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Parent-centric differential evolution algorithm for global optimization problems

  • Theory and Methodology
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Abstract

Differential evolution (DE) is a population based evolutionary search algorithm widely used for solving optimization problems. In the present article we investigate the application of parent-centric approach on the performance of classical DE, without tampering with the basic structure of DE. The parent-centric approach is embedded in the mutation phase of DE. We propose two versions of (DE) called differential evolution with parent-centric crossover (DEPCX) and differential evolution with probabilistic parent-centric crossover (ProDEPCX) in order to improve the performance of classical DE. The proposed algorithms are validated on a test bed of ten benchmark functions and the numerical results are compared with basic DE and a modified version called trigonometric differential evolution (TDE). Empirical analysis of numerical results on the benchmark problems show that the performance of proposed versions is either at par or better in comparison to TDE and basic DE in terms of convergence rate and quality of fitness function value.

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References

  1. Michalewicz, F.D.: How to Solve It: Modern Heuristics. Springer, Berlin (2000)

    Google Scholar 

  2. Van Laarhoven, Aarts, P.: Simulated Annealing: Theory and Applications. Kluwer Academic Publishers (1987)

  3. Fogel, L,: Evolutionary programming in perspective: The top-down view. In: Zurada, J.M., Marks, R. Jr., Robinson, C. (eds.) Computational Intelligence: Imitating Life. IEEE Press, Piscataway, NJ, USA (1994)

    Google Scholar 

  4. Back, T., Hoffmeister, F., Schwefel, H.: A survey of evolution strategies. In: Proceedings of the Fourth International Conference on Genetic Algorithms and their Applications, pp. 2–9 (1991)

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

  6. Kennedy, J., Eberhart, R.C.: Particle swarm optimization. IEEE Int. Conf. on Neural Networks, Perth, Australia, IEEE Service Center, Piscataway, NJ, pp. 1942–1948 (1995)

    Google Scholar 

  7. Storn. R., Price, K.: Differential evolution—A simple and efficient adaptive scheme for global optimization over continuous spaces. Berkeley, CA, Tech. Rep. TR-95-012 (1995)

  8. Paterlini, S., Krink, T.: High performance clustering with differential evolution. In: Proceedings of the IEEE Congress on Evolutionary Computation, vol. 2, pp. 2004–2011 (2004)

    Google Scholar 

  9. Omran, M., Engelbrecht, A., Salman, A.: Differential evolution methods for unsupervised image classification. In: Proceedings of the IEEE Congress on Evolutionary Computation, vol. 2, pp. 966–973 (2005a)

    Article  Google Scholar 

  10. Storn, R.: Differential evolution design for an IIR-filter with requirements for magnitude and group delay. Technical Report TR-95-026, International Computer Science Institute, Berkeley, CA (1995)

    Google Scholar 

  11. Babu, B., Angira, R.: Optimization of non-linear functions using evolutionary computation. In: Proceedings of the 12th ISME International Conference on Mechanical Engineering, India, pp. 153–157 (2001)

  12. Angira, R., Babu, B.: Evolutionary computation for global optimization of non-linear chemical engineering processes. In: Proceedings of International Symposium on Process Systems Engineering and Control, Mumbai, pp. 87–91 (2003)

  13. Abbass, H., “A memetic pareto evolutionary approach to artificial neural networks” Lecture Notes in Artificial Intelligence, vol. 2256. Springer, pp. 1–12 (2002a)

  14. Vesterstroem, J., Thomsen. R.: A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems. Proc. Congr. Evol. Comput., vol. 2, pp. 1980–1987 (2004)

    Google Scholar 

  15. Andre, J., Siarry. P., Dognon. T.: An improvement of the standard genetic algorithm fighting premature convergence in continuous optimization. Advance in Engineering Software 32, pp. 49–60 (2001)

    Article  Google Scholar 

  16. Hrstka, O., Kučerová. A.: Improvement of real coded genetic algorithm based on differential operators preventing premature convergence. Advance in Engineering Software. 35, 237–246 (2004)

    Article  Google Scholar 

  17. Lampinen, J., Zelinka, I.: On stagnation of the differential evolution algorithm. In: Ošmera, Pavel (ed.) Proc. of MENDEL 2000, 6th International Mendel Conference on Soft Computing, pp. 76–83, Brno, Czech Republic, June 7–9 (2000)

  18. Zaharie, D.: Control of population diversity and adaptation in differential evolution algorithms. In: Matousek, D., Osmera, P., (eds.), Proc. of MENDEL 2003, 9th International Conference on Soft Computing, Brno, Czech Republic pp. 41–46, June (2003)

  19. Abbass, H.: The self-adaptive pareto differential evolution algorithm. In: Proc. of the 2002 Congress onEvolutionary Computation, 831–836 (2002)

  20. Omran, M., Salman, A., Engelbrecht. A.P.: Self-adaptive differential evolution, computational intelligence and security. PT 1, Proceedings Lecture Notes in Artificial Intelligence 3801: 192–199 (2005)

    Google Scholar 

  21. Brest, J., Greiner, S., Boškovic. B., Mernik. M., Šumer. V.: Self-adapting Control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Transactions on Evolutionary Computation 10(6), 646–657 (2006)

    Article  Google Scholar 

  22. Das, S., Konar, A., hakraborty. U.K.: Two improved differential evolution schemes for faster global search. ACM-SIGEVO Proceed-ings of GECCO, Washington D.C., pp. 991–998, June (2005)

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

    Article  Google Scholar 

  24. Yang, Z., He, J., Yao, X.: Making a difference to differential evolution, in advances in metaheuristics for hard optimization. Z. Michalewicz, P. Siarry (eds.), pp. 415–432, Springer (2007)

  25. Noman, N, Iba, H.: Enhancing differential evolution performance with local search for high dimensional function optimization. in Proc. of the 2005 Conference on Genetic and Evolutionary Computation, pp. 967–974 (June 2005)

  26. M.M. Ali,: Differential evolution with preferential crossover. European Journal of Operations Research 181, 1088–1113 (2007)

    Article  Google Scholar 

  27. Hui-Yuan Fan, Jouni Lampinen. A trigonometric mutation operation to differential evolution. Journal of Global Optimization 27:105–129 (2003)

    Article  Google Scholar 

  28. Chakraborty, U.K, (ed.): Advances in differential evolution. Springer-Verlag, Heidelberg (2008)

    Google Scholar 

  29. Pant. M., Ali. M., Singh. V.P.: Differential evolution with parent-centric crossover. Second UKSIM European symposium on computer modeling and simulation, Liverpool UK, pp 141–146 (2008)

  30. Garcia-Martinez. C., Lozano. M., Herrera. F., Molina. D., Sanchez. A.M.: Global and local real-coded genetic algorithms based on parent-centric crossover operators. European Journal of Operations Research 185, 1088–1113 (2008)

    Article  Google Scholar 

  31. Deb. K., Anand. A., Joshi. D.: A computationally efficient evolution-ary algorithm for real-parameter optimization. Evol Comput J. 10(4), 371–395 (2002)

    Article  Google Scholar 

  32. Deb. K., A population-based algorithm-generator for real-parameter optimization. soft Comput J. 9, 236–253 (2005)

    Article  Google Scholar 

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  1. Department of Paper Technology, Indian Institute of Technology Roorkee, Saharanpur Campus, Saharanpur, 247001, India

    Millie Pant, Musrrat Ali & V. P. Singh

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  1. Millie Pant
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  2. Musrrat Ali
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  3. V. P. Singh
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Correspondence to Millie Pant.

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Pant, M., Ali, M. & Singh, V.P. Parent-centric differential evolution algorithm for global optimization problems. OPSEARCH 46, 153–168 (2009). https://doi.org/10.1007/s12597-009-0010-5

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