Constrained particle swarm optimization using a bi-objective formulation

  • G. VenterEmail author
  • R. T. Haftka


This paper introduces an approach for dealing with constraints when using particle swarm optimization. The constrained, single objective optimization problem is converted into an unconstrained, bi-objective optimization problem that is solved using a multi-objective implementation of the particle swarm optimization algorithm. A specialized bi-objective particle swarm optimization algorithm is presented and an engineering example problem is used to illustrate the performance of the algorithm. An additional set of 13 test problems from the literature is used to further validate the performance of the newly proposed algorithm. For the example problems considered here, the proposed algorithm produced promising results, indicating that it is an approach that deserves further consideration. The newly proposed algorithm provides performance similar to that of a tuned penalty function approach, without having to tune any penalty parameters.


Constrained particle swarm optimization Multi-objective optimization Composite design problem 


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Mechanical and Mechatronic EngineeringStellenbosch UniversityStellenboschSouth Africa
  2. 2.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA

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