一种基于正态分布交叉的ε-MOEA

A Normal Distribution Crossover for ε-MOEA

实数编码的多目标进化算法常使用模拟二进制交叉(simulated binary crossover,称SBX)算子.通过对SBX以及进化策略中变异算子进行对比分析,并引入进化策略中的离散重组算子,提出了一种正态分布交叉(normal distribution crossover,称NDX)算子.首先在一维搜索空间实例中对NDX与SBX算子进行比较和分析,然后将NDX算子应用于Deb等人提出的稳态多目标进化算法ε-MOEA(ε-dominance based multiobjective evolutionary algorithm)中.采用NDX算子的ε-MOEA(记为ε-MOEA/NDX)算法在多目标优化标准测试集ZDT和DTLZ的10个函数上进行了实验比较.实验结果和分析表明,采用NDX的ε-MOEA所求得的Pareto最优解集质量明显优于经典算法ε-MOEA/SBX和NSGA-Ⅱ.

The simulated binary crossover （SBX） has been extensively adopted in the real-coded multiobjective evolutionary algorithms （MOEAs）. Through the comparisons and analyses of the SBX and the mutation operator in the evolution strategy （ES）, this paper proposes a normal distribution crossover （NDX） with the introduction of discrete recombination operator in ES. The NDX and SBX operators are compared and analyzed through an example designed in the one dimensional search space, and then the NDX is applied to a steady-state multiobjective evolutionary algorithm named ε-MOEA （ε-dominance based multiobjective evolutionary algorithm） proposed by Deb, et al. The algorithm ε-MOEA with NDX （ε-MOEA/NDX） has been tested and compared on the 10 benchmark functions taken from the ZDT and DTLZ standard test suites. Experimental results demonstrate that algorithm ε-MOEA/NDX is distinctly superior to the ε-MOEA/SBX and NSGA-Ⅱ algorithms, which are representatives of the statε-of-thε-art in the area.