A New Bi-level PSO Algorithm based on Dynamic Constraint Processing and Approximate Navigation

Bi-level optimization problems with constraints are well known for wide applications and difficulties. A new particle swarm optimization algorithm (PSO) with dynamic constraint processing is proposed. First, we divide constraints into three cases and design a new PSO based crossover operator to dynamically deal with constraints; second, a normal distribution is added into PSO to work as mutation operator, which will enhance the diversity of the swarm and navigate the search direction. Finally, we give the convergence proof of the proposed algorithm.

I. Introduction

In the real world, there are many complex problems described as bi-level problems. This kind of problems have a hierarchical relationship [1]. There are many similar problems , such as environmental economics [2], Stackelberg Games [3] , [4] and structural optimization [5], [6]. All of these problems have the same characteristics. They have two levels need to be optimized, and the two levels have a clear hierarchy. Because of its complicated structure, we will introduce the bi-level optimization to make a clear description.