HK-MOEA/D: A historical knowledge-guided resource allocation for decomposition multiobjective optimization

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 θ-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.