基于协同进化的约束多目标优化算法

针对约束多目标优化算法存在难以有效地兼顾收敛性和多样性的问题，提出一种基于协同进化的约束多目标优化算法。第一阶段，通过基于稳态演化的可行解搜索方式得到一个具有一定数量可行解的种群；第二阶段，将这个种群拆分为两个子种群，并通过双子种群协同进化的方式实现对收敛性和多样性的兼顾；最后采用标准约束多目标优化问题CF1~CF7、DOC1~DOC7和实际工程问题进行仿真实验，以测试所提算法的求解性能。实验结果表明，与基于约束支配准则的非支配排序遗传算法（NSGA-Ⅱ-CDP）、两阶段算法（ToP）、推拉搜索算法（PPS）和约束多目标优化的双存档进化算法（C-TAEA）相比，所提算法在反向世代距离（IGD）和超体积（HV）两个指标上均取得了良好的结果，说明所提算法可以有效地兼顾收敛性和多样性。

Constrained multi-objective optimization algorithm based on coevolution

In view of the problem that it is difficult for constrained multi-objective optimization algorithms to effectively balance convergence and diversity, a new constrained multi-objective optimization algorithm based on coevolution was proposed. Firstly, a population with certain number of feasible solutions was obtained by using the feasible solution search method based on steady-state evolution. Then, this population was divided into two sub-populations and both convergence and diversity were achieved by coevolution of the two sub-populations. Finally, standard constrained multi-objective optimization problems CF1~CF7, DOC1~DOC7 and the practical engineering problems were used for simulation experiments to test the solution performance of the proposed algorithm. Experimental results show that compared with Nondominated Sorting Genetic Algorithm Ⅱ based on Constrained Dominance Principle (NSGA-Ⅱ-CDP), Two-Phase algorithm (ToP), Push and Pull Search algorithm (PPS) and Two-Archive Evolutionary Algorithm for Constrained multiobjective optimization (C-TAEA), the proposed algorithm achives good results in both Inverted Generational Distance (IGD) and HyperVolume (HV), indicating that the proposed algorithm can effectively balance convergence and diversity.