约束优化距离函数算法的推广

Generalization of Distance Algorithm for Constrained Optimization

距离函数算法是一种适用于求解凸规划的算法 ,本文对其作了推广 .用均值 -水平集代替原算法的中心点来分割可行域 ,使其能求解带非线性不等式约束的总体最优化问题 .首先证明了算法的收敛性 ;其次 ,在算法的具体实现中 ,对现有的均值 -水平集方法作了改进 ,当目标函数是多峰函数特别是具有多个总极值点时可以提高计算效率 ,并对迭代时投点的统计指标 (即接受点数量 )作了定量讨论 ,给出了投点密度条件 ;最后 ,用两个总体最优化算例验证了算法的有效性 .

The distance algorithm is an approach to solve convex programming problem. In this paper, its center point was replaced by mean value level set, then it was generalized to solve nonlinear constrained global optimization problem. Firstly, the convergency of the algorithm was proved. Secondly, when it was implemented by “mean value level set”, an approach named “combination” was proposed, and it can improve the algorithm's efficiency when the objective function has several local optimzations. At the same time, the density condition about the amount of accepted point was discussed. Finally, two examples were tested.