一种基于自适应变异算子优化的MOEA/D算法

A MOEA/D Algorithm Based on Adaptive Mutation Operator Optimization

MOEA/D(基于分解的多目标进化算法)利用一组均匀分布的权重向量将多目标优化问题分解为若干个单目标子问题,并以协作方式同时优化这些子问题。然而,当多目标问题真实Pareto前沿(Pareto front, PF)的形状具有长尾和尖峰特征时,MOEA/D在求解此类多目标问题时,所得到的最优解集在长尾和尖峰区域相对稀疏,性能受到很大影响。为了有效处理这种情况,提出了一种自适应选择变异策略的MOEA/D算法。该算法采用5种不同的变异策略构成候选池,在进化过程中,根据候选池中各变异策略近期的表现,以更高的概率选择近期表现更好的变异策略,使算法能够快速收敛。在算法的差分变异操作中采用理想解充当扰动向量,在PF上获得一组均匀分布的最优解,从而提高算法的性能。实验结果表明,与其他算法相比,本文算法获得的最优解集有更好的收敛性和分布性。

MOEA/D(decomposition based multi-objective evolutionary algorithm) decomposes the multi-objective optimization problem into several single objective subproblems by using a set of uniformly distributed weight vectors, and optimizes these subproblems simultaneously in a cooperative manner. However, when the shape of the real Pareto front(PF) of the multi-objective problem has the characteristics of long tail and peak, the optimal solution set obtained by MOEA/D in solving such multi-objective problem is relatively sparse in the long tail and peak regions, and the performance is greatly affected. In order to deal with this situation effectively, an MOEA/D algorithm with adaptive mutation strategy is proposed. The algorithm uses five different mutation strategies to form a candidate pool. In the process of evolution, according to the recent performance of each mutation strategy in the candidate pool, the mutation strategy with better recent performance is selected with a higher probability, so that the algorithm can converge quickly. In the differential mutation operation of the algorithm, the ideal solution is used as the disturbance vector to obtain a group of uniformly distributed optimal solutions on PF, so as to improve the performance of the algorithm. Experimental results show that compared with other algorithms, the optimal solution set obtained by this algorithm has better convergence and distribution.