Structural and Multidisciplinary Optimization

, Volume 52, Issue 4, pp 813–826

Improved particle swarm optimization algorithm using design of experiment and data mining techniques

RESEARCH PAPER

DOI: 10.1007/s00158-015-1271-7

Cite this article as:
Liu, Z., Zhu, P., Chen, W. et al. Struct Multidisc Optim (2015) 52: 813. doi:10.1007/s00158-015-1271-7

Abstract

Particle swarm optimization (PSO) is a relatively new global optimization algorithm. Benefitting from its simple concept, fast convergence speed and strong ability of optimization, it has gained much attention in recent years. However, PSO suffers from premature convergence problem because of the quick loss of diversity in solution search. In order to improve the optimization capability of PSO, design of experiment method, which spreads the initial particles across a design domain, and data mining technique, which is used to identify the promising optimization regions, are studied in this research to initialize the particle swarm. From the test results, the modified PSO algorithm initialized by OLHD (Optimal Latin Hypercube Design) technique successfully enhances the efficiency of the basic version but has no obvious advantage compared with other modified PSO algorithms. An extension algorithm, namely OLCPSO (Optimal Latin hypercube design and Classification and Regression tree techniques for improving basic PSO), is developed by consciously distributing more particles into potential optimal regions. The proposed method is tested and validated by benchmark functions in contrast with the basic PSO algorithm and five PSO variants. It is found from the test studies that the OLCPSO algorithm successfully enhances the efficiency of the basic PSO and possesses competitive optimization ability and algorithm stability in contrast to the existing initialization PSO methods.

Keywords

Particle swarm optimization Design of experiment Data mining Optimization search Global optimization Algorithm stability 

Nomenclature

PSO

Particle Swarm Optimization

OLHD

Optimal Latin Hypercube Design

OLCPSO

Optimal Latin hypercube design and Classification and regression tree techniques for improving basic PSO

DOE

Design of experiments

CART

Classification and Regression Tree

ESE

Enhanced Stochastic Evolutionary

GPSO

Particle Swarm Optimization initialized by Gaussian distribution

EPSO

Particle Swarm Optimization initialized by Exponential distribution

LNPSO

Particle Swarm Optimization initialized by Lognormal distribution

VC-PSO

Particle Swarm Optimization initialized by Vander Corput sequence

SO-PSO

Particle Swarm Optimization initialized by Sobol sequence

D

Dimension

X

The position vector of a particle

V

The velocity vector of a particle

Pi

The best previously visited position vector

Pg

The global best position vector of the swarm

t

Generation number

c1

Cognitive scaling parameter

c2

Social scaling parameter

w

Inertia weight

r1

Random numbers

r2

Random numbers

y

Vector of classes

M

Number of response

N

Numbers of design variable

xc

Matrix of design variable

xcjR

Best splitting value of variable xcj

ϕp

Optimal criterion for design of experiment

di

Euclidean distance

Ji

Number of pairs separated by di in the design

s

Number of distinct distance values

p

A positive integer

Th

Threshold of the cooling and warming schedule

XE

Current design of DOE

Xtry

Best design based on ESE

S

A uniform random number between 0 and 1

P

Particle number

sf

Sample ratio factor

tc

Supplement coefficient

L

Length of variable’s range

Ps

Particle number in sub-region

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.The State key laboratory of Mechanical System and Vibration, Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures, School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China
  2. 2.Department of Mechanical EngineeringNorthwestern UniversityEvanstonUSA
  3. 3.Research and advanced EngineeringFord Motor CompanyDearbornUSA

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