求解带约束函数优化的两级自适应遗传算法

针对带约束的非线性函数优化问题 ,提出一个两级自适应遗传算法。根据待优化函数和约束构造拉格朗日对偶函数 ,在下级对给定的拉格朗日乘子 ,用遗传算法搜索变量的最优解 ;在上级针对拉格朗日对偶函数 ,用遗传算法搜索拉格朗日乘子的最优解。采用自适应的方法 ,根据个体的适配值和种群的适配值统计特性确定交叉概率和变异概率。计算结果表明 ,该算法是有效的。

Using Two-Level Adaptive Genetic Algorithm to Sovle Constrained Function Optimization Problems

A two-level adaptive genetic algorithm is proposed to solve constrained nonlinear function optimization problems. At first, the Lagrangian function is constructed according to the optimization function and constraints. At the lower level, genetic algorithm is used to search the optimal values of variables for fixed Lagrangian multipliers. At the upper level, genetic algorithm is used to search the optimal values of Lagrangian multipliers to the Lagrangian function. The probabilities of crossover and mutation are adaptively determined according to fitnesses and fitness statistics of chromosomes. Computation shows that this algorithm is efficient.