Application of particle swarm optimization based on CHKS smoothing function for solving nonlinear bilevel programming problem

Particle Swarm Optimization (PSO) is a new optimization technique originating from artificial life and evolutionary computation. It completes optimization through following the personal best solution of each particle and the global best value of the whole swarm. PSO can be used to solve nonlinear programming problems for global optimal solutions efficiently, so a novel approach based on particle swarm optimization is proposed to solve nonlinear bilevel programming problem (NBLP). In the proposed approach, applying Karush–Kuhn–Tucker (KKT) condition to the lower level problem, we transform the NBLP into a regular nonlinear programming with complementary constraints, which is sequentially smoothed by Chen-Harker-Kanzow-Smale (CHKS) smoothing function. The PSO approach is then applied to solve the smoothed nonlinear programming for getting the approximate optimal solution of the NBLP problem. Simulations on 5 benchmark problems and practical example about watershed water trading decision-making problem are made and the results demonstrate the effectiveness of the proposed method for solving NBLP.