基于ε-约束方法的增广Lagrangian多目标协同进化算法

A Coevolutionary Algorithm Based on ε-Constraint and Augmented Lagrangian Methods

介绍了一种利用协同进化算法求解多目标优化问题的算法。这种算法首先采用ε- 约束方法对多目标优化问题进行处理 ,使其转化为一个单目标带约束的优化问题 ;然后 ,采用增广Lagrangian方法把这个单目标约束优化问题转化成一个存在鞍点的二人零和博弈问题 ;最后 ,利用协同进化的思想 ,用两个种群分别表示目标函数和约束这两个局中人 ,对这个二人零和博弈问题求解。进化过程中的选择、重组和变异算子均采用简单遗传算法(SGA)的机制。通过对两个实验测试问题的研究可以看出 ,这种算法比其它同类进化算法所得的结果要精确、稳定。

This paper introduces a coevolutionary method developed for solving multiobjective optimization problems. First theε-constraint method is adopted to transform a multiobjective optimization problem into a constrained optimization problem. Second the augmented Lagrangian method is taken to transform the constrained optimization problem into a zero-sum game with the saddle-point solution. At last, based on the concept of the coevolution, two populations are used to present the two players and solve the equilibrium point. Selection, recombination and mutation are done by using the evolutionary mechanism of simple genetic algorithm (SGA). Some benchmark problems are solved, which demonstrates that the method introduced here is better than other similar evolutionary algorithms in accuracy and stabilization.