jacobi equation, and we show the equivalence between the two variational problems. To obtain the equivalence, we prove that a suitable constraint qualification condition, Assumption S, is fulfilled at the solution of the double obstacle problem. It allows us to apply a strong duality theory, holding under Assumption S. Then, we also provide the proof of existence of Lagrange multipliers. The elements in question can be not only functions in

L^{2}

, but also measures. Full article

(This article belongs to the Special Issue Optimization Models and Applications)

27 pages, 1033 KiB

Open AccessArticle

New Class of K-G-Type Symmetric Second Order Vector Optimization Problem

by Chetan Swarup, Ramesh Kumar, Ramu Dubey and Dowlath Fathima

Axioms 2023, 12(6), 571; https://doi.org/10.3390/axioms12060571 - 8 Jun 2023

Viewed by 1015

Abstract

In this paper, we present meanings of K-

G_{f}

-bonvexity/K-

G_{f}

-pseudobonvexity and their generalization between the above-notice functions. We also construct various concrete non-trivial examples for existing these types of functions. We formulate K-

G_{f}

[...] Read more.

In this paper, we present meanings of K-

G_{f}

-bonvexity/K-

G_{f}

-pseudobonvexity and their generalization between the above-notice functions. We also construct various concrete non-trivial examples for existing these types of functions. We formulate K-

G_{f}

-Wolfe type multiobjective second-order symmetric duality model with cone objective as well as cone constraints and duality theorems have been established under these aforesaid conditions. Further, we have validates the weak duality theorem under those assumptions. Our results are more generalized than previous known results in the literature. Full article

(This article belongs to the Special Issue Optimization Models and Applications)

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22 pages, 11952 KiB

Open AccessArticle

Predicting Sit-to-Stand Body Adaptation Using a Simple Model

by Sarra Gismelseed, Amur Al-Yahmedi, Riadh Zaier, Hassen Ouakad and Issam Bahadur

Axioms 2023, 12(6), 559; https://doi.org/10.3390/axioms12060559 - 5 Jun 2023

Viewed by 1302

Abstract

Mathematical models that simulate human motion are used widely due to their potential in predicting basic characteristics of human motion. These models have been involved in investigating various aspects of gait and human-related tasks, especially walking and running. This study uses a simple [...] Read more.

Mathematical models that simulate human motion are used widely due to their potential in predicting basic characteristics of human motion. These models have been involved in investigating various aspects of gait and human-related tasks, especially walking and running. This study uses a simple model to study the impact of different factors on sit-to-stand motion through the formulation of an optimization problem that aims at minimizing joint torques. The simulated results validated experimental results reported in the literature and showed the ability of the model to predict the changes in kinetic and kinematic parameters as adaptation to any change in the speed of motion, reduction in the joint strength, and change in the seat height. The model discovered that changing one of these determinants would affect joint angular displacement, joint torques, joint angular velocities, center of mass position, and ground reaction force. Full article

(This article belongs to the Special Issue Optimization Models and Applications)

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29 pages, 789 KiB

Open AccessArticle

Efficient Method to Solve the Monge–Kantarovich Problem Using Wavelet Analysis

by Juan Rafael Acosta-Portilla, Carlos González-Flores, Raquiel Rufino López-Martínez and Armando Sánchez-Nungaray

Axioms 2023, 12(6), 555; https://doi.org/10.3390/axioms12060555 - 4 Jun 2023

Viewed by 1360

Abstract

In this paper, we present and justify a methodology to solve the Monge–Kantorovich mass transfer problem through Haar multiresolution analysis and wavelet transform with the advantage of requiring a reduced number of operations to carry out. The methodology has the following steps. We [...] Read more.

In this paper, we present and justify a methodology to solve the Monge–Kantorovich mass transfer problem through Haar multiresolution analysis and wavelet transform with the advantage of requiring a reduced number of operations to carry out. The methodology has the following steps. We apply wavelet analysis on a discretization of the cost function level j and obtain four components comprising one corresponding to a low-pass filter plus three from a high-pass filter. We obtain the solution corresponding to the low-pass component in level

j - 1

denoted by

μ_{j - 1}^{*}

, and using the information of the high-pass filter components, we get a solution in level j denoted by

{\hat{μ}}_{j}

. Finally, we make a local refinement of

{\hat{μ}}_{j}

and obtain the final solution

μ_{j}^{σ}

. Full article

(This article belongs to the Special Issue Optimization Models and Applications)

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12 pages, 7662 KiB

Open AccessArticle

A License Plate Recognition System with Robustness against Adverse Environmental Conditions Using Hopfield’s Neural Network

by Saman Rajebi, Siamak Pedrammehr and Reza Mohajerpoor

Axioms 2023, 12(5), 424; https://doi.org/10.3390/axioms12050424 - 26 Apr 2023

Cited by 3 | Viewed by 3339

Abstract

License plates typically have unique color, size, and shape characteristics in each country. This paper presents a general method for character extraction and pattern matching in license plate recognition systems. The proposed method is based on a combination of morphological operations and edge [...] Read more.

License plates typically have unique color, size, and shape characteristics in each country. This paper presents a general method for character extraction and pattern matching in license plate recognition systems. The proposed method is based on a combination of morphological operations and edge detection techniques, along with the bounding box method for identifying and revealing license plate characters while removing unwanted artifacts such as dust and fog. The mathematical model of foggy images is presented and the sum of gradients of the image, which represents the visibility of the image, is improved. Previous works on license plate recognition have utilized non-intelligent pattern matching techniques. The proposed technique can be applied in a variety of settings, including traffic monitoring, parking management, and law enforcement, among others. The applied algorithm, unlike SOTA-based methods, does not need a huge set of training data and is implemented only by applying standard templates. The main advantages of the proposed algorithm are the lack of a need for a training set, the high speed of the training process, the ability to respond to different standards, the high response speed, and higher accuracy compared to similar tasks. Full article

(This article belongs to the Special Issue Optimization Models and Applications)

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19 pages, 12092 KiB

Open AccessArticle

Application of Evolutionary Optimization Techniques in Reverse Engineering of Helical Gears: An Applied Study

by Vahid Pourmostaghimi, Farshad Heidari, Saman Khalilpourazary and Mohammad Reza Chalak Qazani

Axioms 2023, 12(3), 252; https://doi.org/10.3390/axioms12030252 - 1 Mar 2023

Cited by 8 | Viewed by 2412

Abstract

Reverse engineering plays an important role in the manufacturing and automobile industries in designing complicated spare parts, reducing actual production time, and allowing for multiple redesign possibilities, including shape alterations, different materials, and changes to other significant parameters of the component. Using reverse [...] Read more.

Reverse engineering plays an important role in the manufacturing and automobile industries in designing complicated spare parts, reducing actual production time, and allowing for multiple redesign possibilities, including shape alterations, different materials, and changes to other significant parameters of the component. Using reverse engineering methodology, damaged gears can be identified and modeled meticulously. Influential parameters can be obtained in the shortest time. Because most of the time it is impossible to solve gear-related inverse equations mathematically, metaheuristic methods can be used to reverse-engineer gears. This paper presents a methodology based on measurement over balls and span measurement along with evolutionary optimization techniques to determine the geometry of a pure involute of a cylindrical helical gear. Advanced optimization techniques, i.e., Grey Wolf Optimization, Whale Optimization, Particle Swarm Optimization, and Genetic Algorithm, were applied for the considered reverse engineering case, and the effectiveness and accuracy of the proposed algorithms were compared. Confirmatory calculations and experiments reveal the remarkable efficiency of Grey Wolf Optimization and Particle Swarm Optimization techniques in the reverse engineering of helical gears compared to other techniques and in obtaining influential gear design parameters. Full article

(This article belongs to the Special Issue Optimization Models and Applications)

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17 pages, 3624 KiB

Open AccessArticle

The Synchronization of a Class of Time-Delayed Chaotic Systems Using Sliding Mode Control Based on a Fractional-Order Nonlinear PID Sliding Surface and Its Application in Secure Communication

by Mohammad Rasouli, Assef Zare, Majid Hallaji and Roohallah Alizadehsani

Axioms 2022, 11(12), 738; https://doi.org/10.3390/axioms11120738 - 16 Dec 2022

Cited by 6 | Viewed by 1772

Abstract

A novel approach for the synchronization of a class of chaotic systems with uncertainty, unknown time delays, and external disturbances is presented. The control method given here is expressed by combining sliding mode control approaches with adaptive rules. A sliding surface of fractional [...] Read more.

A novel approach for the synchronization of a class of chaotic systems with uncertainty, unknown time delays, and external disturbances is presented. The control method given here is expressed by combining sliding mode control approaches with adaptive rules. A sliding surface of fractional order has been developed to construct the control strategy of the abovementioned sliding mode by employing the structure of nonlinear fractional PID (NLPID) controllers. The suggested control mechanism using Lyapunov’s theorem developed robust adaptive rules in such a way that the estimation error of the system’s unknown parameters and time delays tends to be zero. Furthermore, the proposed robust control approach’s stability has been demonstrated using Lyapunov stability criteria and Lipschitz conditions. Then, in order to assess the performance of the proposed mechanism, the presented control approach was used to simulate the synchronization of two chaotic jerk systems with uncertainty, unknown time delays, and external distortion. The results of the simulation confirm the robust and desirable synchronization performance. Finally, a secure communications mechanism based on the proposed technique is shown as a practical implementation of the introduced control strategy, in which the message signal is disguised in the transmitter with high security and well recovered in the receiver with high quality, according to the mean squared error (MES) criteria. Full article

(This article belongs to the Special Issue Optimization Models and Applications)

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13 pages, 2435 KiB

Open AccessArticle

Analysis and Design of Robust Controller for Polynomial Fractional Differential Systems Using Sum of Squares

by Hassan Yaghoubi, Assef Zare and Roohallah Alizadehsani

Axioms 2022, 11(11), 623; https://doi.org/10.3390/axioms11110623 - 7 Nov 2022

Cited by 1 | Viewed by 1379

Abstract

This paper discusses the robust stability and stabilization of polynomial fractional differential (PFD) systems with a Caputo derivative using the sum of squares. In addition, it presents a novel method of stability and stabilization for PFD systems. It demonstrates the feasibility of designing [...] Read more.

This paper discusses the robust stability and stabilization of polynomial fractional differential (PFD) systems with a Caputo derivative using the sum of squares. In addition, it presents a novel method of stability and stabilization for PFD systems. It demonstrates the feasibility of designing problems that cannot be represented in LMIs (linear matrix inequalities). First, sufficient conditions of stability are expressed for the PFD equation system. Based on the results, the fractional differential system is Mittag–Leffler stable when there is a polynomial function to satisfy the inequality conditions. These functions are obtained from the sum of the square (SOS) approach. The result presents a valuable method to select the Lyapunov function for the stability of PFD systems. Then, robust Mittag–Leffler stability conditions were able to demonstrate better convergence performance compared to asymptotic stabilization and a robust controller design for a PFD equation system with unknown system parameters, and design performance based on a polynomial state feedback controller for PFD-controlled systems. Finally, simulation results indicate the effectiveness of the proposed theorems. Full article

(This article belongs to the Special Issue Optimization Models and Applications)

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Figure 1
The proposed method. Full article ">Figure 2
Phase portrait of <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo> </mo> </mrow> </semantics></math>for PFDE nonlinear system (28). Full article ">Figure 3
Phase portrait of x1(t), x2(t) for PFDE nonlinear system (34). Full article ">Figure 4
Surface h(x) for large range of x1(t), x2(t) and check the condition h(x) > 0 for stability of nonlinear system (34). Full article ">Figure 5
Surface h(x) for small range of x1(t), x2(t) and check the condition h(x) > 0 for stability of nonlinear system (34). Full article ">Figure 6
Phase portrait of x1(t), x2(t) for nonlinear time-variant system (39). Full article ">Figure 7
Surface h(x) for small range of x1(t), x2(t) and check the condition h(x) > 0 for stability of nonlinear time-variant system (31). Full article ">Figure 8
Surface h(x) for small range of x1(t), x2(t) and check the condition h(x) > 0 for stability nonlinear time-variant system (39). Full article ">

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