Structural and Multidisciplinary Optimization

, Volume 52, Issue 4, pp 813–826 | Cite as

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

  • Zhao Liu
  • Ping ZhuEmail author
  • Wei Chen
  • Ren-Jye Yang


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.


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



Particle Swarm Optimization


Optimal Latin Hypercube Design


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


Design of experiments


Classification and Regression Tree


Enhanced Stochastic Evolutionary


Particle Swarm Optimization initialized by Gaussian distribution


Particle Swarm Optimization initialized by Exponential distribution


Particle Swarm Optimization initialized by Lognormal distribution


Particle Swarm Optimization initialized by Vander Corput sequence


Particle Swarm Optimization initialized by Sobol sequence




The position vector of a particle


The velocity vector of a particle


The best previously visited position vector


The global best position vector of the swarm


Generation number


Cognitive scaling parameter


Social scaling parameter


Inertia weight


Random numbers


Random numbers


Vector of classes


Number of response


Numbers of design variable


Matrix of design variable


Best splitting value of variable xc j


Optimal criterion for design of experiment


Euclidean distance


Number of pairs separated by d i in the design


Number of distinct distance values


A positive integer


Threshold of the cooling and warming schedule


Current design of DOE


Best design based on ESE


A uniform random number between 0 and 1


Particle number


Sample ratio factor


Supplement coefficient


Length of variable’s range


Particle number in sub-region



The authors acknowledge the support from Ford University Research Program (URP) and the Adjunct Professor position provided by the Shanghai Jiao Tong University to Dr. Wei Chen.


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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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