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constrained multiobjective optimization With Escape and Expansion Forces

IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2025年第1期29卷 2-15页

作者： Liu, Zhi-Zhong Wu, Fan Liu, Juan Qin, Yunchuan Li, Kenli Hunan Univ Coll Informat Sci & Elect Engn Changsha 410082 Peoples R China

Constraints may scatter the Pareto optimal solutions of a constrained multiobjective optimization problem (CMOP) into multiple feasible regions. To avoid getting trapped in local optimal feasible regions or a part of the global optimal feasible regions, a constrained multiobjective evolutionary algorithm (CMOEA) should consider both the escape force and the expansion force carefully during the search process. However, most CMOEAs fail to provide these two forces effectively. As a remedy for this limitation, this article proposes a method called three-population evolutionary algorithm (TPEA). TPEA maintains three populations, termed Pop1, Pop2, and Pop3. Pop1 is a regular population, updated with a constrained NSGA-II variant. Pop2 and Pop3 are two auxiliary populations, containing the innermost and outermost nondominated infeasible solutions, respectively. The analysis reveals that these two types of nondominated infeasible solutions can contribute to the generation of escape and expansion forces, respectively. Due to these two forces, TPEA is likely to identify more global optimal feasible regions, which is crucial for constrained multiobjective optimization. Also, a mating selection strategy is developed in TPEA to coordinate the interaction among these three populations. Extensive experiments on 58 benchmark CMOPs and 35 real-world ones demonstrate that TPEA is significantly superior or comparable to six state-of-the-art CMOEAs on most test instances.

关键词： Statistics Sociology Force optimization Linear programming Evolutionary computation Sorting constrained multiobjective optimization escape force expansion force mating selection three population

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An individual adaptive evolution and regional collaboration based evolutionary algorithm for large-scale constrained multiobjective optimization problems

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SWARM AND EVOLUTIONARY COMPUTATION 2025年 95卷

作者： Yu, Kunjie Yang, Zhenyu Liang, Jing Qiao, Kangjia Qu, Boyang Suganthan, Ponnuthurai Nagaratnam Longmen Lab Luoyang 471000 Peoples R China Zhengzhou Univ Sch Elect & Informat Engn Zhengzhou 450001 Peoples R China Henan Inst Technol Sch Elect Engn & Automat Xinxiang 453003 Peoples R China Zhongyuan Univ Technol Sch Elect & Informat Zhengzhou 450007 Peoples R China Qatar Univ Coll Engn KINDI Ctr Comp Res Doha Qatar

Large-scale constrained multiobjective optimization problems (LSCMOPs) refer to constrained multiobjective optimization problems (CMOPs) with large-scale decision variables. When using evolutionary algorithms to solve LSCMOPs, the main challenge lies in balancing feasibility, convergence, and diversity in the high-dimensional search space. However, only a few studies focus on LSCMOPs and most existing related algorithms fail to achieve satisfactory performance. This paper proposes two novel mechanisms (the individual adaptive evolution strategy and the regional collaboration mechanism) to tackle these challenges. The individual adaptive evolution mechanism introduces a dynamic approach to optimize convergence-related and diversity-related variables by allocating computational resources to individuals based on their evolution states. This method effectively balances convergence and diversity in the high-dimensional search space. The regional collaboration mechanism, on the other hand, employs an auxiliary population to explore multiple sub-regions to maintain diversity, guiding the main population towards the constrained Pareto front. By combining these two mechanisms within a two-stage algorithm framework, a new algorithm IAERCEA is proposed. IAERCEA and nine other state-of-the-art algorithms are evaluated on several benchmark suites and three dynamic economic emissions dispatch problems. The results show that IAERCEA has better or competitive performance.

关键词： constrained multiobjective optimization Large-scale variables Individual adaptive evolution Regional collaboration

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Deep reinforcement learning-guided coevolutionary algorithm for constrained multiobjective optimization

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INFORMATION SCIENCES 2025年 692卷

作者： Luo, Wenguan Yu, Xiaobing Yen, Gary G. Wei, Yifan Nanjing Univ Informat Sci & Technol Sch Management Sci & Engn Nanjing Peoples R China Natl Univ Def Technol Coll Syst Engn Changsha Peoples R China Oklahoma State Univ Sch Elect & Comp Engn Stillwater OK 74078 USA

Effectively managing convergence, diversity, and feasibility constitutes a fundamental trinity of tasks in optimizing constrained multiobjective optimization problems (CMOPs). Nevertheless, contemporary constrained multiobjective evolutionary algorithms (CMOEAs) frequently encounter challenges in reconciling these imperatives simultaneously. Drawing inspiration from overwhelming success in artificial intelligence, we propose a deep reinforcement learning-guided coevolutionary algorithm (DRLCEA) to tackle this predicament. DRLCEA employs two populations to optimize the original and unconstrained versions of the CMOP, respectively and then fosters cooperation between them according to the guidance of DRL. The established DRL employs two evaluation metrics to appraise population convergence, diversity, and feasibility, thus remarkably proficient in reflecting and steering the coevolution. Therefore, the proposed DRLCEA could effectively locate the feasible regions and approximate the constrained Pareto front. We assess the proposed algorithm on 32 benchmark CMOPs and one real-world UAV emergency track planning (UETP) application. Experimental results undoubtedly demonstrate the superiority and robustness of the proposed DRLCEA.

关键词： constrained multiobjective optimization Evolutionary algorithm Deep reinforcement learning Coevolutionary algorithm UAV path planning

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Decoupling Constraint: Task Clone-Based Multitasking optimization for constrained multiobjective optimization

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2025年第2期29卷 404-417页

作者： Li, Genghui Wang, Zhenkun Gao, Weifeng Wang, Ling Shenzhen Univ Coll Comp Sci & Software Engn Shenzhen 518060 Peoples R China Southern Univ Sci & Technol Sch Syst Design & Intelligent Mfg Shenzhen 518055 Peoples R China Southern Univ Sci & Technol Dept Comp Sci & Engn Shenzhen 518055 Peoples R China Xidian Univ Sch Math & Stat Xian 710126 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

The coupling of multiple constraints can pose difficulties in solving constrained multiobjective optimization problems (CMOPs). Existing constrained multiobjective evolutionary algorithms (CMOEAs) often overlook this issue by considering all constraints together. This article proposes MTOTC, a novel multitasking optimization algorithm that addresses this challenge through a task clone technique. MTOTC clones the target CMOP with q constraints into q+1 copies, resulting in a total of q+2 tasks. Each cloned task is handled using an independent population that considers a unique constraint-handling sequence, effectively decoupling the constraints in q+1 different ways. Additionally, the algorithm incorporates online information sharing between the target task and cloned tasks, enabling the utilization of valuable search history as much as possible. Experimental results on four recently developed complex CMOP benchmark suites and a series of real-world CMOPs demonstrate the superior performance of MTOTC compared to seven state-of-the-art CMOEAs.

关键词： Task analysis optimization Statistics Sociology Evolutionary computation Convergence Cloning constrained multiobjective optimization constraint decoupling information transfer task clone

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A Pareto Front searching algorithm based on reinforcement learning for constrained multiobjective optimization

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INFORMATION SCIENCES 2025年 705卷

作者： Hu, Yuhang Qu, Yuelin Li, Wei Huang, Ying JiangXi Univ Sci & Technol Sch Informat Engn Ganzhou 341000 Peoples R China Gannan Normal Univ Sch Math & Comp Sci Ganzhou 341000 Peoples R China

Constraint multiobjective algorithms are the most widely applied direction in intelligent optimization, with excellent research value. Currently, most multiobjective multi-constraints algorithms are designed based on the relationship between feasible and infeasible solutions, but they ignore the complex associations between constraints. At the same time, the most significant difficulty in constraint problems lies in the irregularity of constrained Pareto front (CPF) and the lack of a powerful strategy for exploration. The paper proposes a Pareto front searching based on reinforcement learning (PFRL) for multi-constraints multiobjective optimization problems. The algorithm employs reinforcement learning to guide the evolution process through interaction with the environment and adaptively learns the shape and characteristics of CPF to cover the structure of CPF effectively. The environment and CPF information gained by reinforcement learning are utilized for CPF translation and extension to deal with various irregular feasible regions. In addition, the paper also designs a constraint priority evaluation mechanism based on the correlation distance (CD) metric to process constraint relationships. It allows the algorithm to effectively cross over Pareto front (PF) of a single constraint that is unrelated to CPF, improving algorithm efficiency. The introduced algorithm implemented the above strategy using only one population. The effectiveness of the introduced algorithm was verified and compared with nine state-of-the-art algorithms and four real-world constrained multiobjective optimization problems (CMOPs). Experimental results show that the algorithm provides a low-resource and efficient method for solving CMOPs.

关键词： constrained multiobjective optimization Reinforcement learning Pareto Front searching Constraint-handling priority

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Promising boundaries explore and resource allocation evolutionary algorithm for constrained multiobjective optimization

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SWARM AND EVOLUTIONARY COMPUTATION 2025年 92卷

作者： Qu, Yuelin Hu, Yuhang Li, Wei Huang, Ying JiangXi Univ Sci & Technol Sch Informat Engn Ganzhou 341000 Peoples R China Gannan Normal Univ Sch Math & Comp Sci Ganzhou 341000 Peoples R China

constrained multiobjective optimization problems (CMOPs) typically present numerous local optima, which can be deceptive. Current constrained multiobjective algorithms (CMOEAs) encounter challenges in maintaining diversity and escaping these local optima because of the single function of the population in the same spacetime. Because they cannot keep exploring diversity and cannot balance their exploration focus. To this end, a dual-stage and dual-population algorithm named BPRRA is proposed in this article. Specifically, BPRRA utilizes new techniques to explore promising boundaries and allocate computing resources. In the first stage, one of the populations evolves to explore one promising boundary by ignoring constraints, and the other population explores another promising boundary by considering constraints. In the second stage, the two populations explore different regions from different promising boundaries using the diversity archiving strategy. Moreover, a novel resource allocation strategy is designed to dynamically allocate limited computational resources based on the ratio of potential offspring. The experiments involve five test suites and nine real-world problems to validate the performance of the proposed method. The results demonstrate that BPRRA has superior performance and can better solve CMOPs.

关键词： constrained multiobjective optimization Constraint handling Evolutionary algorithm Resource allocation technology

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Dual-stage dual-population diversity maintenance for global and local exploration of constrained multiobjective optimization

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 268卷

作者： He, Zhao Liu, Hui Cent South Univ Inst Artificial Intelligence & Robot IAIR Sch Traff & Transportat Engn Key Lab Traff Safety TrackMinist Educ Changsha 410075 Hunan Peoples R China

In the field of constrained multiobjective optimization, some constrained multiobjective optimization problems (CMOPs) have large infeasible regions and discrete small feasible regions. Solutions to these problems are increasingly challenging due to the necessity for the population to traverse extensive infeasible regions while preserving diversity. To address this challenge, this paper introduces a constrained multiobjective evolutionary algorithm with diversity maintenance for global and local exploration, termed DMGLE. Specifically, the global exploration stage aims to converge to an unconstrained Pareto front, and the two populations focus on convergence and diversity without considering any constraints. In this stage, diversity is maintained through a global search operator that integrates an affinity propagation algorithm and a global differential evolutionary algorithm. In the local exploration stage, the two populations focus on feasibility and diversity. A global search operator and a local search operator are employed to sustain diversity and prevent premature convergence. An improved e-constraint handling technique is also introduced to guide populations gradually towards the true constrained Pareto front. Additionally, the exchange of information between the two populations bolsters the diversity of the algorithm. Compared to seven current state-of-the-art multiobjective evolutionary algorithms on three benchmark test suites and 10 real-world CMOPs, the proposed DMGLE achieved superior or highly competitive performance, especially for CMOPs with large infeasible regions and discontinuous small feasible regions.

关键词： Diversity maintenance Affinity propagation constrained multiobjective optimization Evolutionary algorithm

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A two-stage coevolutionary algorithm based on adaptive weights for complex constrained multiobjective optimization

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APPLIED SOFT COMPUTING 2025年 173卷

作者： Li, Guangpeng Li, Li Cai, Guoyong Guilin Univ Elect Technol Guangxi Key Lab Trusted Software Guilin 541004 Peoples R China

In the constrained multiobjective optimization problems (CMOPs), various complex constraints need to be satisfied simultaneously, which further challenges evolutionary algorithms in balancing feasibility, convergence and diversity. Recent advances in evolutionary computation have led to the development of multi-stage and multi-population strategies for handling CMOPs. However, most algorithms have shown poor performance when dealing with problems with low feasible ratio or discontinuous feasible regions. To address this issue, we propose a two-stage coevolutionary algorithm based on adaptive weights (AW-TCEA), aiming to balance convergence, diversity and feasibility to handle CMOPs with complex Pareto fronts (PFs). Specifically, the first stage uses two populations to explore the objective space and feasible regions respectively, one driven by objective information and the other by feasible information. The second stage adopts a set of weight vectors to search for unexplored feasible regions to enhance diversity. In addition, for handling complex constrained PFs, a novel adaptive weight adjustment strategy is proposed to explore ineffective directions and develop potential regions. Experimental comparisons with multiple state-of-the-art algorithms are performed on 50 test problems and 5 real-world problems. The results show that the proposed algorithm exhibits better performance on various CMOPs.

关键词： constrained multiobjective optimization Two-stage coevolutionary algorithm Complex constrained PF Adaptive weight adjustment strategy

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A Tractive Population-Assisted Dual-Population and Two-Phase Evolutionary Algorithm for constrained multiobjective optimization

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2025年第1期29卷 31-45页

作者： Xie, Shumin Li, Kangshun Wang, Wenxiang Wang, Hui Peng, Chaoda Jalil, Hassan South China Agr Univ Coll Math & Informat Guangzhou 510642 Peoples R China Shenzhen Inst Informat Technol Sch Software Engn Shenzhen 518172 Peoples R China

Both dual-population and two-phase strategies are effective for utilizing infeasible solution information and significantly enhancing the ability of algorithms to solve constrained multiobjective optimization problems. However, most existing algorithms tend to underperform when facing problems with complex constraints. To address these issues, a constrained multiobjective evolutionary algorithm named DPTPEA, which combines dual-population and two-phase strategies, is proposed in this article. DPTPEA employs two collaborative populations [the exploitive population (expPop) and the tractive population (tracPop)] and divides the evolutionary process of the tracPop into two phases (Phase 1 and Phase 2). In Phase 1, the tracPop ignores constraints and drags the expPop across the infeasible region by sharing offspring information. In Phase 2, the tracPop adopts the epsilon-constrained method to converge toward the constrained Pareto front and to guide the expPop exploiting different feasible regions. Moreover, a dynamic cooperation strategy, a boundary point direction sampling strategy, and a dynamic environmental selection are proposed to improve the exploration ability of tracPop for solving complex problems. Comprehensive experiments on three popular test suites demonstrate that DPTPEA outperforms seven state-of-the-art algorithms on most test problems.

关键词： Statistics Sociology optimization Evolutionary computation Convergence Classification algorithms Pareto optimization constrained multiobjective optimization dual-population evolutionary algorithm two-phase

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A Bayesian optimization Approach to Algorithm Parameter Tuning in constrained multiobjective optimization 7th

A Bayesian Optimization Approach to Algorithm Parameter Tuni...

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7th International Conference on optimization and Learning

作者： Cork, Jordan N. Filipic, Bogdan Jozef Stefan Inst Jamova Cesta 39 Ljubljana 1000 Slovenia Jozef Stefan Int Postgrad Sch Jamova Cesta 39 Ljubljana 1000 Slovenia

ISBN: (纸本)9783031779404;9783031779411

Algorithm parameter tuning is an often neglected step in the optimization process. This study shows that constrained multiobjective optimization can benefit significantly from tuning, in both the specialized (for an individual problem) and generalized (over a number of problems) parameter setting approaches. Numerical experiments conducted with three multiobjective optimization algorithms on 139 test problems from 13 benchmark suites quantify the algorithm performance improvement on individual problems. Additionally, regarding the generalized approach, alternative default parameter settings are identified. The study also identifies Bayesian optimization as an adequate method for tuning multiobjective evolutionary algorithms with constraint handling. Overall, it is concluded that, given sufficient computational resources to apply to a problem, parameter tuning, using an approach such as Bayesian optimization, should be conducted. If computational resources do not allow such tuning, then the proposed default parameters are applicable.

关键词： constrained multiobjective optimization multiobjective evolutionary algorithms Algorithm parameter tuning Bayesian optimization Benchmark problems

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