基于粒子群算法的非线性二层规划问题的求解算法

Particle Swarm Optimization Based Approach to Solving Nonlinear Bilevel Programming Problems

粒子群算法(Particle Swarm Optimization,PSO)是一种新兴的优化技术,其思想来源于人工生命和演化计算理论。PSO通过粒子追随自己找到的最好解和整个群的最好解来完成优化。该算法简单易实现,可调参数少,已得到了广泛研究和应用。本文根据该算法能够有效的求出非凸数学规划全局最优解的特点,对非线性二层规划的上下层问题求解,并根据二层规划的特点,给出了求解非线性二层规划问题全局最优解的有效算法。数值计算结果表明该算法有效。

Particle swarm optimization （PSO） is a new optimization technique originating in artificial life and evolutionary computation. It completes the optimization following the personal best solution of each particle and the global best value of the whole swarm. PSO can be easily implemented and few parameters need to be tuned. It has been successfully applied to many areas. According to particle swarm optimization non-convex mathematical problems of global optimization, the upper-level and lower-level problems of nonlinear bilevel programming problem （BPP） can be solved, and according to the feature of bilevel programming, an efficient algorithm is presented in solving nonlinear BPP in this paper. The numerical computation results indicate the proposed algorithm is effective.