中文摘要：

为提高约束多目标优化算法的分布性和收敛性,提出一种基于双种群的约束多目标优化算法.首先,改进的Harmonic距离一方面去除了Pareto等级较差个体和较远个体的影响,从而改善可行解集的分布性;另一方面有效减少了计算量,可以提高算法效率.其次,新的不可行解集更新方式与可行解集紧密联系,保留目标函数值和约束违反度同时较优的个体,将有助于产生更优可行解,同时提高了种群的多样性和搜索效率.最后,新的变异策略充分利用最优可行解和优秀不可行解的优良信息来引导种群进化,很好地兼顾了探索和开发能力,进而平衡全局搜索和局部搜索.将提出算法与其他3种优秀的约束多目标进化算法在CTP测试集上进行对比实验,结果表明提出算法相比其他算法具有一定的优势,不仅提升了算法的收敛性能,而且保证了Pareto解集良好的分布性.

英文摘要：

In order to improve the distribution and convergence of constrained multi-objective optimization algorithms,this paper proposes a constrained multi-objective optimization algorithm based on dual populations.The improved Harmonic distance eliminates the effect of the individuals whose Pareto grade is weak and distance is far,consequently the distribution of population can be enhanced.Also it reduces the amount of calculation effectively and improves the efficiency of the suggested algorithm.Then,the new update method of the infeasible solution set is closely linked with the feasible solution set,and these infeasible individuals both the objective function value and the constraint violation are excellent can be retained,so the better feasible individuals will be produced in the following evolution process,and the diversity of the populations and the search efficiency are improved simultaneously.Finally,the new variation strategy makes full use of the information of the best feasible individuals and the good infeasible individuals,which ensures the good ability of exploration and exploitation and balances the global and local search.The proposed algorithm is compared with 3state-of-the-art constrained multi-objective optimization algorithms on CTP test problems.Simulation results show that the presented algorithm has certain advantages than other algorithms because it can ensure good convergence while it has uniform distribution.