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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.
Real-coded multi-objective evolutionary algorithms often use simulated binary crossover (SBX) operators.By comparing the mutation operators in SBX and evolutionary strategies and introducing discrete reorganization operators in evolutionary strategies A Normal Distribution Crossover (NDX) Operator. Firstly, NDX and SBX operators are compared and analyzed in a one-dimensional search space instance, and then the NDX operator is applied to the steady state proposed by Deb et al. MOEA (ε-MOEA / NDX) algorithm of NDX operator is used in the optimization of multi-objective optimization set of 10 functions of ZDT and DTLZ The experimental results and analysis show that the quality of the Pareto optimal solution set obtained by ε-MOEA of NDX is obviously better than the classical algorithms ε-MOEA / SBX and NSGA-Ⅱ.