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

  • Noha M. HamzaEmail author
  • Daryl L. Essam
  • Ruhul A. Sarker
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Constrained optimization Constraint consensus Differential evolution 

References

  1. 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. 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)CrossRefGoogle Scholar
  3. 3.
    Dantzig, G., Mukund, N.: Linear Programming 1: Introduction. Springer, New York (1997)zbMATHGoogle Scholar
  4. 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)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, MA (1989)zbMATHGoogle Scholar
  6. 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. 7.
    Fogel, L., Owens, J., Walsh, M.: Artificial Intelligence Through Simulated Evolution. Wiley, New York (1966)zbMATHGoogle Scholar
  8. 8.
    Deb, K.: Multi-objective genetic algorithms: problem difficulties and construction of test problems. Evol. Comput. 7(3), 205–230 (1999)CrossRefGoogle Scholar
  9. 9.
    Chinneck, J.W.: The constraint consensus method for finding approximately feasible points in nonlinear programs. INFORMS J. Comput. 16(3), 255–265 (2004)CrossRefMathSciNetzbMATHGoogle Scholar
  10. 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)CrossRefMathSciNetzbMATHGoogle Scholar
  11. 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 2012Google Scholar
  12. 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 2011Google Scholar
  13. 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)CrossRefMathSciNetGoogle Scholar
  14. 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)CrossRefMathSciNetzbMATHGoogle Scholar
  15. 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. 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)CrossRefGoogle Scholar
  17. 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)CrossRefMathSciNetzbMATHGoogle Scholar
  18. 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. 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)CrossRefMathSciNetzbMATHGoogle Scholar
  20. 20.
    Smith, L.: Improved placement of local solver launch points for large-scale global optimization. Carleton University (2011)Google Scholar
  21. 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)CrossRefGoogle Scholar
  22. 22.
    Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Meth. Appl. Mech. Eng. 186, 311–338 (2000)CrossRefzbMATHGoogle Scholar
  23. 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)MathSciNetGoogle Scholar
  24. 24.
    Elsayed, S., Sarker, R.: Differential evolution with automatic population injection scheme. In: IEEE Symposium Series on Computational Intelligence, Singapore, accepted, 16–19 April 2013Google Scholar
  25. 25.
    Corder, G.W., Foreman, D.I.: Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach. John Wiley, Hoboken (2009)CrossRefGoogle Scholar
  26. 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. 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)CrossRefGoogle Scholar
  28. 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

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Noha M. Hamza
    • 1
    Email author
  • Daryl L. Essam
    • 1
  • Ruhul A. Sarker
    • 1
  1. 1.School of Engineering and Information TechnologyUniversity of New South Wales at CanberraCanberraAustralia

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