Abstract: When solving multiobjective problems, Multiobjective Evolutionary Algorithm based on Decomposition（MOEA/D） is simple and effective. But most MOEA/D use fixed control parameters. It will lead to poor ability of global search and make it difficult to balance convergence and diversity. To solve these problems, a multiobjective optimization algorithm based on adaptive mutation operator and neighborhood value is proposed in this paper. The algorithm adjusts the mutation operator adaptively based on the degree of dispersion or concentration of individual fitness values in the population. It can enhance the global search ability of the algorithm. The size of neighborhood is adjusted adaptively according to the stages of evolution and the degree of concentration of individual fitness values. Each individual has a neighborhood size in each generation. The number of individuals are counted, which dominate the individual corresponding to the subproblem in the neighborhood of subproblem. If this number exceeds the set upper limit, the Pareto dominance relationship will be also used as one of the criteria for judging the individual quality in the neighborhood. The proposed algorithm is compared with traditional MOEA/D in the standard test problem. The result shows that the solution set obtained by the proposed algorithm not only has better convergence and diversity, but also has a competitive performance in solving multiobjective problems.

Key words: adaptive, mutation operator, neighborhood size, domination relationship, multiobjective

摘要： 基于分解的多目标进化算法（MOEA/D）在解决多目标问题时，具有简单有效的特点。但多数MOEA/D采用固定的控制参数，导致全局搜索能力差，难以平衡收敛性和多样性。针对以上问题提出一种基于变异算子和邻域值自适应的多目标优化算法。该算法根据种群中个体适应度值的分散或集中程度进行判断，并据此对变异算子进行自适应的调节，从而增强算法的全局搜索能力；根据进化所处的阶段以及个体适应度值的集中程度，自适应地调节邻域值大小，保证每个个体在不同的进化代数都有一个邻域值大小；在子问题邻域中，统计子问题对应个体的被支配数，通过判断被支配数是否超过设定的上限，来决定是否将Pareto支配关系也作为邻域内判断个体好坏的准则之一。将提出的算法与传统的MOEA/D在标准测试问题上进行对比。实验结果表明，提出的算法求得的解集具有更好的收敛性和多样性，在求解性能上具有一定的优势。

关键词: 自适应, 变异算子, 邻域值, 支配关系, 多目标