Abstract:

The current research on Multi-Objective Evolutionary Algorithm （MOEA） in dealing with Constrained Multi-objective Optimization Problems （CMOPs） is mainly to solve the single type of constraints， and in dealing with different kinds of complex constraints， the algorithm is difficult to converge or has poor population distribution. To solve this problem， based on the framework of MOEA based on Decomposition （MOEA/D）， an Adaptive Reference Vector based Constrained Multi-Objective Evolutionary Algorithm （ARVCMOEA） was proposed. Firstly， the reference vectors were divided into two parts： the main reference vectors and the auxiliary reference vectors. Then， in the initial phase of the algorithm， the unconstrained auxiliary reference vectors were used to guide the population to quickly cross the infeasible interval. Finally， the distribution and search ability of the algorithm were improved by adaptively adjusting positions of the auxiliary reference vectors and weakening the distribution requirements. Experiments were carried out on 30 test functions with different kinds of complex constraints. The results show that the proposed algorithm can converge well with different kinds of constraints， and it is superior to Non-dominated Sorting Genetic Algorithm II （NSGA-II）， Constraint-MOEA/D （C-MOEA/D） and MOEA/D with Detect-And-Escape strategy （MOEA/D-DAE） in overall performance， and it can obtain better results on some test functions than the current excellent Coevolutionary Constrained Multi-objective Optimization framework （CCMO）， verifying that the proposed algorithm has excellent performance in the face of different kinds of CMOPs.

Key words: Multi-Objective Evolutionary Algorithm (MOEA), constrained optimization, complex constraint, decomposition, reference vector

摘要：

针对目前用多目标进化算法（MOEA）处理约束多目标优化问题（CMOP）的研究通常以解决单一类型约束为主，而在面对不同种类的复杂约束时算法难以收敛或者种群分布性差的问题，以基于分解的多目标进化算法（MOEA/D）框架为基础，提出一种基于参考向量的自适应约束多目标进化算法（ARVCMOEA）。首先将参考向量分成主参考向量及辅助参考向量两部分，然后在算法起始阶段通过无约束的辅助参考向量指导种群快速跨越不可行区间，最后通过自适应地调整辅助参考向量的位置及弱化对其的分布性要求来提高算法分布性及搜索能力。实验在30个具有不同种类复杂约束的测试函数上进行了验证，结果表明所提算法面对不同种类的约束时均可以很好地收敛，在总体性能上均优于NSGA-II（Non-dominated Sorting Genetic Algorithm II）、C-MOEA/D（Constraint-MOEA/D）及MOEA/D-DAE，并且相较于目前性能优异的CCMO（Coevolutionary Constrained Multi-objective Optimization framework）在部分测试函数上可以得到更优异的结果。可见，所提算法在面对不同种类的CMOP时具有优异的性能。

关键词: 多目标进化算法, 约束优化, 复杂约束, 分解, 参考向量