Solving Unconstrained Global Optimization Problems via Hybrid Swarm Intelligence Approaches

Jui-Yu Wu

doi:10.1155/2013/256180

Abstract

Stochastic global optimization (SGO) algorithms such as the particle swarm optimization (PSO) approach have become popular for solving unconstrained global optimization (UGO) problems. The PSO approach, which belongs to the swarm intelligence domain, does not require gradient information, enabling it to overcome this limitation of traditional nonlinear programming methods. Unfortunately, PSO algorithm implementation and performance depend on several parameters, such as cognitive parameter, social parameter, and constriction coefficient. These parameters are tuned by using trial and error. To reduce the parametrization of a PSO method, this work presents two efficient hybrid SGO approaches, namely, a real-coded genetic algorithm-based PSO (RGA-PSO) method and an artificial immune algorithm-based PSO (AIA-PSO) method. The specific parameters of the internal PSO algorithm are optimized using the external RGA and AIA approaches, and then the internal PSO algorithm is applied to solve UGO problems. The performances of the proposed RGA-PSO and AIA-PSO algorithms are then evaluated using a set of benchmark UGO problems. Numerical results indicate that, besides their ability to converge to a global minimum for each test UGO problem, the proposed RGA-PSO and AIA-PSO algorithms outperform many hybrid SGO algorithms. Thus, the RGA-PSO and AIA-PSO approaches can be considered alternative SGO approaches for solving standard-dimensional UGO problems.

Highlights

An unconstrained global optimization (UGO) problem can generally be formulated as follows: Minimize f (x), x = [x1, x2, . . . , xN]T ∈ RN, (1)where f(x) is an objective function and x represents a decision variable vector
The numerical results indicate that the real-coded GA (RGA)-particle swarm optimization (PSO) algorithm can obtain the global minimum for each test UGO problem since these MEs equal or closely approximate “0,” and the real-coded genetic algorithm-based PSO (RGA-PSO) algorithm has an acceptable mean computational CPU time (MCCT) for each test problem (TP)
Numerical results indicate that the algorithm-based PSO (AIA-PSO) algorithm can obtain the global minimum for each test UGO problem since these MEs equal or closely approximate “0,” and that the artificial immune algorithms (AIAs)-PSO algorithm has an acceptable MCCT for each TP

Summary

Introduction

Many conventional nonlinear programming (NLP) techniques, such as the golden search, quadratic approximation, Nelder-Mead, steepest descent, Newton, and conjugate gradient methods, have been used to solve UGO problems [1]. Such NLP methods have difficulty in solving UGO problems when an objective function of an UGO problem is nondifferential. Many stochastic global optimization (SGO) approaches developed to overcome this limitation of the traditional NLP methods include genetic algorithms (GAs), particle swarm optimization (PSO), ant colony optimization (ACO), and artificial immune algorithms (AIAs). Chen [3] presented a two-layer PSO method to solve nine UGO problems. Kelsey and Timmis [6] presented an AIA method based on the clonal selection principle for solving 12 UGO problems

Methods

Results

Conclusion