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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 the application of genetic algorithm in solving nonsmooth optimization problems. The non-smooth optimization method is devoted to solve the mathematical programming problem that objective function is continuous and non-differentiable function. Because of the non-differentiability of the objective function, the traditional gradient-based deterministic algorithm encounters obstacles in solving nonsmooth problems. Therefore, genetic algorithms that do not require gradient information but only require the objective function value information are used to solve the nonsmooth problem Is a good choice. Genetic algorithm is an optimization algorithm based on the process of biological genetic variation in nature. It first encodes the feasible solutions of the problem. The coding methods include 0-1 coding, Gray coding and real coding, and then use crossover operator, mutation operator And select operator to generate next generation population. When the population reaches a certain number of iterations, the optimal chromosome in the population will converge to the optimal solution to the original problem. The genetic algorithm designed in this paper is based on the real number coding, operators are used arithmetic crossover operator, non-uniform mutation operator, the best choice operator.