Decomposition-based multiobjective evolutionary algorithms is one of the prevailing algorithmic frameworks for multiobjective optimization. This framework distributes the same amount of evolutionary computing resource...
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Decomposition-based multiobjective evolutionary algorithms is one of the prevailing algorithmic frameworks for multiobjective optimization. This framework distributes the same amount of evolutionary computing resources to each subproblems, but it ignores the variable contributions of different subproblems to population during the evolution. Resource allocation strategies (RAs) have been proposed to dynamically allocate appropriate evolutionary computational resources to different subproblems, with the aim of addressing this limitation. However, the majority of RA strategies result in inefficiencies and mistakes when performing subproblem assessment, thus generating unsuitable algorithmic results. To address this problem, this paper proposes a decomposition-based multiobjective evolutionary algorithm (HK-MOEA/D). The HK-MOEA/D algorithm uses a historical knowledge-guided RA strategy to evaluate the subproblem's evolvability, allocate evolutionary computational resources based on the evaluation value, and adaptively select genetic operators based on the evaluation value to either help the subproblem converge or move away from a local optimum. Additionally, the density-first individual selection mechanism of the external archive is utilized to improve the diversity of the algorithm. An external archive update mechanism based on theta-dominance is also used to store solutions that are truly worth keeping to guide the evaluation of subproblem evolvability. The efficacy of the proposed algorithm is evaluated by comparing it with seven state-of-the-art algorithms on three types of benchmark functions and three types of real-world application problems. The experimental results show that HK-MOEA/D accurately evaluates the evolvability of the subproblems and displays reliable performance in a variety of complex Pareto front optimization problems.
Decomposition-based multi-objective evolutionary algorithm decomposes a multi-objective optimization problem into a set of scalar subproblems and then optimizes them simultaneously. However, it does not take into acco...
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Decomposition-based multi-objective evolutionary algorithm decomposes a multi-objective optimization problem into a set of scalar subproblems and then optimizes them simultaneously. However, it does not take into account that subproblems of different difficulties need unequal computing resources. The resource allocation (RA) strategy based on MOEA/D was proposed to solve this problem. But most RA strategies generate a large number of solutions around some easy optimization subproblems, which cause the deterioration of the distribution. And the way they measure the subproblem difficulty ignores that subproblems may lose their evolvability in an evolutionary period. This paper aims to balance the convergence and diversity in RA strategy. Firstly, we introduce the accumulated escape probability (AEP) to calculate the historical improvement probability of each subproblem and then measure the subproblem evolvability, which can detect whether the subproblem has lost its evolvability in an evolutionary period. Secondly, we propose a density penalty-based individual screening mechanism (ISM) to enhance diversity. It gives priority to update the subproblem surrounded with more solutions and greater relative improvement on aggregated function. Finally, the above two methods are cooperated in MOEA/D and named it MOEA/D-BRA. Then the effectiveness of these two methods and the comprehensive performance of MOEA/D-BRA are tested. Furthermore, the BRA strategy is applied to more cases to balance convergence and diversity. Several experimental results indicate that the BRA strategy performers well on tackling a set of complicated optimization problems. (c) 2020 Elsevier B.V. All rights reserved.
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