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Constrained particle swarm optimization using a bi-objective formulation

RESEARCH PAPER

Abstract

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.

Keywords

Constrained particle swarm optimization Multi-objective optimization Composite design problem 

References

  1. Barbosa H, Lemonge A (2003) A new adaptive penalty scheme for genetic algorithms. Inf Sci 156(3–4):215–251CrossRefMathSciNetGoogle Scholar
  2. Bratton D, Kennedy J (2007) Defining a standard for particle swarm optimization. In: Proceedings of the 2007 IEEE swarm intelligence symposium. IEEE, Piscataway, pp 120–127CrossRefGoogle Scholar
  3. Coello Coello C (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191(11–12):1245–1287MATHCrossRefMathSciNetGoogle Scholar
  4. Deb K, Agarwal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Proceedings of the parallel problem solving from nature VI conference. Springer, New York, pp 849–858CrossRefGoogle Scholar
  5. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  6. Fletcher R, Leyffer S (2002) Nonlinear programming without a penalty function. Math Program 91(2):239–269MATHCrossRefMathSciNetGoogle Scholar
  7. Grosset L, LeRiche R, Haftka RT (2005) A double-distributed statistical algorithm for composite laminate optimization. Struct Multidiscipl Optim 31(1):49–59CrossRefGoogle Scholar
  8. Hamida B, Schoenauer M (2000) An adaptive algorithm for constrained optimization problems. In: Proceedings of the 6th conference on parallel problems solving from nature. Springer, New York, pp 529–539CrossRefGoogle Scholar
  9. Koziel S, Michalewicz Z (1999) Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evol Comput 7(1):19–44CrossRefGoogle Scholar
  10. Liang J, Runarsson T, Mezura-Montes E, Clerc M, Suganthan P, Coello Coello C, Deb K (2006) Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization. Technical report, Nanyang Technological University, SingaporeGoogle Scholar
  11. Liu CA (2007) New multiobjective PSO algorithm for nonlinear constrained programming problems. In: Advances in cognitive neurodynamics ICCN 2007. Springer, New York, pp 955–962Google Scholar
  12. Poon N, Martins J (2007) An adaptive approach to constraint aggregation using adjoint sensitivity analysis. Struct Multidiscipl Optim 34(1):61–73CrossRefGoogle Scholar
  13. Reyes-Sierra M, Coello Coello C (2005) Improving PSO-based multi-objective optimization using crowding, mutation and ϵ-dominance. In: Third international conference on evolutionary multi-criterion optimization, Guanajuato, 9–11 March 2005, pp 505–519Google Scholar
  14. Reyes-Sierra M, Coello Coello C (2006) Multi-objective particle swarm optimizers: a survey of the state-of-the-art. Int J Comput Intel Res 2(3):287–308MathSciNetGoogle Scholar
  15. Sienz J, Innocente M (2008) Trends in engineering computational technology, chap. particle swarm optimization: fundamental study and its application to optimization and to Jetty scheduling problems. Saxe-Coburg, Stirling, pp 103–126Google Scholar
  16. Surry P, Radcliffe N (1997) The COMOGA method: constrained optimisation by multi-objective genetic algorithms. Control Cybern 26(3):391–412MathSciNetGoogle Scholar
  17. Vanderplaats GN (2005) Numerical optimization techniques for engineering design, 4rd edn. Vanderplaats Research and Development, Colorado SpringsGoogle Scholar
  18. Venkatraman S, Yen G (2005) A generic framework for constrained optimization using genetic algorithms. IEEE Trans Evol Comput 9:424–435CrossRefGoogle Scholar
  19. Venter G, Sobieszczanski-Sobieski J (2003) Particle swarm optimization. AIAA J 41(8):1583–1589CrossRefGoogle Scholar
  20. Venter G, Sobieszczanski-Sobieski J (2004) Multidisciplinary optimization of a transport aircraft wing using particle swarm optimization. Struct Multidiscipl Optim 26(1):121–131CrossRefGoogle Scholar
  21. Venter G, Sobieszczanski-Sobieski J (2006) A parallel particle swarm optimization algorithm accelerated by asynchronous evaluations. J Aerosp Comput Inf Commun 3(3):123–137CrossRefGoogle Scholar
  22. Zhou Y, Li Y, He J, Kang L (2003) Multi-objective and MGG evolutionary algorithm for constrained optimization. In: The 2003 Congress on evolutionary computation, Canberra, 8–12 December 2003, pp 1–5Google Scholar

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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