递归替换寻优策略的分解多目标进化算法

Decomposition Multi-objective Evolutionary Algorithm for Recursive Replacement Optimization Strategy

基于分解的多目标进化算法(MOEA/D)在求解多目标优化问题时,有着较强的搜索能力、高效的适应度评价、良好的收敛性等优点.然而,在更新子问题时,新解在固定邻域内替换所有较差的解,导致解集副本过多,一定程度上丢失解集的多样性.为维持多样性的同时提高解集的收敛性,提出一种基于递归替换寻优策略的分解多目标进化算法.首先,根据解到对应方向向量的垂直距离确定替换邻域,保持解在目标空间中的均匀分布,维持解集的多样性;进而,提出递归替换寻优策略,被新解所替换的解不立刻丢弃,而是在当前邻域内替换比该解还差的解,尽可能快速引导解集朝Pareto前沿进化,提高解的收敛性.将该算法在WFG系列和DTLZ系列测试函数上进行仿真实验,并与MOEA/D、MOEA/D-DRA、MOEA/D-GR、MOEA/D-DU四个算法进行对比,实验结果表明,本文所提出的MOEA/D-LR算法解集的整体质量明显优于其他算法,且该算法在维持多样性的同时其收敛性显著提高.

The multi-objective evolutionary algorithm based on decomposition（ MOEA/D） owes strong search ability,efficient fitness evaluation,good convergence in solving multi-objective optimization problems. However,when MOEA/D updates sub-problems,the new solution replaces all the poor solutions within the fixed neighborhood,resulting in too many copies of the solution and losing of the diversity of the solution in some degree. In order to maintain diversity and improve the convergence of solution set,a multi-objective evolutionary algorithm based on recursive replacement optimization strategy is proposed. Firstly,the replacement neighborhood is determined according to the perpendicular distance from the solution to the corresponding direction vector,and the uniform distribution of the solution in the target space and the diversity of the solution set is maintained. Furthermore,the recursive replacement strategy is proposed. To improve the convergence of the solution,the solution replaced by the new solution is not immediately discarded,but in the current neighborhood to find the solution which is worse than this solution to replace as soon as possible to guide the solution towards the Pareto front evolution. The performance of the new algorithm are evaluated in the test problems such as WFG,DTLZ,and compared with MOEA/D,MOEA/D-DRA,MOEA/D-GR,MOEA/D-DU. The experimental results show that the overall quality of the proposed MOEA/D-LR algorithm is better than other algorithms,and the algorithm improves the convergence of the algorithm while maintaining the diversity.