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A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems

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Abstract

In the real-world applications, most optimization problems are subject to different types of constraints. These problems are known as constrained optimization problems (COPs). Solving COPs is a very important area in the optimization field. In this paper, a hybrid multi-swarm particle swarm optimization (HMPSO) is proposed to deal with COPs. This method adopts a parallel search operator in which the current swarm is partitioned into several subswarms and particle swarm optimization (PSO) is severed as the search engine for each sub-swarm. Moreover, in order to explore more promising regions of the search space, differential evolution (DE) is incorporated to improve the personal best of each particle. First, the method is tested on 13 benchmark test functions and compared with three stateof-the-art approaches. The simulation results indicate that the proposed HMPSO is highly competitive in solving the 13 benchmark test functions. Afterward, the effectiveness of some mechanisms proposed in this paper and the effect of the parameter setting were validated by various experiments. Finally, HMPSO is further applied to solve 24 benchmark test functions collected in the 2006 IEEE Congress on Evolutionary Computation (CEC2006) and the experimental results indicate that HMPSO is able to deal with 22 test functions.

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References

  1. Michalewicz Z, Schoenauer M. Evolutionary algorithm for constrained parameter optimization problems. Evolutionary Computation, 1996, 4(1): 1–32

    Article  Google Scholar 

  2. Coello Coello C A. Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Computer Methods in Applied Mechanics and Engineering, 2002, 191(11–12): 1245–1287

    Article  MATH  MathSciNet  Google Scholar 

  3. Mezura-Montes E, Coello Coello C A. A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Transactions on Evolutionary Computation, 2005, 9(1): 1–17

    Article  Google Scholar 

  4. Cai Z, Wang Y. A multiobjective optimization-based evolutionary algorithm for constrained optimization. IEEE Transactions on Evolutionary Computation, 2006, 10(6): 658–675

    Article  Google Scholar 

  5. Wang Y, Cai Z, Zhou Y, Zeng W. An adaptive trade-off model for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation, 2008,12(1): 80–92

    Article  Google Scholar 

  6. Wang Y, Cai Z, Guo G, Zhou Y. Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems. IEEE Transactions on Systems Man and Cybernetics, Part B: Cybernetics, 2007, 37(3): 560–575

    Article  Google Scholar 

  7. Wang Y, Liu H, Cai Z, Zhou Y. An orthogonal design based constrained evolutionary optimization algorithm. Engineering Optimization, 2007, 39 (6): 715–736

    Article  MathSciNet  Google Scholar 

  8. Kennedy J, Eberhart R. Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, 1995, 1942–1948

  9. Liang J J, Suganthan P N. Dynamic multi-swarm particle swarm optimizer with a novel constraint-handling mechanism. In: Proceedings of the Congress on Evolutionary Computation (CEC’2006). IEEE Press, 2006, 9–16

  10. Krohling R A, Coelho L S. Coevolutionary particle swarm optimization using Gaussian distribution for solving constrained optimization problems. IEEE Transactions on Systems Man and Cybernetics, Part B: Cybernetics, 2006, 36(6): 1407–1416

    Article  Google Scholar 

  11. He Q, Wang L. An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Engineering Application of Artificial Intelligence, 2007, 20(1): 89–99

    Article  Google Scholar 

  12. He Q, Wang L. A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Applied Mathematics and Computation, 2007, 186(2): 1407–1422

    Article  MATH  MathSciNet  Google Scholar 

  13. Deb K. An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering, 2000, 18(2–4): 311–338

    Article  Google Scholar 

  14. Pulido T G, Coello Coello C A. A constraint-handling mechanism for particle swarm optimization. In: Proceedings of 2004 Congress on Evolutionary Computation (CEC’2004). IEEE Press, 2004, 1396–1403

  15. Munoz-Zavala A E, Hernandez-Aguirre A, Villa-Diharce E R, Botello-Rionda S. PESO+ for constrained optimization. In: Proceedings of the Congress on Evolutionary Computation (CEC’2006). IEEE Press, 2006, 231–238

  16. Zielinski K, Laur R. Constrained single-objective optimization using particle swarm optimization. In: Proceedings of the Congress on Evolutionary Computation (CEC’2006). IEEE Press, 2006, 443–450

  17. Parsopoulos K E, Vrahatis M N. On the computation of all global minimizers through particle swarm optimization. IEEE Transactions on Evolutionary Computation, 2004, 8(3): 211–224

    Article  MathSciNet  Google Scholar 

  18. Shi Y, Eberhart R C. A modified particle swarm optimizer. In: Proceedings of IEEE Conference on Evolutionary Computation, 1998, 69–73

  19. Clerc M, Kennedy J. The particle swarm-explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 2002, 6(1): 58–73

    Article  Google Scholar 

  20. Storn R, Price K. Differential evolution — a simple and efficient adaptive scheme for global optimization over continuous spaces. International Computer Science Institute, Berkeley, Technical Report TR-95-012, 1995

  21. Brest J, Zumer V, Maucec M S. Self-adaptive differential evolution algorithm in constrained real-parameter optimization. In: Proceedings of the Congress on Evolutionary Computation (CEC’2006). IEEE Press, 2006, 215–222

  22. Runarsson T P, Yao X. Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation, 2000, 4(3): 284–294

    Article  Google Scholar 

  23. Takahama T, Sakai S. Constrained optimization by applying the α constrained method to the nonlinear simplex method with mutations. IEEE Transactions on Evolutionary Computation, 2005, 9(5): 437–451

    Article  Google Scholar 

  24. Runarsson T P, Yao X. Search bias in constrained evolutionary optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part C, 2005, 35(2): 233–243

    Article  Google Scholar 

  25. Liang J J, Runarsson T P, Mezura-Montes E, Clerc M, Suganthan P N, Coello Coello C A, Deb K. Problem definitions and evaluation criteria for the CEC 2006. Special Session on Constrained Real-Parameter Optimization, Technical Report. Singapore Nanyang Technological University, 2006

  26. Brest J, Greiner S, Boskovic B, Mernik M, Zumer V. Self-adapting control parameters in differential evolution: A comparative study on numerical benchmark problems. IEEE Transactions on Evolutionary Computation, 2006, 10(6): 646–657

    Article  Google Scholar 

  27. Rahnamayan S, Tizhoosh H R, Salama M M A. Opposition-based differential evolution. IEEE Transactions on Evolutionary Computation, 2008, 12(1): 64–79

    Article  Google Scholar 

  28. Noman N, Iba H. Accelerating differential evolution using an adaptive local search. IEEE Transactions on Evolutionary Computation, 2008, 12(1): 107–125

    Article  Google Scholar 

  29. Yang Z, Tang K, Yao X. Large scale evolutionary optimization using cooperative coevolution. Information Sciences, 2008, 78(15): 2985–2999

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, China

    Yong Wang & Zixing Cai

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  1. Yong Wang
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  2. Zixing Cai
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Correspondence to Yong Wang.

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Wang, Y., Cai, Z. A hybrid multi-swarm particle swarm optimization to solve constrained optimization problems. Front. Comput. Sci. China 3, 38–52 (2009). https://doi.org/10.1007/s11704-009-0010-x

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  • DOI: https://doi.org/10.1007/s11704-009-0010-x

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