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A novel multi-population evolutionary algorithm based on hybrid collaboration for constrained multi-objective optimization

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SWARM AND EVOLUTIONARY COMPUTATION 2024年 87卷

作者： Wang, Qiuzhen Li, Yanhong Hou, Zhanglu Zou, Juan Zheng, Jinhua Xiangtan Univ Sch Comp Sci Key Lab Intelligent Comp & Informat Proc Minist Educ Xiangtan Hunan Peoples R China Xiangtan Univ Sch Cyberspace Sci Xiangtan Hunan Peoples R China Xiangtan Univ Fac Sch Comp Sci Xiangtan 411105 Peoples R China

multi -population -based methods are widely employed for solving constrained multiobjective optimization problems (CMOPs). The population collaboration strategy is a critical part of multi -population algorithms, and different collaboration strategies perform well on different complex CMOPs. However, these single -population collaboration strategies are still challenging to adapt to various CMOPs with different characteristics. To address this issue, we propose a novel tri-population hybrid collaboration evolutionary algorithm called TPHCEA, which includes a constraint -relaxed population (denoted as mainpop ), a constraint -ignored auxiliary population (denoted as auxpop 1 ), and an auxiliary population (denoted as auxpop 2 ) for the original CMOP, to search optimal solutions in the feasible region. Specifically, due to the different complementarities of the two auxiliary populations, mainpop collaborates with auxpop 1 and auxpop 2 in a dynamic choice between strong and weak cooperation. The effectiveness of TP-HCEA is validated through comparative analysis with seven state-of-the-art algorithms in four CMOP benchmark suites and nine real -world problems.

关键词： constrained multi-objective optimization multi-population algorithms Hybrid collaboration Constraint handling

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Adaptive Truncation technique for constrained multi-objective optimization

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KSII TRANSACTIONS ON INTERNET AND INFORMATION SYSTEMS 2019年第11期13卷 5489-5511页

作者： Zhang, Lei Bi, Xiaojun Wang, Yanjiao Yangtze Univ Sch Elect & Informat Jingzhou 434000 Peoples R China Harbin Engn Univ Sch Informat & Commun Engn Harbin 150000 Heilongjiang Peoples R China Northeast Elect Power Univ Sch Informat Engn Jilin 132000 Jilin Peoples R China

The performance of evolutionary algorithms can be seriously weakened when constraints limit the feasible region of the search space. In this paper we present a constrained multi-objective optimization algorithm based on adaptive epsilon-truncation (epsilon-T-CMOA) to further improve distribution and convergence of the obtained solutions. First of all, as a novel constraint handling technique, epsilon-truncation technique keeps an effective balance between feasible solutions and infeasible solutions by permitting some excellent infeasible solutions with good objective value and low constraint violation to take part in the evolution, so diversity is improved, and convergence is also coordinated. Next, an exponential variation is introduced after differential mutation and crossover to boost the local exploitation ability. At last, the improved crowding density method only selects some Pareto solutions and near solutions to join in calculation, thus it can evaluate the distribution more accurately. The comparative results with other state-of-the-art algorithms show that epsilon-T-CMOA is more diverse than the other algorithms and it gains better in terms of convergence in some extent.

关键词： evolutionary computing constrained multi-objective optimization constraint handling diversity maintenance convergence

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Global and local feasible solution search for solving constrained multi-objective optimization

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INFORMATION SCIENCES 2023年 649卷

作者： Huang, Weixiong Zou, Juan Liu, Yuan Yang, Shengxiang Zheng, Jinhua Xiangtan Univ Key Lab Hunan Prov Internet Things & Informat Secu Xiangtan 411105 Peoples R China Xiangtan Univ Key Lab Intelligent Comp & Informat Proc Minist Educ Xiangtan 411105 Peoples R China Xiangtan Univ Sch Comp Sci Xiangtan 411105 Peoples R China Univ Xiangtan Sch Cyberspace Sci Xiangtan 411105 Peoples R China De Montfort Univ Sch Comp Sci & Informat Leicester LE1 9BH England

constrained multi-objective optimization problems (CMOPs) are challenging due to the complexity of feasible regions caused by constraints, especially when facing small feasible ranges, multiple feasible regions, and complex distribution of feasible regions. Existing algorithms struggle to balance population convergence, diversity, and feasibility. This paper proposes a constrained multi-objective evolutionary algorithm framework based on global and local feasible solutions search to address this issue. The proposed framework is divided into three stages, and an adaptive method is proposed to decide when to switch the search state. In the first two stages, the evolution of the population is relatively free and not subject to constraint restrictions. Feasible solutions in the population are saved in the FeasiblePool for environmental selection during these two stages. The FeasiblePool does not affect the evolving population during these stages. In the first stage, the framework uses global search operator to fully explore the decision space and determine the rough range of feasible solutions in the decision space. In the second stage, the framework uses local search operator to enhance the diversity of FeasiblePool within this determined range. In the last stage, the framework reuses these excellent feasible solutions information to guide population evolution while considering constraints. The proposed framework has been compared with four state-of-the-art constrained multi-objective algorithms on four benchmark suites and three real-world applications. The complete experimental results show that the proposed framework has high competitiveness for solving CMOPs.

关键词： constrained multi-objective optimization Evolutionary algorithm Constraint handing technology

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A constrained multi-objective optimization algorithm based on coordinated strategy of archive and weight vectors

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EXPERT SYSTEMS WITH APPLICATIONS 2024年 244卷

作者： Gu, Qinghua Liu, Ruchang Hui, Zegang Wang, Dan Xian Univ Architecture & Technol Sch Management Xian 710055 Shaanxi Peoples R China Xian Univ Architecture & Technol Xian Key Lab Intelligent Ind Percept Calculat & De Xian 710055 Peoples R China Xian Univ Architecture & Technol Sch Resources Engn Xian 710055 Shaanxi Peoples R China James Madison Univ Integrated Sci & Technol Harrisonburg VA 22807 USA

When dealing with constrained multi-objective optimization Problems (CMOPs) and struggling to enhance feasibility, convergence and diversity, the researchers of constrained multi-objective optimization Evolutionary Algorithms (CMOEAs) gravitate toward feasibility or take precedence to preserve well-converged solutions ignoring diversity in the past. To compensate for the defects, the paper proposes CMOEA-MSWA to guide the search of infeasible regions by coordinated strategy of archive and weight vectors. Firstly, the archive carrying the information of population diversity updates the weight vectors. Secondly, the updated weight vectors perpetuate the diversity information to the search of infeasible regions. The circular effects between strategies promote the detection of infeasible solutions with good objectives and exhibit competitive performance in terms of spread and evenness. To testify the versatility the CMOEA-MSWA in enhancing diversity, the comprehensive performance is evaluated firstly and the diversity analysis of the CMOEA-MSWA is carried out on four benchmark suites with 34 test instances, where the number of objectives for some of test problems is scaled from three to five. In comparison with five state-of-the-art CMOEAs, the proposed algorithm yields highly competitive performance in diversity on different types of CMOPs. In addition, the effectiveness of collaboration between archive and weight vectors on handling infeasible solutions is also verified.

关键词： constrained multi-objective optimization Coordinated strategy of archive and weight vectors Diversity maintenance Weight vectors adjustment

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Adaptively Allocating Constraint-Handling Techniques for constrained multi-objective optimization Problems

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INTERNATIONAL JOURNAL OF PATTERN RECOGNITION AND ARTIFICIAL INTELLIGENCE 2021年第8期35卷 2159032-2159032页

作者： Yang, Ning Liu, Hai-Lin Guangdong Univ Technol Sch Automat Guangzhou Peoples R China Guangdong Univ Technol Sch Appl Math Guangzhou Peoples R China

For solving constrained multi-objective optimization problems (CMOPs), an effective constraint-handling technique (CHT) is of great importance. Recently, many CHTs have been proposed for solving CMOPs. However, no single CHT can outperform all kinds of CMOPs. This paper proposes an algorithm, namely, ACHT-M2M, which adaptively allocates the existing CHTs in an M2M framework for solving CMOPs. To be more specific, a CMOP is first decomposed into several constrained multi-objective optimization subproblems by ACHT-M2M. Each subproblem has a subpopulation in a subregion. CHT for each subregion is adaptively allocated according to a proposed composite performance measure. Population for the next generation is selected from subregions by selection operators with different CHTs and the obtained nondominated feasible solutions in each generation are used to update a predefined archive. ACHT-M2M assembles the advantages of different CHTs and makes them cooperate with each other. The proposed ACHT-M2M is finally compared with the other 12 representative algorithms on benchmark CMOPs and the experimental results further confirm the effectiveness of ACHT-M2M for solving CMOPs.

关键词： Adaptive allocation constraint-handling technique constrained multi-objective optimization evolutionary algorithm M2M

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Two-stage differential evolution with dynamic population assignment for constrained multi-objective optimization

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SWARM AND EVOLUTIONARY COMPUTATION 2024年 90卷

作者： Xu, Bin Zhang, Haifeng Tao, Lili Shanghai Univ Engn Sci Sch Mech & Automot Engn Shanghai 201620 Peoples R China Shanghai Polytech Univ Sch Intelligent Mfg & Control Engn Shanghai 201209 Peoples R China

Using infeasible information to balance objective optimization and constraint satisfaction is a very promising research direction to address constrained multi-objective problems (CMOPs) via evolutionary algorithms (EAs). The existing constrained multi-objective evolutionary algorithms (CMOEAs) still face the issue of striking a good balance when solving CMOPs with diverse characteristics. To alleviate this issue, in this paper we develop a two-stage different evolution with a dynamic population assignment strategy for CMOPs. In this approach, two cooperative populations are used to provide feasible driving forces and infeasible guiding knowledge. To adequately utilize the infeasibility information, a dynamic population assignment model is employed to determine the primary population, which is used as the parents to generate offspring. The entire search process is divided into two stages, in which the two populations work in weak and strong cooperative ways, respectively. Furthermore, multistrategy-based differential evolution operators are adopted to create aggressive offspring. The superior exploration and exploitation ability of the proposed algorithm is validated via some state-of-the-art CMOEAs over artificial benchmarks and real-world problems. The experimental results show that our proposed algorithm gained a better, or more competitive, performance than the other competitors, and it is an effective approach to balancing objective optimization and constraint satisfaction.

关键词： constrained multi-objective optimization Differential evolution Infeasible information Two stages Dynamic population assignment multiple strategies

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A tri-population based co-evolutionary framework for constrained multi-objective optimization problems

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SWARM AND EVOLUTIONARY COMPUTATION 2022年第0期70卷 101055-101055页

作者： Ming, Fei Gong, Wenyin Wang, Ling Lu, Chao China Univ Geosci Sch Comp Sci Wuhan 430074 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

Balancing between the optimization of objective functions and constraint satisfaction is essential to handle constrained multi-objective optimization problems (CMOPs). Recently, various methods have been presented to enhance the performance for the constrained multi-objective optimization evolutionary algorithms (CMOEAs). However, most of them encounter difficulties when dealing with the CMOPs with complex feasible regions. To overcome this drawback, this paper proposes a tri-population based co-evolutionary framework (TriP): i) the first and second populations are evolved through a weak co-evolutionary relation for the original and unconstrained problems respectively to handle CMOPs with relatively simple constraints;and ii) the third population is evolved solely for the constraint relaxed problem with constraint relaxation technique. The cooperation of three populations preserve the advantages of weak co-evolution and constraint relaxation. Experiments on six benchmark CMOPs with 65 instances and diverse features are performed. Compared to 9 state-of-the-art CMOEAs, the proposed framework yields highly competitive performance and the best versatility. In addition, the effectiveness of the proposed framework on handling real-world CMOPs is also verified.

关键词： constrained multi-objective optimization Evolutionary algorithm Co-evolution Tri-population

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A dual-population evolutionary algorithm based on adaptive constraint strength for constrained multi-objective optimization

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SWARM AND EVOLUTIONARY COMPUTATION 2023年 77卷

作者： Yang, Kaixi Zheng, Jinhua Zou, Juan Yu, Fan Yang, Shengxiang Xiangtan Univ Engn Res Ctr Intelligent Syst Optimizat & Secur Xiangtan 411105 Hunan Peoples R China Xiangtan Univ Key Lab Intelligent Comp & Informat Proc Minist Educ China Xiangtan 411105 Hunan Peoples R China Xiangtan Univ Key Lab Hunan Prov Internet Things & Informat Secu Xiangtan 411105 Hunan Peoples R China De Montfort Univ Sch Comp Sci & Informat Leicester LE1 9BH England

It is challenging to balance convergence and diversity while fully satisfying feasibility when dealing with constrained multi-objective optimization problems (CMOPs). Overemphasizing the feasibility optimization of constraint satisfaction may lead to the search falling into local optimum, and overemphasizing the objective optimization of ignoring constraints may cause a lot of computational resources to be wasted in searching for infeasible solutions. This paper proposes a dual-population algorithm called dp-ACS, aiming to seek a balance between constraint satisfaction and objective optimization. The algorithm proposes a dominance relation to speed up the algorithm's convergence and an adaptive constraint strength strategy to consider the information of excellent infeasible solutions. Specifically, the former defines a new domination relationship to distinguish the pros and cons of nondominated solutions. The population converges faster by selecting better nondominated solutions into the matching pool. The latter is informed by infeasible solutions with good objective values by maintaining two cooperatively complementary populations (i.e., main Pop and aux Pop). uses an adaptive constraint strength function that optimizes the objective of the original problem while satisfying the current constraint strengths. Dynamic adjustment of constraint strength can improve the diversity when the population converges to the boundary of the feasible local region. aux Pop optimizes the unconstrained objective of the original problem, which can provide mainPop with favorable information outside the feasible region it explores to guide the evolution of mainPop. Experimental results show that the proposed algorithm was more competitive on four constrained test suites and four real-world CMOPs, compared with seven state-of-the-art CMOEAs.

关键词： Adaptive constraint strength constrained multi-objective optimization Dual populations Evolutionary algorithm

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A niche-based evolutionary algorithm with dual cooperative archive for solving constrained multi-objective optimization problems

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EGYPTIAN INFORMATICS JOURNAL 2024年 25卷

作者： Guo, Fengyu Li, Hecheng Qinghai Normal Univ Sch Comp Sci & Technol Xining 810016 Peoples R China Qinghai Normal Univ Sch Math & Stat Xining 810016 Peoples R China

constrained multi-objective optimization problems (CMOPs) are commonly encountered in engineering practice. The key to effectively solving these problems lies in achieving a timely balance between convergence, diversity, and feasibility during iterations. Furthermore, the appropriate utilization of infeasible solutions is crucial for identifying potential feasible regions. In order to accomplish this comprehensive objective, we propose a novel dual-stage constrained multi-objective evolutionary algorithm (CMOEA) called NACMOEA in this paper. It can be characterized by the following features: 1) Introducing a novel niche-based individual selection and infeasible solution utilization strategy to enhance convergence, diversity, and feasibility. 2) Presenting a cooperative search strategy assisted by dual archives to approximate the constrained Pareto front (CPF) from both feasible and infeasible perspectives, thereby improving the efficiency of obtaining the complete CPF. 3) Designing a new stage switch method based on non-dominant coverage rate to ensure proper completion of search stage switching. Extensive experiments demonstrate that NACMOEA exhibits competitive comprehensive performance when compared with other advanced CMOEAs.

关键词： constrained multi-objective optimization Dual stage algorithm Infeasible individual utilization Niche-based selection method

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An adaptive co-evolutionary competitive particle swarm optimizer for constrained multi-objective optimization problems

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SWARM AND EVOLUTIONARY COMPUTATION 2024年 91卷

作者： Meng, Xiaoding Li, Hecheng Qinghai Normal Univ Sch Comp Sci & Technol Xining 810008 Peoples R China Qinghai Normal Univ Sch Math & Stat Xining 810008 Qinghai Peoples R China

In constrained multi-objective optimization problems, it is challenging to balance the convergence, diversity and feasibility of the population, especially encountering complex infeasible regions. In order to effectively balance the three indicators, from the aspects of the handling of infeasible solution and the quality of individuals, a multi-population co-evolutionary competitive particle swarm optimization algorithm hybridized with infeasible solution transfer and an adaptive technique (ACCPSO) is proposed. Firstly, the information of feasible and infeasible individuals is fully utilized and the individuals are classified by Hamming distance. Then, a novel constraint handling technique based on learning from the promising feasible direction is designed to make individuals cross large infeasible regions and explore more potential feasible regions. Moreover, aiming to provide robust search capability and consequently further generate high-quality solutions, the genetic operators and the particle swarm optimization operator with the competitive mechanism are introduced as operators with an adaptive mechanism. Finally, compared with the state-of-the-art methods, the performance of the proposed algorithm is verified on LIR-CMOP, MW and DTLZ, as well as two real-world problems. The results indicate that ACCPSO exhibits stronger competitiveness in terms of convergence, the solution quality, and distribution diversity on the feasible Pareto front.

关键词： constrained multi-objective optimization Infeasible solution transfer Adaptive technique Co-evolution Competitive particle swarm optimizer

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