求解无约束优化问题的知识进化算法及其收敛性分析

Knowledge evolution algorithm for solving unconstraint optimization problems and its convergence analysis

中文关键词  无约束优化  知识进化  传承算子  创新算子  更新算子  收敛性

英文关键词  unconstraint optimization  knowledge evolution  inheritance operator  innovation operator  update operator  convergence

中文摘要

      针对传统方法的随机盲目性和易陷入局部最优值等缺陷, 提出一种求解无约束优化问题的知识进化算法(简称为UOP-KEA), 并对算法的全局收敛性进行了分析. 该算法的主要思想是: 首先建立初始知识库, 然后利用传承算子来实现对优秀知识个体的传承, 利用创新算子来产生新的知识个体, 利用更新算子来更新知识库, 从而实现知识的进化, 最后从知识库的最优知识个体中获取问题的最优解. 将该算法应用于无约束非线性测试函数的最小值优化求解, 获得了成功的结果. 与遗传算法相比, 该算法可以使用较小的种群规模, 以较快的速度寻找到全局最优解, 表明了它的可行性和有效性.

英文摘要

      To deal with the limitations in traditional algorithms, such as the random blindness and the traps of the local optima, we develop a knowledge evolution algorithm for solving unconstraint optimization problems(called UOP-KEA), and analyze its global convergence. Firstly, an initial knowledge base is formed; next, excellent knowledge individuals are inherited by inheritance operator; new knowledge individuals are produced by innovation operator; knowledge base is updated by update operator. Thus, knowledge evolution is realized. Finally, the optimal solution of issues is obtained from the optimal knowledge individuals. Experiments have been performed on optimization of unconstraint nonlinear test functions. Compared with genetic algorithms, this algorithm finds the global optimal solution with smaller size of population and in a higher speed. The successful results show that this algorithm is feasible and valid.