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Handling multiobjective optimization Problems With Complex Constraints: A Constraints Grouping-Based Approach

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2025年第6期55卷 3866-3880页

作者： Xu, Biao Zheng, Yiwu Li, Wenji Gao, Xiaozhi Gong, Dunwei He, Jie Fan, Zhun Shantou Univ Dept Elect & Informat Engn Shantou 515063 Peoples R China Wuzhou Univ Guangxi Key Lab Machine Vis & Intelligent Control Wuzhou 543002 Peoples R China Jilin Univ Key Lab Symbol Computat & Knowledge Engn Minist Educ Changchun 130012 Peoples R China Univ Eastern Finland Dept Comp Sci Joensuu 80101 Finland Qingdao Univ Sci & Technol Coll Automat & Elect Engn Qingdao 266100 Peoples R China Univ Elect Sci & Technol China Shenzhen Inst Adv Study Shenzhen 518110 Peoples R China

Real-world production scenarios often involve multiobjective optimization problems with intricate constraints. Although there has been a growing interest in multiobjective problems with complex constraints, such as the vehicle routing problem with time windows, existing multiobjective evolutionary optimization techniques still face significant challenges, particularly when addressing the fragmented and narrow feasible regions that arise from these constraints. Our research introduces a refined framework tailored for complex constrained multiobjective evolutionary optimization. The methodology conducts an initial strong-weak analysis to categorize constraints and merges each strong constraint with all weak constraints to form subsets. Each subset, combined with the original objective functions, defines a subproblem. Independent optimization of the original problem and subproblems is carried out by utilizing multiple populations. Information acquired from the subproblems' populations is transferred into the population of the original issue, thereby expediting the detection of the feasible region and simplifying the resolution of the original problem. The efficacy of our innovative algorithm, when benchmarked against traditional constrained multiobjective evolutionary algorithms across 72 test functions, has demonstrated superior convergence, diversity, and competitiveness.

关键词： optimization Linear programming Search problems Production Partitioning algorithms Pareto optimization Intelligent control Fans Convergence Vectors Co-evolutionary complex constraints constraints grouping multiobjective optimization

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On the convergence of Newton-type proximal gradient method for multiobjective optimization problems

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optimization METHODS & SOFTWARE 2025年

作者： Chen, J. Jiang, X. X. Tang, L. P. Yang, X. M. Chongqing Normal Univ Natl Ctr Appl Math Chongqing Chongqing 401331 Peoples R China Univ Elect Sci & Technol China Sch Math Sci Chengdu Peoples R China Sichuan Univ Coll Math Chengdu Peoples R China Chongqing Normal Univ Sch Math Sci Chongqing 401331 Peoples R China

Recently, Ansary (Optim. Methods Softw. 38(2023), pp. 570-590) proposed a Newton-type proximal gradient method for nonlinear multiobjective optimization problems (NPGMO). However, the favourable convergence properties typically associated with Newton-type methods for NPGMO were not established in Ansary's work. In response to this gap, we develop a new analytic framework, rooted in an auxiliary inequality, to analyse the convergence behaviour of NPGMO. Specifically, we establish the quadratic termination of NPGMO for problems with strongly convex quadratic smooth terms. Under the assumption of strong convexity, we demonstrate that the NPGMO enjoys superlinear convergence, and quadratic convergence for problems that involve twice continuously differentiable, and twice Lipschitz continuously differentiable smooth terms, respectively. The novel study on the analytic framework simplifies the existing convergence analysis of second-order methods for multiobjective optimization problems.

关键词： multiobjective optimization Newton-type method proximal gradient method convergence

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Multilevel and multiobjective optimization of a Six-Phase SRM with Bezier Curve

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JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY 2025年第1期20卷 281-292页

作者： Sun, Xiaodong Xu, Naixi Ge, Shuaishuai Guo, Dong Wan, Bingkuan Chongqing Univ Technol Int Joint Lab Intelligent Mfg & Control Key Parts Minist Educ Chongqing 400054 Peoples R China Jiangsu Univ Automot Engn Res Inst Zhenjiang 212013 Peoples R China

This paper presents parameter optimization based on multilevel optimization strategy (MOS) and shape optimization based on the Bezier curve for a 12/10 switched reluctance motor (SRM). First, the multiobjective optimization problem, including objectives and constraints, are defined. Then, the finite-element model (FEM) is validated by the experiment and the Kriging model is validated by FEMs to prove the accuracy of this optimization. Second, parameter optimization is conducted based on MOS. The parameters are divided into three subspaces according to the result of comprehensive sensitivity analysis, and each subspace's optimization is performed sequentially. Finally, the shape optimization based on the Bezier curve is conducted when the performance of the investigated motor cannot be improved by parameter optimization. The initial and optimal designs are compared and discussed. From the discussion, it can be found that the performance of the motor can be effectively improved through param-eter optimization and shape optimization.

关键词： multiobjective optimization Parameter optimization Shape optimization Switched reluctance motors (SRMs)

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Gaussian process regression for evolutionary dynamic multiobjective optimization in complex environments

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SWARM AND EVOLUTIONARY COMPUTATION 2025年 94卷

作者： Deng, Youpeng Zheng, Yan Meng, Zhaopeng Gao, Haobo Hua, Yueyang Jin, Qiangguo Cao, Leilei Tianjin Univ Coll Intelligence & Comp 135 Yaguan Rd Tianjin 300350 Peoples R China China Acad Launch Vehicle Technol 9200 Mailbox 1 Sub Box Beijing 100076 Peoples R China Northwestern Polytech Univ Sch Software 127 West Youyi Rd Xian 710072 Shaanxi Peoples R China Zhejiang Univ Innovat Ctr Yangtze River Delta 828 Zhongxing Rd Jiaxing 314100 Zhejiang Peoples R China

multiobjective Evolutionary Algorithms (MOEAs) face significant challenges when addressing dynamic multiobjective optimization problems, particularly those with frequent changes. The complexity of dynamic environments makes it difficult for MOEAs to accurately approximate the true Pareto-optimal solutions before subsequent changes occur. Typically, historical approximations of Pareto-optimal solutions are utilized to predict solutions in future environments. However, existing predictors often overlook the nondeterministic nature of historical solutions, potentially compromising prediction accuracy. In this paper, we propose a novel predictor based on Gaussian Process Regression (GPR) for evolutionary dynamic multiobjective optimization. Unlike traditional deterministic predictors, our approach aims to provide a probability distribution of predicted results, thereby addressing the inherent nondeterminism of historical solutions. We employ GPR to model relationships among historical solutions across different time steps. Within the framework of the classical MOEA, MOEA/D, we introduce a new method MOEA/D-GPR for Evolutionary Dynamic multiobjective optimization (EDMO). Experimental results demonstrate that our method achieves state-of-the-art performance.

关键词： multiobjective optimization Dynamic environments Evolutionary algorithms Nondeterminism Gaussian process regression

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Design and multiobjective optimization of a two-point contact ladder-climbing robot using a genetic algorithm

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JOURNAL OF FIELD ROBOTICS 2025年第1期42卷 219-241页

作者： Shah, Darshita Dave, Jatin Chauhan, Mihir Ukani, Vijay Patel, Suhani Nirma Univ Inst Technol Mech Engn Dept Ahmadabad 382481 Gujarat India Nirma Univ Inst Technol Comp Sci & Engn Dept Ahmadabad Gujarat India

This paper presents the design and optimization of a climbing robot. The design of a ladder-climbing robot is done with fundamental mathematical considerations. The designed robot is robust enough to manage all environmental calamities, and at the same time, it is optimized for lightweight to reduce the actuator's cost and ease of transportation. An analytical evaluation is carried out for both static and dynamic conditions to determine strength and motion characteristics. The multiobjective optimization of the design parameters of a ladder-climbing robot is done to obtain optimized values of design parameters. The formulation of an optimization problem that considers the minimization of weight and natural frequency is performed. Using an evolutionary genetic algorithm (GA) for the multicriteria optimization problem is solved, and a Pareto front solution is obtained. The optimal values of the parameters are decided based on the knee selection technique. As both objective functions are contradictory, the optimum results significantly improve the robot's performance. Controlling the proportional-integral-derivative (PID) parameters is crucial as the robot climbs with a two-point contact gait pattern. The controlling parameters impart stability to the robot. PID parameters like proportional, integral and derivative gain are tunned using the GA. Finally, the developed prototype is tested on the ladders of the tower, and satisfactory climbing motion is achieved.

关键词： climbing mechanism genetic algorithm maintenance multiobjective optimization Pareto front PID robotics stability analysis telecom tower

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Inexact proximal point method with a Bregman regularization for quasiconvex multiobjective optimization problems via limiting subdifferentials

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ANNALS OF OPERATIONS RESEARCH 2025年第1期345卷 417-466页

作者： Upadhyay, Balendu Bhooshan Poddar, Subham Yao, Jen-Chih Zhao, Xiaopeng Indian Inst Technol Patna Dept Math Patna India China Med Univ Ctr Gen Educ Taichung 40447 Taiwan Acad Romanian Scientists Bucharest 50044 Romania Tiangong Univ Sch Math Sci Tianjin 300387 Peoples R China

In this paper, we investigate a class of unconstrained multiobjective optimization problems (abbreviated as, MPQs), where the components of the objective function are locally Lipschitz and quasiconvex. To solve MPQs, we introduce an inexact proximal point method with Bregman distances (abbreviated as, IPPMB) via Mordukhovich limiting subdifferentials. We establish the well-definedness of the sequence generated by the IPPMB algorithm. Based on two versions of error criteria, we introduce two variants of IPPMB, namely, IPPMB1 and IPPMB2. Moreover, we establish that the sequences generated by the IPPMB1 and IPPMB2 algorithms converge to the Pareto-Mordukhovich critical point of the problem MPQ. In addition, we derive that if the components of the objective function of MPQ are convex, then the sequences converge to the weak Pareto efficient solution of MPQ. Furthermore, we discuss the linear and superlinear convergence of the sequence generated by the IPPMB2 algorithm. We furnish several non-trivial numerical examples to demonstrate the effectiveness of the proposed algorithms and solve them by employing MATLAB R2023b. To demonstrate the applicability and significance of the IPPMB algorithm, we solve a nonsmooth large-scale sparse quasiconvex multiobjective optimization by employing MATLAB R2023b.

关键词： multiobjective optimization Mordukhovich subdifferential Generalized convexity Proximal point method Bregman distance Sparse optimization

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multiobjective optimization Control for Nonideal Single-Inductor Dual-Output Buck Converter

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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS 2025年

作者： Yang, Lin Wu, Jiarong Luo, Liping Wu, Weilin Ma, Hailong Guangxi Minzu Univ Coll Elect Informat Nanning 530006 Peoples R China Guangxi Coll & Univ Engn Res Ctr Multimodal Inform Nanning 530006 Peoples R China Hechi Univ Key Lab AI & Informat Proc Hechi 546300 Peoples R China Educ Dept Hechi 546300 Guangxi Zhuang Peoples R China

Single-inductor dual-output (SIDO) buck converter has been widely applied in fields of portable electronic products and smart homes due to their advantages of small size and multiple outputs. However, cross regulation seriously deteriorates the stability of the converter. In addition, parasitic parameters of circuit components reduce the conversion efficiency of the converter and have a significant impact on cross regulation. To suppress the cross regulation and improve the conversion efficiency of the nonideal SIDO buck converter, a multiobjective optimization control strategy is proposed. Considering the parasitic parameters of circuit components, a large signal model of the converter is established, and a predictive equation is constructed based on the model predictive control theory. Furthermore, an objective function for optimizing output error is established based on weighting the output voltage error and inductor current error. Then, a method is proposed to achieve real-time correction of the state variable reference values. The power loss of the system is analyzed and weighted onto the objective function to improve the conversion efficiency. Compared with the common mode voltage-differential mode voltage control method, simulation and experimental results show that the proposed strategy provides smaller cross regulation and better dynamic performance. The conversion efficiency is improved by 6.6%.

关键词： optimization Buck converters Regulation Mathematical models Linear programming Voltage control Inductors Predictive control Sliding mode control Resistors Cross regulation model predictive control (MPC) multiobjective optimization nonideal single-inductor dual-output (SIDO) buck converter

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multiobjective optimization Design of High-Directivity Microstrip Tight-Coupling Directional Coupler With Node-Segment-Type Structure

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MICROWAVE AND OPTICAL TECHNOLOGY LETTERS 2025年第3期67卷

作者： Hu, Gongda He, Yuan Wang, Gang Univ Sci & Technol China Dept Elect Engn & Informat Sci Hefei Peoples R China

In this paper, a novel technique for the design of microstrip tight-coupling directional coupler with node-segment-type structure (NSTS) is proposed. The NSTS is configured by connecting microstrip line segments among free nodes distributed on the print circuit board (PCB). L-shaped line segments characterized by constraint nodes and individual width are proposed for detailed geometry description of NSTS. The optimal NSTS can be acquired by implementing multiobjective optimization search for the optimal distribution of the nodes and the line widths. For demonstration, a 3-dB microstrip directional coupler working at 1.75 GHz is designed with NSTS in a compact size. The measurement indicates that high directivity over 36 dB and amplitude imbalance of < +/- 1 dB in an operation bandwidth of 33% can be obtained.

关键词： high directivity microstrip directional coupler multiobjective optimization node-segment-type structure (NSTS) tight coupling

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On the convergence analysis of a proximal gradient method for multiobjective optimization

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TOP 2025年第1期33卷 102-132页

作者： Zhao, Xiaopeng Ghosh, Debdas Qin, Xiaolong Tammer, Christiane Yao, Jen-Chih Tiangong Univ Sch Math Sci Tianjin 300387 Peoples R China Indian Inst Technol BHU Dept Math Sci Varanasi 221005 Uttar Pradesh India Zhejiang Normal Univ Dept Math Jinhua 321004 Peoples R China Martin Luther Univ Halle Wittenberg Dept Math D-06099 Halle Saale Germany China Med Univ China Med Univ Hosp Res Ctr Interneural Comp Taichung 40447 Taiwan Acad Romanian Scientists Bucharest 50044 Romania

We propose a proximal gradient method for unconstrained nondifferentiable multiobjective optimization problems with the objective function being the sum of a proper lower semicontinuous convex function and a continuously differentiable function. We have shown under appropriate assumptions that each accumulation point of the sequence generated by the algorithm is Pareto stationary. Further, when imposing convexity on the smooth component of the objective function, the convergence of the generated iterative sequence to a weak Pareto optimal point of the problem is established. Meanwhile, the convergence rate of the proposed method is analyzed when the smooth component function in the objective function is non-convex (O(1/k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(\sqrt{1/k})$$\end{document}), convex (O(1/k)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(1/k)$$\end{document}), and strongly convex (O(rk)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {O}(r<^>k)$$\end{document} for some r is an element of(0,1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r\in (0,1)$$\end{document}), respectively, here k is the number of iterations. The performance of the proposed method on a few test problems with an & ell;1\docum

关键词： multiobjective optimization Proximal gradient method Pareto optimality Iteration complexity

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Migrant Resettlement by Evolutionary multiobjective optimization

IEEE Transactions on Artificial Intelligence

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IEEE Transactions on Artificial Intelligence 2025年第1期6卷 51-65页

作者： Liu, Dan-Xuan Gu, Yu-Ran Qian, Chao Mu, Xin Tang, Ke Nanjing University National Key Laboratory for Novel Software Technology School of Artificial Intelligence Nanjing210023 China Peng Cheng Laboratory Shenzhen518000 China Southern University of Science and Technology Department of Computer Science and Engineering Shenzhen518055 China

Migration has been a universal phenomenon, which brings opportunities as well as challenges for global development. As the number of migrants (e.g., refugees) increases rapidly, a key challenge faced by each country is the problem of migrant resettlement. This problem has attracted scientific research attention, from the perspective of maximizing the employment rate. Previous works mainly formulated migrant resettlement as an approximately submodular optimization problem subject to multiple matroid constraints and employed the greedy algorithm, whose performance, however, may be limited due to its greedy nature. In this article, we propose a new framework called migrant resettlement by evolutionary multiobjective optimization (MR-EMO), which reformulates migrant resettlement as a biobjective optimization problem that maximizes the expected number of employed migrants and minimizes the number of dispatched migrants simultaneously, and employs a multiobjective evolutionary algorithm (MOEA) to solve the biobjective problem. We implement MR-EMO using three MOEAs: the popular nondominated sorting genetic algorithm II (NSGA-II), MOEA based on decomposition (MOEA/D) as well as the theoretically grounded global simple evolutionary multiobjective optimizer (GSEMO). To further improve the performance of MR-EMO, we propose a specific MOEA, called GSEMO using matrix-swap mutation and repair mechanism (GSEMO-SR), which has a better ability to search for feasible solutions. We prove that MR-EMO using either GSEMO or GSEMO-SR can achieve better theoretical guarantees than the previous greedy algorithm. Experimental results under the interview and coordination migration models clearly show the superiority of MR-EMO (with either NSGA-II, MOEA/D, GSEMO or GSEMO-SR) over previous algorithms, and that using GSEMO-SR leads to the best performance of MR-EMO. © 2024 IEEE.

关键词： multiobjective optimization

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