基于一种新模型的多目标遗传算法及性能分析

Multi-objective genetic algorithm based on a new model and analysis of its performance

在多目标优化中,各目标通常相互冲突,其最优解往往有无穷多个,如何在最优解集中求出一组分布均匀且数量多的Pareto最优解供决策者选择十分重要.本文给出了多目标优化的一种新解法.首先定义了种群序值的理想方差和种群密度的方差,然后把目标个数任意的多目标函数优化问题Ⅰ转化成了用种群序值的理想方差和种群密度的方差构成的两个目标函数的优化问题Ⅱ,并对转化后的优化问题Ⅱ提出了一种新的多目标遗传算法(RDMOEA).计算机仿真表明RDMOEA算法对不同的实验函数均可求出在最优解集合中分布均匀且数量充足的Pareto最优解.

Multi-objective optimization problems often involve incommensurable and competing objectives, and the number of their Pareto optimal solutions is usually infinite, thus it is very important to find a sufficient number of uniformly distributed Pareto optimal solutions for the decision maker. A novel algorithm is presented to solve the multiobjective optimization problem in this paper. The ideal variance of rank of the population and the variance of density of the population are firstly given. Using the ideal variance of rank of the population and the variance of density of the population as two objective functions, the multi-objective optimization problem Ⅰ is then converted into a bi-objective optimization problem Ⅱ. For the transformed problem Ⅱ, a novel multi-objective optimization genetic algorithm （RDMOEA） is also proposed. Finally, computer simulations for the three difficult standard benchmark functions are performed to verify the results.