基于层次粒子群算法的非线性双层规划问题求解策略

Solution strategy for bi-level nonlinear programming problem based on hierarchical particle swarm optimization

在交通与物流网络系统规划中的许多决策问题可以归结为双层规划模型,这类问题大多属于非凸优化问题.现有算法要么难以获得全局最优解,要么在解决大规模问题时存在算法复杂度及计算效率问题.本文基于进化博弈及多目标优化非支配排序的思想设计了层次粒子群算法,通过两个粒子群算法的交互迭代来模拟决策者之间的博弈寻优过程,从而获得使各方利益最大化的双层规划问题的最优解.最后通过测试函数验证算法的有效性.

Many decision-making problems in traffic and logistics network system planning can be formu- lated as bilevel programming models, which are intrinsically nonconvex and existing algorithms are either difficult to obtain the global optimal solution or to solve large scale problems with the complexity and efficiency issues. In this paper, based on the idea of evolution game and multi-objective optimization non- dominated sort, a hierarchical particle swarm algorithm for the model has been designed, by the interaction of two particle swarm algorithm iterations to simulate the interaction between policy-makers during the game searching, and to obtain the optimal solution of bilevel programming problems, in order to maximize the interests of all parties. Finally, the application of the model and its algorithm are illustrated with test function.