一种有效的解无约束全局优化的进化算法

Efficient evolutionary algorithm for unconstraint global optimization

中文关键词  全局优化  进化算法  全局收敛性

英文关键词  global optimization  evolutionary algorithm  global convergence

中文摘要

      为了解决进化算法在求解全局优化时易陷入局部最优和收敛速度慢的问题, 设计了一个杂交算子, 利用种群中最好点与其他点间的关系确定搜索方向, 从而快速地找到实值函数的下降方向, 一旦算法找到优于种群中最好点的点, 利用所构造的两条直线交点的投影对其进行进一步优化, 使函数值更迅速地下降. 提出了适合杂交算子的初始种群生成方法. 设计了一个既能提高收敛速度又能摆脱局部最优的变异算子以增强算法的效果. 在此基础上, 提出了一个求解全局优化问题的高效进化算法, 并从理论上证明了全局收敛性, 从数值上验证了有效性.

英文摘要

      In solving global optimization problems, evolutionary algorithms converge slowly and tend to be trapped in local optimal solutions. A crossover operator is designed which searches the descent-directions based on the relationship between the best individual and the others in the population. Once it finds an individual better than the best one in the population, the objective function is further optimized by using the projection of the intersection of two constructed lines, so that the function can decrease faster. A method is presented to generate the initial population for the crossover operator. To improve the performance of the algorithm, a mutation operator which increases the convergence rate and avoids to be trapped in the local optima is given. Based on all these, an evolutionary algorithm for global optimization is proposed and its global convergence is proved. Numerical results show the efficiency of the proposed algorithm for all test functions.