A Framework for Constrained Optimization Problems Based on a Modified Particle Swarm Optimization

Biwei Tang,Zhanxia Zhu,Jianjun Luo

doi:10.1155/2016/8627083

Abstract

This paper develops a particle swarm optimization (PSO) based framework for constrained optimization problems (COPs). Aiming at enhancing the performance of PSO, a modified PSO algorithm, named SASPSO 2011, is proposed by adding a newly developed self-adaptive strategy to the standard particle swarm optimization 2011 (SPSO 2011) algorithm. Since the convergence of PSO is of great importance and significantly influences the performance of PSO, this paper first theoretically investigates the convergence of SASPSO 2011. Then, a parameter selection principle guaranteeing the convergence of SASPSO 2011 is provided. Subsequently, a SASPSO 2011-based framework is established to solve COPs. Attempting to increase the diversity of solutions and decrease optimization difficulties, the adaptive relaxation method, which is combined with the feasibility-based rule, is applied to handle constraints of COPs and evaluate candidate solutions in the developed framework. Finally, the proposed method is verified through 4 benchmark test functions and 2 real-world engineering problems against six PSO variants and some well-known methods proposed in the literature. Simulation results confirm that the proposed method is highly competitive in terms of the solution quality and can be considered as a vital alternative to solve COPs.

Highlights

Over the last few decades, constrained optimization problems (COPs) have rapidly gained increasing research interests, since they are frequently encountered in different areas such as path planning [1], resource allocation [2], and economic environmental scheduling [3] to name but a few
Considering the advantage and the disadvantage of SPSO 2011, we propose a modified particle swarm optimization (PSO) algorithm, called SASPSO 2011, which is developed based on SPSO 2011
Considering the weakness of SPSO 2011, we propose a modified PSO algorithm, which is developed based on SPSO 2011 and is named SASPSO 2011

Summary

Introduction

Over the last few decades, constrained optimization problems (COPs) have rapidly gained increasing research interests, since they are frequently encountered in different areas such as path planning [1], resource allocation [2], and economic environmental scheduling [3] to name but a few. SASPSO 2011 is developed based on SPSO 2011, there are significant differences between these two algorithms, since (1) a novel self-adaptive strategy is proposed for finetuning the three control parameters of particles in SASPSO 2011,. According to the basic philosophies noted above, SPSO 2011 is a nonstagnation algorithm, it cannot strike a good balance between exploration and exploitation, since its three control parameters remain unchanged and there is no difference between φ1 and φ2. The main purpose of the development of this PSO is to adaptively adjust the exploration and exploitation abilities of SASPSO 2011 To achieve this goal, a novel self-adaptive strategy that is used to update the three control parameters of particles in SASPSO 2011 is proposed as follows: wi

Analytical Investigations on SASPSO 2011

Local Convergence Proof of SASPSO 2011

Applying SASPSO 2011 for Solving COPs

Numerical Simulations and Analysis

Methods

Conclusion and Future Work