MOEA/D线性插入方向向量策略研究

Improved MOEA/D with Linear Search Direction

MOEA/D具有良好的收敛性、均匀的分布性、求解效率高等优点,普遍应用于求解多目标优化问题.然而对于Pareto前端复杂的多目标优化问题,预先设定均匀的权重向量并不能够维持Pareto最优解集的良好分布性.本文,首先分析均匀分布的权重向量、均匀分布的搜索方向二者与均匀分布的解集之间的关系,提出一种新的权重向量设置方式;其次基于进化过程中解集的分布,提出线性插入搜索方向策略,并将其转换为对应的权重向量,同时在MOEA/D中周期性应用该策略调整搜索方向,获取分布均匀的解集;最后将该算法在WFG系列测试问题上进行性能测试,并采用世代距离指标(GD)、Spacing指标(S)、超体积指标(HV)对算法收敛性和多样性进行对比分析,实验结果表明,与原始的MOEA/D、使用均匀分布的搜索方向MOEA/D、使用预处理的M OEA/D、M OEA/D-DU相比,改进的算法求出解集的多样性极大提高,收敛性明显增强,解集的整体质量显著提高.

The multi-objective evolutionary algorithm based on decomposition(MOEA/D),which has a strong search ability,efficient fitness evolution,and good convergence merits,has been widely used in solving multi-objective optimization problem.In the recent studies about MOEA/D,the uniform distribution weight vectors has been used to obtain uniform distribution Pareto optimal solutions.However,using uniform weight vector cannot maintain the good distribution of the Pareto optimal solution when the Pareto Front(PF)of multi-objective problem is complicated(such as the discontinuous PF or the uneven distribution PF).In this paper,we first analyze the relationship between uniform weight vectors and uniform solutions to evaluate the impact of uniform search directions on uniform solutions.Then a new setting weight vectors strategy is proposed.Secondly,According to distribution of solution set during the evolution,the approach of inserting search direction linearly is given.Meanwhile,the weight vectors are converted,and the proposed approach is applied in MOEA/D periodicity,by this way,it can achieve the uniform solutions by periodically adjusting the search directions.In the experiment,we test the performance of the strategy on the WFG problems.The generational distance(GD),spacing(S),hyper-volume(HV)indicators are used to evaluate the performance of the different algorithms.Compared with the original algorithm MOEA/D,the MOEA/D with per-uniform search directions,the MOEA/D using the pre-organization procedure and MOEA/D-DU,experimental results show that the algorithm adapting the inserting search direction linearly policy achieve greatly improvement for the diversity performance,it performs better,also the convergence of the algorithm is obvious enhanced,the total quality of solutions is significantly improved.