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A two-stage evolutionary algorithm assisted by multi-archives for constrained multi-objective optimization

APPLIED SOFT COMPUTING 2024年 162卷

作者： Zhang, Wenjuan Liu, Jianchang Zhang, Wei Liu, Yuanchao Tan, Shubin Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Peoples R China

Due to the widespread existence of constrained multi -objective optimization problems (CMOPs) in real life, many researchers start to research the constrained multi -objective evolutionary algorithms (CMOEAs). Therefore, a variety of CMOEAs have emerged. However, some of them still suffer from great difficulties when coping with CMOPs with complex feasible regions. To solve the issue, this article puts forward a twostage evolutionary algorithm assisted by multi -archives for constrained multi -objective optimization, called MA-TSEA. In MA-TSEA, the evolution process is divided into two stages. In Stage 1, non -dominated solutions obtained by non -dominated sorting based on ( M +1) objectives ( i.e., M objectives and the constraint violation degree ( CV ) ) are stored in a temporary archive and merged with the parent population to improve the exploration ability of population. Then, MA-TSEA drives the populations to evolve from diverse directions by a multi -objective evolutionary algorithm, while the feasible solutions are saved in a formal archive. Next, the formal archive is updated to improve convergence and diversity. In Stage 2, the main population and archive population cooperate to evolve towards the constrained Pareto front (CPF), where the formal archive and population of Stage 1 are respectively used as the main population and archive population. The experimental studies on five benchmark test suites and five real -world applications demonstrate the superiority of MA-TSEA over the other seven state -of -art CMOEAs.

关键词： constrained multi-objective optimization Evolutionary algorithm Two-stage framework multi-archives

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An Enhanced Two-stage Evolutionary Algorithm for constrained multi-objective optimization

International Core Journal of Engineering

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International Core Journal of Engineering 2023年第12期9卷 337-351页

作者： Maowei He Lina Yan Liling Sun Yabao Hu Haoyue Wang

multi-objective optimization (MOP) is a form of optimization problem, in which there are multiple competing objective functions. The goal of multi-objective optimization is to find a set of solutions that are as close to or as close to the optimal value of all objective functions as possible. In order to solve this problem, a variety of methods can be used, such as genetic algorithm, particle swarm optimization and multi-objective evolutionary algorithm. However, these methods may be conflicting, thus requiring a balanced solution that satisfies as many objective functions as possible. At present, many scholars have designed many approaches, but because the constrained multi-objective optimization problems (CMOPs) have many diverse characteristics, most of the approaches cannot effectively and generally solve the cops with different characteristics. To solve the above problems, an enhanced two-stage evolutionary algorithm (MCTSEA) is proposed. To be specific, the search process includes two stages: (i) The constraints are ignored in stage 1 and quickly reaches the PF frontier. In this process, the solution with good performance is stored in the archive. Stage 1 focuses on diversity and convergence. (ii) Constraints combine constraint processing technology are considered with optimization algorithm to approach the CPF in stage 2. The population of archive is the initial population of stage 2. A new framework called MCTSEA is proposed in which the algorithm's performance is evaluated using 55 instances selected from 6 benchmark suites. Compared with 5 advanced CMOEAs, the results indicates that MCTSEA has certain advantages or competitiveness, which verifies the versatility of the proposed method.

关键词： Two-stage Framework Evolutionary Algorithm constrained multi-objective optimization

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An Improved Coevolutionary Algorithm for constrained multi-objective optimization Problems

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INTERNATIONAL JOURNAL OF COGNITIVE INFORMATICS AND NATURAL INTELLIGENCE 2024年第1期18卷 1页

作者： Xie, Shumin Zhu, Zhenjia Wang, Hui Shenzhen Inst Informat Technol Shenzhen Peoples R China

constrained multi-objective optimization problems are ubiquitous in engineering applications. In recent years, constrained multi-objective optimization algorithms based on the dual population coevolutionary framework have been widely studied due to their excellent performance. However, when facing optimization problems with complex constraints, the performance of existing algorithms still needs further improvement. This paper proposes an improved constrained multi-objective coevolutionary algorithm (iCMOCA). The algorithm mainly includes two populations: One population takes into account constraints, while the other population disregards them. Meanwhile, the iCMOCA employs effective collaboration between two populations during the process of offspring generation and environmental selection, and it utilizes an environmental selection strategy based on multi-objective to multi-objective decomposition to improve the performance. Comparative analysis conducted on the DAS-CMOP and MW test suites provides empirical evidence that iCMOCA outperforms five state-of-the-art algorithms.

关键词： constrained multi-objective optimization Dual-Population Coevolutionary Algorithm

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A fuzzy constraint handling technique for decomposition-based constrained multi- and many-objective optimization

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INFORMATION SCIENCES 2022年 597卷 318-340页

作者： Han, Dong Du, Wenli Jin, Yaochu Du, Wei Yu, Guo East China Univ Sci & Technol Key Lab Smart Mfg Energy Chem Proc Minist Educ Shanghai 200237 Peoples R China Univ Surrey Dept Comp Sci Guildford GU2 7XH Surrey England Bielefeld Univ Fac Technol D-33619 Bielefeld Germany

The challenge in solving constrained multi-objective optimization problems (CMOPs) is how to balance minimizing objectives and satisfying constraints, especially when the infeasible region is very large. To address this issue, this work proposes a fuzzy constraint handling technique, which uses the fuzzy set theory to accurately characterize the differ-ence between solutions on objective function values and constraint violation degrees. On this basis, a new concept, called "fuzzy advantage", is introduced to comprehensively quantify the degree to which one solution is better than others, allowing the infeasible solutions with promising fitness to survive. The proposed method is integrated with a decomposition-based multi-objective evolutionary algorithm to verify its effectiveness. Compared with nine state-of-the-art MOEAs on a number of test problems and a real -world optimization problem, the proposed algorithm shows high competitiveness in solv -ing a variety of CMOPs.(c) 2022 Published by Elsevier Inc.

关键词： constrained multi-objective optimization Evolutionary algorithm Constraint handling technique Fuzzy set

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Hybrid driven strategy for constrained evolutionary multi-objective optimization

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INFORMATION SCIENCES 2022年 585卷 344-365页

作者： Feng, Xue Pan, Anqi Ren, Zhengyun Fan, Zhiping Donghua Univ Sch Informat Sci & Technol 2999 Renmin North Rd Shanghai 201620 Peoples R China

In the constrained multi-objective optimization problems, the pursuit of feasibility could improve convergence but will lead to the loss of diversity. For optimization algorithm, balancing the weight between convergence and diversity dynamically is a challenge, especially in problems with low proportion of feasible regions. In this paper, a constrained multi-objective optimization algorithm is proposed based on a hybrid driven strategy to enhance both the feasibility and diversity performance of the approximate Pareto solutions. The proposed algorithm contains two archives, that one is driven by feasibility information and the other is driven by diversity information. A self-adaptive archive selection mechanism and a conditional tournament selection strategy are proposed to provide mating parent solutions according to the evolutionary stage. Moreover, in the update of the feasibility archive, an evolutionary direction prediction mechanism is proposed and adopted to improve the evolutionary efficiency. Compared to four other multi-objective algorithms on three benchmark suits of different types, the performance of the proposed algorithm is better than the peer algorithms, especially in large-infeasible-regions multi objective optimization problems. (c) 2021 Elsevier Inc. All rights reserved.

关键词： Evolutionary algorithm constrained multi-objective optimization Large-infeasible-regions Two-archive Hybrid driven strategy

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Probability of improvement methods for constrained multi-objective optimization

Probability of improvement methods for constrained multi-obj...

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2008 IET 7th International Conference on Computation in Electromagnetics

作者： G. I. Hawe J. K. Sykulski School of Electronics and Computer Science University of Southampton Southampton UK

This paper shows how the simultaneous consideration of multiple Kriging models can lead to useful metrics for the selection of design vectors in constrained multi-objective optimization. The savings in computational c... 详细信息

ISBN: (纸本)9780863418914

关键词： constrained multi-objective optimization Kriging Kriging Probability geophysical techniques electromagnetic design

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An Archive-assisted Two-stage and Dual-population Evolutionary Algorithm for constrained multi-objective optimization Problems

An Archive-assisted Two-stage and Dual-population Evolutiona...

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第43届中国控制会议

作者： Wenjuan Zhang Huan Ma Wei Zhang Yuanchao Liu Shubin Tan Jianchang Liu the College of Information Science and Engineering Northeastern University the National Frontiers Science Center for Industrial Intelligent Systems Optimization Northeastern University Beiying Iron and Steel (Group) Co. Ltd.

ISBN: (数字)9789887581581

ISBN: (纸本)9798350366907

The key to solving constrained multiobjective optimization problems(CMOPs) is to balance objective optimization and constraint satisfaction. But the existing evolutionary algorithms suffer from great difficulties in striking a balance between them, especially in dealing with CMOPs with complex constraints. To solve the issue, an archive-assisted two-stage and dualpopulation evolutionary algorithm, referred as ATD-CMOEA, is proposed. The aim of Stage 1 is to explore the entire objective space and discover the promising regions, which is achieved by two populations with different priorities of constraints and objectives. Meanwhile, feasible solutions discovered during the evolutionary process are archived in normal archive. The purpose of Stage 2 is to get a series of well-distributed Pareto optimal solutions by the simultaneous evolution of the main population, the assistant population and normal archive. Experimental results on two test suites demonstrate the competitiveness of the proposed ATD-CMOEA when compared with other seven state-of-art algorithms.

关键词： constrained multi-objective optimization Evolutionary algorithm Two-stage framework Dual-population

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Do We Really Need to Use Constraint Violation in constrained Evolutionary multi-objective optimization? 17th

Do We Really Need to Use Constraint Violation in Constrained...

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17th International Conference on Parallel Problem Solving from Nature (PPSN)

作者： Li, Shuang Li, Ke Li, Wei Harbin Inst Technol Control & Simulat Ctr Harbin Peoples R China Univ Exeter Dept Comp Sci Exeter EX4 5DS Devon England

ISBN: (纸本)9783031147210;9783031147203

Constraint violation has been a building block to design evolutionary multi-objective optimization algorithms for solving constrained multi-objective optimization problems. However, it is not uncommon that the constraint violation is hardly approachable in real-world blackbox optimization scenarios. It is unclear that whether the existing constrained evolutionary multi-objective optimization algorithms, whose environmental selection mechanism are built upon the constraint violation, can still work or not when the formulations of the constraint functions are unknown. Bearing this consideration in mind, this paper picks up four widely used constrained evolutionary multi-objective optimization algorithms as the baseline and develop the corresponding variants that replace the constraint violation by a crisp value. From our experiments on both synthetic and real-world benchmark test problems, we find that the performance of the selected algorithms have not been significantly influenced when the constraint violation is not used to guide the environmental selection. The supplementary material of this paper can be found in https://***/23dtdne8.

关键词： constrained multi-objective optimization Constraint handling techniques Evolutionary multi-objective optimization

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Robust evolutionary algorithm for constrained multi-objective optimization problems

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Jisuanji Yanjiu yu Fazhan/Computer Research and Development 2004年第6期41卷 985-990页

作者： Zou, Xiu-Fen Liu, Min-Zhong Wu, Zhi-Jian Kang, Li-Shan Sch. of Math. and Stat. Wuhan Univ. Wuhan 430072 China Lab. of Software Eng. Wuhan Univ. Wuhan 430072 China

A partial-order relation is defined by combining constrained conditions and the objective functions, and a definition of constrained-domination between two solutions is suggested, which is an extension to the definition of domination. The consistency between Pareto optimal set obtained by means of the new definition and the Pareto optimal set satisfying the constrained conditions has been proved. So when the individuals are evaluated or ranked, it isn't needed to care about whether the individuals are feasible, therefore implementing a penalty-parameterless constraint-handling approach. By using the theory of finite Markov chain, the convergence properties of this algorithm are proved. Several benchmark MO optimization problems are taken to test this algorithm. The numerical experiments show that the proposed approach provides good performance in terms of convergence and diversity of solutions.

关键词： constrained multi-objective optimization constrained-domination Convergence Evolutionary algorithm Partial order

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multi-objective optimal power flow problem using constrained dynamic multitasking multi-objective optimization algorithm

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SWARM AND EVOLUTIONARY COMPUTATION 2025年 93卷

作者： Zhu, Junhua Yu, Xiaobing Wang, Feng Mao, Yaqi Nanjing Univ Informat Sci & Technol Res Inst Risk Governance & Emergency Decis Making Sch Management Sci & Engn Nanjing 210044 Peoples R China Nanjing Univ Informat Sci & Technol Collaborat Innovat Ctr Forecast & Evaluat Meteorol Nanjing 210044 Peoples R China

The multi-objective optimal power flow (MOOPF) problem involves conflicting objectives and complex constraints, presenting a significant challenge for existing optimization methods. To address constrained multi- objective optimization problems (CMOPs), a recent evolutionary multi-tasking (EMT) framework has been proposed, involving a primary task and several auxiliary tasks running in parallel. The design of these auxiliary tasks is critical for supporting the solution of the primary task. This paper introduces a novel constrained dynamic multitasking multi-objective optimization algorithm (CDMTMO) to solve CMOPs. The proposed algorithm comprises three populations, each assigned a specific task: the first population focuses on solving the primary CMOP, the second population tackles a constraint-relaxed problem, and the third population gradually transitions from solving an unconstrained problem to the CMOP. To ensure effective collaboration among auxiliary tasks and the main task, CDMTMO incorporates an improved epsilon-constrained method and an enhanced dual ranking method. Furthermore, a pre-selection strategy for solution sets is integrated to discern promising individuals and facilitate knowledge transfer. CDMTMO has been evaluated using two IEEE standard systems, to demonstrate its capability and suitability in efficiently tackling the MOOPF problem. A thorough analysis of CDMTMO's results was performed, comparing it with seven state-of-the-art algorithms: AGEMOEA, CCMO, DSPCMDE, CMOEMT, ToP, EMCMO and DEST. After evaluating across eight test cases, CDMTMO achieved the best inverted generational distance plus (IGD+) and hypervolume (HV) values in seven cases. Furthermore, CDMTMO achieves a feasible rate (FR) of 1 in all cases, demonstrating its consistent ability to find feasible solutions.

关键词： Optimal power flow constrained multi-objective optimization Constraint handling technique Auxiliary task Knowledge transfer

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