Multi-objective decomposition optimization algorithm based on adaptive weight vector and matching strategy

摘要

Multi-objective evolutionary algorithm based on decomposition (MOEA/D) uses pre-set weight vector and random matching mechanism between sub-problems and individuals, which makes the algorithm simple and efficient. However, when solving the problem of discontinuous Pareto Front, this will lead to not only the decline of the diversity of population, but also the degradation of the performance of solution set. To solve these problems, a multi-objective decomposition optimization algorithm based on adaptive weight vector and matching strategy (MOEA/D-AVM) is proposed in the article. Firstly, the algorithm finds the invalid sub-problems in the discontinuous region, and then updates these sub-problems according to the current evolutionary stage. It can reduce the possibility that the invalid sub-problems mislead evolutionary process. Secondly, the matching mechanism is established according to the value of penalty-based boundary intersection (PBI) and the Euclidean distance between the sub-problems and individuals. This mechanism can enhance the relationship between individuals and sub-problems. Finally, individuals who perform well in the neighborhood replacement operation are saved in the external archive. It can improve the diversity of the optimal solution set obtained by the algorithm. The proposed algorithm is compared with other related algorithms in the standard test problem. The result shows that the solution set obtained by MOEA/D-AVM not only can better cover the Pareto Front, but also has a competitive performance in solving the problem of discontinuous Pareto Front.