求解非光滑优化问题的改进大洪水算法

Improved Great Deluge Algorithm for Nonsmooth Optimization Problems

应用启发式算法求解非光滑优化问题,解决基于次梯度信息的确定性算法在求解时困难较大的问题.首先分析了基本大洪水算法的优化机理及特征并给出其求解步骤,然后针对无约束及盒子约束问题分别设计了改进的大洪水算法,将基本大洪水算法所依赖的参数up省去.对于无约束情形,提出了进行邻域搜索的随机行走法;对于盒子约束情形,提出了选择初始可行点的方法和进行邻域搜索的混沌优化算法.最后通过算例进行测试并与其他算法进行对比,测试结果表明了改进的大洪水算法在求解非光滑优化问题时的有效性与优越性,故其可作为求解非光滑优化问题的一种实用方法.

Since nonsmooth optimization problems are difficult to solve by deterministic algorithms based on subgradient information,the heuristic algorithm was considered.The optimization mechanism and characteristics of the basic great deluge algorithm（GDA）were analyzed and the solving steps were given as well.Then improved GDAs for unconstrained and box constrained problems were proposed respectively,where the parameter up was omitted.For the unconstrained case,the random walk algorithm with respect to neighborhood search was proposed.For the box constrained case,the method of choosing a feasible initial point and a chaos optimization algorithm with respect to neighborhood search were proposed.The improved GDAs were tested by taking several typical nonsmooth optimization problems as examples and were compared with other algorithms.The test results show that the improved GDAs are efficient and superior to other algorithms mentioned in the paper.So it can be used as a practical method for solving nonsmooth optimization problems.