基因算法在求解非光滑优化问题中的应用(英文)

The Application of Genetic Algorithm in Solving Nonsmooth Optimization Problems

本文考虑了基因算法在求解非光滑优化问题中的应用。非光滑优化方法致力于求解目标函数为连续不可微函数的数学规划问题。因为目标函数的不可微性,传统的以梯度为基础的确定性算法在求解非光滑问题时会遇到障碍,所以运用不需要梯度信息而只需要目标函数值信息的遗传算法来求解非光滑问题是一个不错的选择。遗传算法是基于自然界生物遗传变异过程而设计的一种优化算法,它首先对问题的可行解进行编码,编码方法有0-1编码,格雷编码和实数编码,然后运用交叉算子,变异算子和选择算子产生下一代种群。当种群迭代达到一定的次数后,种群中的最优染色体就会收敛到原问题的最优解。本文设计的基因算法基于实数编码,算子分别采用算术交叉算子,非一致变异算子,最佳选择算子。

This paper considers an application of genetic algorithm in solving nonsmooth optimization problems. Nonsmooth optimization devote itself to solve programming problems whose objective function are continuous nondifferentiable. Since the objective function is nondifferentiable, the classical deterministic methods based on gradient may confront numerical dif ficuhies. Therefore, it would be a good choice to use genetic algorithm,in which j ust information of objective function value but not information of gradient is needed to solve nonsmooth optimization problems. Genetic algorithm is a stochastic meth od based on the evolutionary process of nature. It firstly codes the original optimization problem by means of binary enco ding,Gary encoding or real number encoding. And then the next population generation is generated by applying crossover operator, mutation operator and selection operator. When the iteration time approach a sufficiently large number, the best chromosome in the current population will converge to the optimal solution or approximately optimal solution of the origi nal problem. The genetic algorithm proposed in this paper uses real-number encoding, arithmetic crossover, nonuniform mutation. And it selects the best population size of individuals in the selection step. Some minimax problems, which are nonsmooth optimization problems,are tested and their results are compared with some deterministic nonsmooth optimiza- tion methods.