基于在线感知Pareto前沿划分目标空间的多目标进化优化

多目标进化优化是求解多目标优化问题的可行方法.但是, 由于没有准确感知并充分利用问题的Pareto前沿, 已有方法难以高效求解复杂的多目标优化问题.本文提出一种基于在线感知Pareto前沿划分目标空间的多目标进化优化方法, 以利用感知的结果, 采用有针对性的进化优化方法求解多目标优化问题.首先, 根据个体之间的拥挤距离与给定阈值的关系感知优化问题的Pareto前沿上的间断点, 并基于此将目标空间划分为若干子空间; 然后, 在每一子空间中采用MOEA/D (Multi-objective evolutionary algorithm based on decomposition)得到一个外部保存集; 最后, 基于所有外部保存集生成问题的Pareto解集.将提出的方法应用于15个基准数值函数优化问题, 并与NSGA-Ⅱ、RPEA、MOEA/D、MOEA/DPBI、MOEA/D-STM和MOEA/D-ACD等比较.结果表明, 提出的方法能够产生收敛和分布性更优的Pareto解集, 是一种非常有竞争力的方法.

Multi-objective Evolutionary Optimization With Objective Space Partition Based on Online Perception of Pareto Front

Multi-objective evolutionary optimization is a feasible way to solve multi-objective optimization problems. However, previous methods have di–culties in e–ciently tackling a complex multi-objective optimization problem, since they cannot accurately perceive the shape of the Pareto front and take full advantages of it. A multi-objective evolutionary algorithm with objective space partition based on online perceiving the Pareto front of an optimization problem is proposed in this study. In the proposed method, a series of discontinuous points on a Pareto front which is getting from the relationship between the crowded distance of individuals and a given threshold are flrst detected. Then, the objective space is divided into a number of sub-spaces based on these points. In each sub-space, the multi-objective evolutionary algorithm based on decomposition (MOEA/D) is employed to obtain an external archive set. Finally, the Pareto optimal set of the problem is formed based on all the external sets. The proposed method is compared with NSGA-Ⅱ, RPEA, MOEA/D, MOEA/D-PBI, MOEA/D-STM, and MOEA/D-ACD on 15 benchmark optimization problems. The results empirically demonstrate that the proposed method has capabilities in obtaining a Pareto optimal set with good performance in convergence and diversity, and is a competitive alternative for multi-objective optimization.