多个体参与交叉的Pareto多目标遗传算法

摘要

Pareto multiobjective genetic algorithm is one kind of vector optimization methods derived from concept of Pareto optimal,and the whole Pareto optimal set can be got using this method. Because conventional Pareto GA runs with two chromosomes crossover, it consumes much time on Niche which makes the efficency of this algorithm somewhat low. In this paper, a new Pareto multiobjective GA with multiple-chromosomes crossover is presented,and the individual is expressed with real-valued representations which makes it much faster than conventional algorithms. Based on the proof of corresponding schema theorem, variance and entropy are proposed as measurements of diversity of population in genetic algorithms. The influence that the Pareto MOGA with multiple-chromosomes crossover acts upon variance and entropy is analyzed. At last, one example is presented to compare between method in this paper and traditional methods so as to prove the superiority of this method.%Pareto多目标遗传算法是利用Pareto最优的概念发展出的一种求解多目标优化问题的向量优化方法，能够得到Pareto最优解集。由于采用常规的两个体参与交叉的遗传算法，使整个算法耗费在小生境(Niche)算子上的时间太多，导致算法的效率较低。本文发展出多个体参与交叉的Pareto多目标遗传算法，群体中的个体采用真实值表示，使该算法的速度大大提高，同时证明了相应的模式定理，并提出用方差和熵来分析该算法对解群多样性的影响。最后用算例说明了采用多个体参与交叉的Pareto多目标遗传算法与常规算法比较的结果，证明了本文提出算法的优越性。