求解非线性极大极小问题的一种新的混合算法

A New Hybrid Approach for Nonlinear Mini-max Problems

对于一类非线性极大极小问题,由于凝聚函数法简单且易实施,所以一直是较流行的光滑处理技术,然而选择一个合适的惩罚因子不是一件容易的事。本文通过引入Hook-jeveese搜索法和可行基规则,提出一个求解非线性极大极小问题的新的混合算法—Hook-jeveese搜索法和与可行基规则相结合粒子群算法的混合算法。与凝聚函数法相比,可行基规则不需要额外的参数,且指引粒子迅速飞向可行域。利用两个典型实例问题进行计算比较,计算结果表明了新算法是求解非线性极大极小问题的一个高效的算法,而且获得了一些比以往文献精度更好的解。

For a class of nonlinear min-max problems,because aggregate function method is simple and easy to implement,it has always been more popular smooth processing technology,However,it is not easy to choose a suitable penalty factor.By employing the feasibility-based rule,this paper proposes the hybrid Hook-jeveese search method and particle swarm optimization with a feasibility-based rule for nonlinear min-max problems.Compared with the aggregate function,feasible basis rule does not require additional parameters,and it dictates particles to the feasible domain fly quickly.Simulation and comparisons based on two well-known problems demonstrate the effectiveness,efficiency and robustness on initial populations of the proposed method.Moreover,the new method obtains some solutions better than those previously reported in the literature.