基于变化的权重向量的MOEA/D研究

Research on MOEA/D Based on Variable Weight Vector

MOEA/D使用聚合函数将多目标问题分解成一定数量的单目标子问题并行优化,因其具有较强的搜索能力,良好的收敛性等,越来越受人关注。然而,该算法的性能极大程度上依赖权重向量与解替换的邻域构成。首先,分析预先设置固定的权重向量导致最终解集性能下降的原因;其次,在此基础上,提出依赖边界区域变化调整权重向量的策略,根据算法迭代中解集边界预测近似Pareto前端的整体分布,结合预先设定的权重向量与均匀设计调整权重向量;进一步,为提高算法求解的收敛速度,提出导引式杂交策略,引导种群进化,结合两种策略,提出一种改进的分解多目标进化算法。仿真试验中,本文在ZDT系列问题上对算法进行性能测试。与NSGA-II,原始的MOEA/D、带均匀设计的MOEA/D+UD相比。结果表明,结合变化的权重向量调整与导引式杂交策略,算法收敛的速度提高,获得解集分布性相对更为均匀,产生解集的整体质量更高。

MOEA/D uses aggregate function to decompose multi-objective problems into a number of sin- gle-object sub-problems for parallel optimization. Because of its strong search ability and good conver- gence, it has attracted more and more attention; however, the performance of the algorithm relies heavily on the weight vector and the neighborhood of the solution replacement. This paper firstly analyzes the rea sons why the fixed weight vector is preset to cause the final solution set performance to degrade. Secondly, the strategy of adjusting the weight vector dependent on the boundary region change is proposed. Based on the solution set boundary in the algorithm iteration, the overall distribution of the Pareto front end is pre- dieted, and the weight vector with the preset weight vector and uniform design is adjusted. Finally, in or- der to improve the convergence speed of the algorithm, the guided hybridization strategy is proposed to guide the population evolution and two strategies are combined to propose an improved decomposition multi-objective evolutionary algorithm. In the simulation experiment, this paper tests the performance of the algorithm on the ZDT series. The results show that, compared with NSGA-II, original MOEA/D, MOEA/D＋ UD with uniform design, with the combination of the weight vector adjustment and the guided hybridization strategy, the convergence speed of the algorithm is improved; the distribution of the solution set is relatively more uniform, and the overall quality of the solution set is higher.