基于差分进化与NSGA-Ⅱ的多目标优化算法

摘要

In order to avoid conflict between the sub objectives and improve the quality of Pareto optimal solution for the multi-objective optimization problem,a Hybrid algorithm based on Differential Evolution(DE)and Non-dominated Sorting Genetic Algorithm Ⅱ(HDE-NSGA-Ⅱ) is proposed.First of all,DE algorithm with self-adaptive parameters is used for mutation and crossover operations of initial population,so that population diversity is improved.Secondly,a new population marking strategy is adopted to dominate the initial population and testing population of DE to obtain a new population whose individuals are marked.The strategy enables DE to dispose multi-objective problem.Finally,the new population,as the initial population of NSGA-Ⅱ,will generate the next generation population by NSGA-Ⅱ.The quality of Pareto optimal solutions will be further promoted by this step.Four multi-objective benchmark functions are tested by HDE-NSGA-Ⅱ,NSGA-Ⅱ and SADE.Experimental results show that the convergence rate of the proposed algorithm is faster and the spatial distributions of Pareto optimal solution set is more uniform than the other two algorithms.%为避免多目标优化过程中子目标相互冲突，提高 Pareto 最优解的质量，提出一种基于差分进化（DE）和第二代非支配遗传算法（NSGA-Ⅱ）的混合算法。采用带有自适应参数的 DE 算法对初始种群进行变异和交叉操作，以提高种群的多样性。应用新种群标记策略对 DE的初始种群和测试种群进行支配得到新种群，并标记其中每个个体，使 DE能够处理多目标问题。将新种群作为 NSGA-Ⅱ的初始种群，通过 NSGA-Ⅱ产生下一代种群，进一步提升 Pareto最优解的质量。使用4个基准多目标函数进行测试，结果表明，与 NSGA-Ⅱ和 SADE算法相比，该算法的收敛速度更快，Pareto最优解集空间分布更均匀。