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A multi-population evolutionary algorithm based on knowledge transfer for constrained many-objective optimization

ENGINEERING optimization 2025年第3期57卷 813-843页

作者： Ge, Wenlong Zhang, Shanxin Song, Weida Wang, Wei Jiangnan Univ Sch Internet Things Engn Wuxi Peoples R China

constrained many-objective optimization Problems (CMaOPs) are challenging in handling objectives and constraints simultaneously. Here, a novel constrained many-objective optimization Evolutionary Algorithm (CMaOEA) based on Multi-population, Knowledge transfer and Improved environmental selection called CMaMKI is proposed to handle CMaOPs. The proposed framework evolves a task population to solve the original CMaOP and evolves another population to solve a helper problem derived from the original one. To assist solving the original CMaOP, a knowledge expression and transfer strategy is designed to share useful information in the helper population with the task population. Meanwhile, to balance population convergence, diversity and feasibility, an enhanced environmental selection strategy is devised by combining the epsilon-constrained technique, theta-dominance and subregional density evaluation. The proposed algorithm is evaluated and contrasted with six state-of-the-art algorithms on a set of benchmark CMaOPs. The experimental results demonstrate the superiority and competitiveness of the proposed method.

关键词： constrained many-objective optimization evolutionary algorithm environmental selection multi-population knowledge transfer

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A constrained many-objective optimization Evolutionary Algorithm With Enhanced Mating and Environmental Selections

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IEEE TRANSACTIONS ON CYBERNETICS 2023年第8期53卷 4934-4946页

作者： Ming, Fei Gong, Wenyin Wang, Ling Gao, Liang China Univ Geosci Sch Comp Sci Wuhan 430074 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China Huazhong Univ Sci & Technol State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Peoples R China

Unlike the considerable research on solving many-objective optimization problems (MaOPs) with evolutionary algorithms (EAs), there has been much less research on constrained MaOPs (CMaOPs). Generally, to effectively solve CMaOPs, an algorithm needs to balance feasibility, convergence, and diversity simultaneously. It is essential for handling CMaOPs yet most of the existing research encounters difficulties. This article proposes a novel constrained many-objective optimization EA with enhanced mating and environmental selections, namely, CMME. It can be featured as: 1) two novel ranking strategies are proposed and used in the mating and environmental selections to enrich feasibility, diversity, and convergence;2) a novel individual density estimation is designed, and the crowding distance is integrated to promote diversity;and 3) the \theta-dominance is used to strengthen the selection pressure on promoting both the convergence and diversity. The synergy of these components can achieve the goal of balancing feasibility, convergence, and diversity for solving CMaOPs. The proposed CMME is extensively evaluated on 13 CMaOPs and 3 real-world applications. Experimental results demonstrate the superiority and competitiveness of CMME over nine related algorithms.

关键词： Convergence optimization Machine-to-machine communications Evolutionary computation Linear programming Estimation Vehicle routing constrained many-objective optimization environmental selection evolutionary algorithm (EA) mating selection ranking

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A strengthened constrained-dominance based evolutionary algorithm for constrained many-objective optimization

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APPLIED SOFT COMPUTING 2024年 167卷

作者： Zhang, Wei Liu, Jianchang Liu, Junhua Liu, Yuanchao Tan, Shubin Northeastern Univ Natl Frontiers Sci Ctr Ind Intelligent & Syst Opti Shenyang Peoples R China Northeastern Univ Coll Informat Sci & Engn Shenyang Peoples R China Xian Polytech Univ Sch Comp Sci Xian Peoples R China

Solving constrained multi-objective optimization problems have received increasing attention. However, there are few researches based on constrained many-objective optimization problems that widely exist in real life. Given the above fact, we propose a strengthened constrained-dominance based evolutionary algorithm for constrained many-objective optimization (SCEA). The proposed SCEA includes the following main components. First, a dual-assistance mating selection is developed to select elite parents for variation, and further accelerate the generation of feasible solutions. Second, a strengthened constrained-dominance relation is proposed, which favors feasible solutions but still leaves the room for selecting infeasible solutions. This is achieved by simultaneously considering the objective optimization and constraint satisfaction. Third, the designed unconstrained aggregation (UA) indicator and crowded detector cooperate reference points to promote the convergence and diversity of population. Finally, a cooperation mechanism based on the constrained aggregation (CA) indicator and hierarchical clustering is designed to drive individuals toward different feasible regions, and further balance the objective optimization and constraint satisfaction. Extensive experimental studies are conducted on three benchmark test suites and two real-world applications to validate the performance of SCEA. The corresponding experiment results have demonstrated that SCEA is more competitive than its peer competitors.

关键词： constrained many-objective optimization Evolutionary algorithm Strengthened constrained-dominance Dual-assistance mating selection

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Tri-Goal Evolution Framework for constrained many-objective optimization

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2020年第8期50卷 3086-3099页

作者： Zhou, Yalan Zhu, Min Wang, Jiahai Zhang, Zizhen Xiang, Yi Zhang, Jun Guangdong Univ Finance & Econ Coll Informat Guangzhou 510320 Peoples R China Sun Yat Sen Univ Sch Comp Sci Guangzhou 510275 Peoples R China Sun Yat Sen Univ Key Lab Machine Intelligence & Adv Comp Minist Educ Guangzhou 510275 Peoples R China Sun Yat Sen Univ Guangdong Key Lab Big Data Anal & Proc Guangzhou 510275 Peoples R China South China Univ Technol Sch Software Guangzhou 510006 Peoples R China South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China

It is generally accepted that the essential goal of many-objective optimization is the balance between convergence and diversity. For constrained many-objective optimization problems (CMaOPs), the feasibility of solutions should be considered as well. Then the real challenge of constrained many-objective optimization can be generalized to the balance among convergence, diversity, and feasibility. In this paper, a tri-goal evolution framework is proposed for CMaOPs. The proposed framework carefully designs two indicators for convergence and diversity, respectively, and converts the constraints into the third indicator for feasibility. Since the essential goal of constrained many-objective optimization is to balance convergence, diversity, and feasibility, the philosophy of the proposed framework matches the essential goal of constrained many-objective optimization well. Thus, it is natural to use the proposed framework to deal with CMaOPs. Further, the proposed framework is conceptually simple and easy to instantiate for constrained many-objective optimization. A variety of balance schemes and ranking methods can be used to achieve the balance among convergence, diversity and feasibility. Three typical instantiations of the proposed framework are then designed. Experimental results on a constrained many-objective optimization test suite show that the proposed framework is highly competitive with existing state-of-the-art constrained many-objective evolutionary algorithms for CMaOPs.

关键词： Convergence Linear programming Pareto optimization Stochastic processes Evolutionary computation Computer science constrained many-objective optimization constraint handling convergence diversity feasibility tri-goal evolution (TiGE)

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Handling constrained many-objective optimization problems via determinantal point processes

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INFORMATION SCIENCES 2023年第1期643卷

作者： Ming, Fei Gong, Wenyin Li, Shuijia Wang, Ling Liao, Zuowen China Univ Geosci Sch Comp Sci Wuhan 430074 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China Beibu Gulf Univ Beibu Gulf Ocean Dev Res Ctr Qinzhou 535000 Peoples R China

Although various research studies have been performed to solve constrained multi-objective optimization and many-objective optimization problems, more attention should be paid to the widely existing constrained many-objective optimization problems (CMaOPs). Balancing convergence, diversity and feasibility is an essential issue for CMaOPs. To this end, traditional methods tend to adopt one-by-one selection or deletion strategies. However, these strategies rarely consider the quality of the entirety. Consequently, some poorly performed yet promising solutions might be discarded, finally degrading the performance. To overcome this drawback, this article first introduces the determinantal point processes (DPPs) in Machine Learning to handle CMaOPs. A new algorithm is proposed by applying the DPPs rather than traditional selection strategies for selecting population and archive. To effectively utilize DPPs, two novel Kernel Matrices are designed to represent convergence, diversity, and feasibility qualities of solutions in population and archive, respectively. Besides, a new e-constrained technique is tailored for the update strategies of archive and corner solution set to handle CMaOPs, especially those with complex constraints. Experiments on 16 different CMaOPs of 77 instances with up to 15 objectives demonstrated the superiority of the proposed method to the state-of-the-art algorithms.

关键词： constrained many-objective optimization Evolutionary algorithm Machine learning Determinantal point process Kernel matrix e-constrained technique

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An angle based evolutionary algorithm with infeasibility information for constrained many-objective optimization

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APPLIED SOFT COMPUTING 2020年 86卷

作者： Wang, Chao Xu, Ran Anhui Univ Key Lab Intelligent Comp & Signal Proc Minist Educ Sch Comp Sci & Technol Hefei 230039 Anhui Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110000 Liaoning Peoples R China

Recently, angle-based approaches have shown promising for unconstrained many-objective optimization problems (MaOPs), but few of them are extended to solve constrained MaOPs (CMaOPs). Moreover, due to the difficulty in searching for feasible solutions in high-dimensional objective space, the use of infeasible solutions comes to be more important in solving CMaOPs. In this paper, an angle based evolutionary algorithm with infeasibility information is proposed for constrained many-objective optimization, where different kinds of infeasible solutions are utilized in environmental selection and mating selection. To be specific, an angle-based constrained dominance relation is proposed for non-dominated sorting, which gives infeasible solutions with good diversity the same priority to feasible solutions for escaping from the locally feasible regions. As for diversity maintenance, an angle-based density estimation is developed to give the infeasible solutions with good convergence a chance to survive for next generation, which is helpful to get across the large infeasible barrier. In addition, in order to utilize the potential of infeasible solutions in creating high-quality offspring, a modified mating selection is designed by considering the convergence, diversity and feasibility of solutions simultaneously. Experimental results on two constrained many-objective optimization test suites demonstrate the competitiveness of the proposed algorithm in comparison with five existing constrained many-objective evolutionary algorithms for CMaOPs. Moreover, the effectiveness of the proposed algorithm on a real-world problem is showcased. (C) 2019 Elsevier B.V. All rights reserved.

关键词： constrained many-objective optimization Infeasibility information constrained dominance relation Convergence Diversity

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On the Importance of Isolated Solutions in constrained Decomposition-based many-objective optimization 17

On the Importance of Isolated Solutions in Constrained Decom...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Elarbi, Maha Bechikh, Slim Ben Said, Lamjed Univ Tunis SMART lab CS Dept Tunis Tunisia

ISBN: (纸本)9781450349208

During the few past years, decomposition has shown a high performance in solving Multi-objective optimization Problems (MOPs) involving more than three objectives, called as many-objective optimization Problems (MaOPs). The performance of most of the existing decomposition-based algorithms has been assessed on the widely used DTLZ and WFG unconstrained test problems. However, the number of works that have been devoted to tackle the problematic of constrained many-objective optimization is relatively very small when compared to the number of works handling the unconstrained case. Recently, there has been some interest to exploit infeasible isolated solutions when solving constrained MaOPs (CMaOPs). Motivated by this observation, we firstly propose an IS-update procedure (Isolated Solution-based update procedure) that has the ability to: (1) handle CMaOPs characterized by various types of difficulties and (2) favor the selection of not only infeasible solutions associated to isolated sub-regions but also infeasible solutions with smaller Constraint Violation (CV) values. The IS-update procedure is subsequently embedded within the Multi-objective Evolutionary Algorithm-based on Decomposition (MOEA/D). The new obtained algorithm, named ISC-MOEA/D (Isolated Solution-based constrained MOEA/D), has been shown to provide competitive and better results when compared against three recent works on the CDTLZ benchmark problems.

关键词： constrained many-objective optimization decomposition-based evolutionary algorithms constraint handling isolated solutions

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A Constraint-Handling Technique for Decomposition-Based constrained many-objective Evolutionary Algorithms

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2023年第12期53卷 7783-7793页

To solve the constrained many-objective optimization problems (CMaOPs), the tradeoff among conver-gence, diversity, and feasibility is a crucial and challenging task. This article proposes a new constraint-handling technique tailored for decomposition-based many-objective evolutionary algorithms to deal with the CMaOPs effectively. Specifically, the proposed method, namely, constrained penalty boundary intersection (CPBI), is an improved aggregation function based on the penalty boundary intersection. In CPBI, the normalized overall constraint violation (CV) is embedded to pursue feasibility. In this way, by the optimization of CPBI, convergence, diversity, and feasibility can be optimized simul-taneously. Furthermore, the weight of the normalized overall CV is adjusted adaptively based on the feasible ratio of the current population. To evaluate the performance of CPBI, it is combined with three decomposition-based algorithms. Ten benchmark problems with 50 instances are chosen as the test suite. In addition, the proposed method is compared with nine advanced algorithms. Experimental results have demonstrated the promising performance of CPBI for different problems.

关键词： constrained many-objective optimization constraint-handling technique (CHT) decomposition evolutionary algorithm (EA) penalty boundary intersection

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Adaptive ε-Constraint Multi-objective Evolutionary Algorithm Based on Decomposition and Differential Evolution

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IEEE ACCESS 2021年 9卷 17596-17609页

作者： Liu, Bing-Jie Bi, Xiao-Jun Harbin Engn Univ Coll Informat & Commun Engn Harbin 150001 Peoples R China Minzu Univ China Dept Informat Engn Beijing 100081 Peoples R China

To improve distribution and convergence of the obtained solution set in constrained multi-objective optimization problems, this paper presents an adaptive epsilon-constraint multi-objective evolutionary algorithm based on decomposition and differential evolution (epsilon-MOEA/D-DE). First, an adaptive epsilon-constraint strategy based on both evolution generation and constraint violation is designed to make better use of excellent evolution individuals and improve population diversity. Then, an adaptive differential evolution (DE) mutation strategy with full utilization of infeasible individuals is proposed to increase search efficiency and avoid falling into the local optimum. Finally, a replacement mechanism is suggested to take advantage of the infeasible individuals in the population with better objective function values and constraint violation degree, and thus both diversity and convergence are well coordinated. A comparative experiment with four other excellent constrained multi-objective algorithms was implemented on standard constrained multi-objective optimization problems (CF series), and the results showed that the diversity and convergence of our algorithm were both improved.

关键词： Statistics Sociology optimization Convergence Linear programming Search problems Diversity reception constrained many-objective optimization epsilon-constrain handling techniques differential evolution algorithm MOEA/D

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A constrained many-objective evolutionary algorithm with learning vector quantization-based reference point adaptation

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SWARM AND EVOLUTIONARY COMPUTATION 2023年 82卷

作者： Wang, Chao Huang, Huitao Pan, Huimin Anhui Univ Informat Mat & Intelligent Sensing Lab Anhui Prov Hefei 230601 Peoples R China Anhui Univ Engn Res Ctr Autonomous Unmanned Syst Technol Sch Artificial Intelligence Minist Educ Hefei 230601 Peoples R China

constrained many-objective optimization problems (CMaOPs) are frequently encountered in real-world ap-plications, generally having constrained Pareto fronts (PFs) that are often incomplete and irregular in high-dimensional objective space. Due to the advantage of reference point-based decomposition algorithms on unconstrained many-objective optimization, they have been widely applied into dealing with CMaOPs. However, these algorithms may not be well suited for solving the constrained problems with irregular PFs, since their adopted uniformly distributed reference points may not properly fit the distribution of feasible regions. To address this issue, we propose a constrained many-objective evolutionary algorithm with reference point adaptation. To be specific, the learning vector quantization network is used to collect the feasibility information during the evolutionary search process in the supervised manner. By regarding the feasible and infeasible solutions as two classes of training samples, the network can gradually model the topological structure of the PF and adaptively generate the reference points in the feasible regions. In order to make full use of infeasible solutions to assist in the modeling of the PF, an adaptive e-truncation based constraint-handling technique is proposed to introduce the elite infeasible solutions during the evolutionary process. Experimental results on several public constrained many-objective optimization test suites demonstrate the competitiveness of the proposed algorithm in comparison with seven state of-the-art algorithms.

关键词： constrained many-objective optimization Evolutionary algorithm Reference point adaptation Learning vector quantization

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