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Differential Evolution algorithm with Separated Groups for multi-dimensional optimization problems

Listed author(s):
  • Piotrowski, Adam P.
  • Napiorkowski, Jaroslaw J.
  • Kiczko, Adam
Registered author(s):

    The classical Differential Evolution (DE) algorithm, one of population-based Evolutionary Computation methods, proved to be a successful approach for relatively simple problems, but does not perform well for difficult multi-dimensional non-convex functions. A number of significant modifications of DE have been proposed in recent years, including very few approaches referring to the idea of distributed Evolutionary Algorithms. The present paper presents a new algorithm to improve optimization performance, namely DE with Separated Groups (DE-SG), which distributes population into small groups, defines rules of exchange of information and individuals between the groups and uses two different strategies to keep balance between exploration and exploitation capabilities. The performance of DE-SG is compared to that of eight algorithms belonging to the class of Evolutionary Strategies (Covariance Matrix Adaptation ES), Particle Swarm Optimization (Comprehensive Learning PSO and Efficient Population Utilization Strategy PSO), Differential Evolution (Distributed DE with explorative-exploitative population families, Self-adaptive DE, DE with global and local neighbours and Grouping Differential Evolution) and multi-algorithms (AMALGAM). The comparison is carried out for a set of 10-, 30- and 50-dimensional rotated test problems of varying difficulty, including 10- and 30-dimensional composition functions from CEC2005. Although slow for simple functions, the proposed DE-SG algorithm achieves a great success rate for more difficult 30- and 50-dimensional problems.

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    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 216 (2012)
    Issue (Month): 1 ()
    Pages: 33-46

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    Handle: RePEc:eee:ejores:v:216:y:2012:i:1:p:33-46
    DOI: 10.1016/j.ejor.2011.07.038
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    1. Omran, Mahamed G.H. & Engelbrecht, Andries P. & Salman, Ayed, 2009. "Bare bones differential evolution," European Journal of Operational Research, Elsevier, vol. 196(1), pages 128-139, July.
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    3. Mishra, SK, 2006. "Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions," MPRA Paper 1005, University Library of Munich, Germany.
    4. Al-Anzi, Fawaz S. & Allahverdi, Ali, 2007. "A self-adaptive differential evolution heuristic for two-stage assembly scheduling problem to minimize maximum lateness with setup times," European Journal of Operational Research, Elsevier, vol. 182(1), pages 80-94, October.
    5. Hedar, Abdel-Rahman & Fukushima, Masao, 2006. "Tabu Search directed by direct search methods for nonlinear global optimization," European Journal of Operational Research, Elsevier, vol. 170(2), pages 329-349, April.
    6. Kaelo, P. & Ali, M.M., 2006. "A numerical study of some modified differential evolution algorithms," European Journal of Operational Research, Elsevier, vol. 169(3), pages 1176-1184, March.
    7. Beynon, Malcolm J. & Andrews, Rhys & Boyne, George A., 2010. "Evidence-based modelling of strategic fit: An introduction to RCaRBS," European Journal of Operational Research, Elsevier, vol. 207(2), pages 886-896, December.
    8. Cruz, F.R.B. & van Woensel, T. & MacGregor Smith, J. & Lieckens, K., 2010. "On the system optimum of traffic assignment in M/G/c/c state-dependent queueing networks," European Journal of Operational Research, Elsevier, vol. 201(1), pages 183-193, February.
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