An Effective Solution to Nonlinear Bilevel Programming Problems Using Improved Particle Swarm Optimization Algorithm

Abstract

Nonlinear bilevel programming has a hierarchical structure and has been proved to be NP-hard. In this paper, a class of nonlinear bilevel programming problems is studied. The follower's problem is converted into a series of constraints for the leader's problem by using KKT optimality conditions. For the resultant problem, a method called Chen-Harker-Kanzow-Smalen smoothing method is applied to solve this kind of problem. Later, an improved particle swarm optimization algorithm is designed, and two numerical examples are used to validate the algorithm, and the results show that the algorithm is effective.