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Exploring the Feasible Space Using Constraint Consensus in Solving Constrained Optimization Problems

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Artificial Life and Computational Intelligence (ACALCI 2016)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9592))

Abstract

Over the last few years, constraint consensus methods have been used for the movement of infeasible solutions towards feasible space, when solving constrained optimization problem. In this paper, a novel approach is proposed that is based on the concept of constraint consensus to improve feasible individuals, rather than infeasible ones, in which a feasible individual is considered as an infeasible one, if its fitness value is worse than a dynamic reference point. The obtained new solutions are then passed to differential evolution to be evolved. The proposed algorithm has been tested on the CEC2010 benchmark constrained problems. The results demonstrate better performance of the proposed algorithm, in terms of quality of solutions and computational time, in comparison with a standard differential evolution algorithm, as well as a set of state-of-the-art algorithms.

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References

  1. Barkat-Ullah, A.S.S.M.: An integrated evolutionary system for solving optimization problems. University of New South Wales At Australian Defence Force Academy (2009)

    Google Scholar 

  2. Sarker, R., Kamruzzaman, J., Newton, C.: Evolutionary optimization (EvOpt): a brief review and analysis. Int. J. Comput. Intell. Appl. 3(4), 311–330 (2003)

    Article  Google Scholar 

  3. Dantzig, G., Mukund, N.: Linear Programming 1: Introduction. Springer, New York (1997)

    MATH  Google Scholar 

  4. Elsayed, S.M., Sarker, R.A., Essam, D.L.: Multi-operator based evolutionary algorithms for solving constrained optimization Problems. Comput. Oper. Res. 38(12), 1877–1896 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, MA (1989)

    MATH  Google Scholar 

  6. Storn, R., Price, K.: Differential evolution - a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report, International Computer Science Institute (1995)

    Google Scholar 

  7. Fogel, L., Owens, J., Walsh, M.: Artificial Intelligence Through Simulated Evolution. Wiley, New York (1966)

    MATH  Google Scholar 

  8. Deb, K.: Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol. Comput. 7(3), 205–230 (1999)

    Article  Google Scholar 

  9. Chinneck, J.W.: The constraint consensus method for finding approximately feasible points in nonlinear programs. INFORMS J. Comput. 16(3), 255–265 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Hamza, N., Sarker, R., Essam, D.: Differential evolution with multi-constraint consensus methods for constrained optimization. J. Glob. Optim. 57(2), 583–611 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hamza, N.M., Sarker, R.A., Essam, D.L.: Differential evolution with a mix of constraint consenus methods for solving a real-world optimization problem. In: 2012 IEEE Congress on Evolutionary Computation (CEC), pp. 1–7, 10-15 June 2012

    Google Scholar 

  12. Hamza, N.M., Elsayed, S.M., Essam, D.L., Sarker, R.A.: Differential evolution combined with constraint consensus for constrained optimization. In: IEEE Congress on Evolutionary Computation, pp. 865–872, 5-8 June 2011

    Google Scholar 

  13. Hamza, N.M., Sarker, R.A., Essam, D.L., Deb, K., Elsayed, S.M.: A constraint consensus memetic algorithm for solving constrained optimization problems. Eng. Optim. 46(11), 1447–1464 (2013)

    Article  MathSciNet  Google Scholar 

  14. Ibrahim, W., Chinneck, J.W.: Improving solver success in reaching feasibility for sets of nonlinear constraints. Comput. Oper. Res. 35(5), 1394–1411 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Mallipeddi, R., Suganthan, P.N.: Problem definitions and evaluation criteria for the CEC 2010 competition and special session on single objective constrained real-parameter optimization. Technical report, Nangyang Technological University, Singapore (2010)

    Google Scholar 

  16. Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15(1), 4–31 (2011)

    Article  Google Scholar 

  17. Pan, Q.-K., Suganthan, P.N., Wang, L., Gao, L., Mallipeddi, R.: A differential evolution algorithm with self-adapting strategy and control parameters. Comput. Oper. Res. 38(1), 394–408 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  18. Storn, R.: On the usage of differential evolution for function optimization. In: Biennial Conference of the North American Fuzzy Information Processing Society (NAFIPS), pp. 519–523 (1996)

    Google Scholar 

  19. Censor, Y., Gordon, D., Gordon, R.: Component averaging: an efficient iterative parallel algorithm for large and sparse unstructured problems. Parallel Comput. 27(6), 777–808 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  20. Smith, L.: Improved placement of local solver launch points for large-scale global optimization. Carleton University (2011)

    Google Scholar 

  21. Yong, W., Zixing, C., Guo, G., Yuren, Z.: Multiobjective optimization and hybrid evolutionary algorithm to solve constrained optimization problems. IEEE Trans. Syst. Man Cybern. Part B Cybern. 37(3), 560–575 (2007)

    Article  Google Scholar 

  22. Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Meth. Appl. Mech. Eng. 186, 311–338 (2000)

    Article  MATH  Google Scholar 

  23. Hamza, N., Sarker, R., Essam, D.: Differential evolution with multi-constraint consensus methods for constrained optimization. J. Glob. Optim. 57(2), 1–29 (2012)

    MathSciNet  Google Scholar 

  24. Elsayed, S., Sarker, R.: Differential evolution with automatic population injection scheme. In: IEEE Symposium Series on Computational Intelligence, Singapore, accepted, 16–19 April 2013

    Google Scholar 

  25. Corder, G.W., Foreman, D.I.: Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach. John Wiley, Hoboken (2009)

    Book  Google Scholar 

  26. Takahama, T., Sakai, S.: Constrained optimization by the ε constrained differential evolution with an archive and gradient-based mutation. In: IEEE Congress on Evolutionary Computation, pp. 1–9 (2010)

    Google Scholar 

  27. Gong, W., Cai, Z., Liang, D.: Adaptive ranking mutation operator based differential evolution for constrained optimization. IEEE Trans. Cybern. 45(4), 716–727 (2014)

    Article  Google Scholar 

  28. Liang, J.J., Shang, Z., Li, Z.: Coevolutionary comprehensive learning particle swarm optimizer. In: IEEE Congress on Evolutionary Computation, 18-23 July 2010, pp. 1–8 (2010)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Engineering and Information Technology, University of New South Wales at Canberra, Canberra, Australia

    Noha M. Hamza, Daryl L. Essam & Ruhul A. Sarker

Authors
  1. Noha M. Hamza
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  2. Daryl L. Essam
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  3. Ruhul A. Sarker
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Corresponding author

Correspondence to Noha M. Hamza .

Editor information

Editors and Affiliations

  1. Canberra, Aust Capital Terr, Australia

    Tapabrata Ray

  2. University of New South Wales, Canberra, Aust Capital Terr, Australia

    Ruhul Sarker

  3. RMIT University, Melbourne, Victoria, Australia

    Xiaodong Li

Appendix A

Appendix A

See Appendix Table 4.

Table 4. Function values obtained by DE, EFS-CC-DE, εDEag, ECHT-ARMOR-DE and CO-CLIPSO for the CEC2010 (30D) test problems
Full size table

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Hamza, N.M., Essam, D.L., Sarker, R.A. (2016). Exploring the Feasible Space Using Constraint Consensus in Solving Constrained Optimization Problems. In: Ray, T., Sarker, R., Li, X. (eds) Artificial Life and Computational Intelligence. ACALCI 2016. Lecture Notes in Computer Science(), vol 9592. Springer, Cham. https://doi.org/10.1007/978-3-319-28270-1_8

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  • DOI: https://doi.org/10.1007/978-3-319-28270-1_8

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