An Adaptive Hybrid Particle Swarm Optimizer for Constrained Optimization Problem

Abstract

Particle Swarm Optimization (PSO) is a well-known nature-inspired algorithm that is inspired by the social behavior of bird flocking and fish schooling. It has proved efficient in solving real-time problems due to its simplicity and good exploitation ability. However, due to poor exploration of search space, PSO gets trapped in local optima and gives less accurate results. On the other hand, Butterfly Optimization Algorithm (BOA) is good in exploration but converges slowly. This paper proposes a novel hybrid based on PSO and BOA, namely PSOBOA with few improvements based on the advantage and uniqueness of these algorithms. Firstly, a parameter-free penalty function is used to handle constraint violations so that the search process does not slacken when handling the constraints. Secondly, a self-adaptive approach has been adopted in PSO as well as BOA to ensure a smooth transition from exploration to exploitation, and no user interference. Thirdly, to improve the convergence rate and avoid local optima stagnation, a conditional approach has been used in the local and global search of BOA. The proposed algorithm PSOBOA overcomes the shortcomings of PSO and BOA and maximizes the performance. It is applied to solve structural optimization problems, such as pressure vessel design and welded-beam design problem, where the objectives, decision variables, and constraints are different. The experimental results and the convergence curves demonstrate better optimization performance of PSOBOA compared with quite a few state-of-the-art algorithms.