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A novel differential evolution algorithm for binary optimization

Author

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  • Mina Husseinzadeh Kashan
  • Ali Husseinzadeh Kashan
  • Nasim Nahavandi

Abstract

Differential evolution (DE) is one of the most powerful stochastic search methods which was introduced originally for continuous optimization. In this sense, it is of low efficiency in dealing with discrete problems. In this paper we try to cover this deficiency through introducing a new version of DE algorithm, particularly designed for binary optimization. It is well-known that in its original form, DE maintains a differential mutation, a crossover and a selection operator for optimizing non-linear continuous functions. Therefore, developing the new binary version of DE algorithm, calls for introducing operators having the major characteristics of the original ones and being respondent to the structure of binary optimization problems. Using a measure of dissimilarity between binary vectors, we propose a differential mutation operator that works in continuous space while its consequence is used in the construction of the complete solution in binary space. This approach essentially enables us to utilize the structural knowledge of the problem through heuristic procedures, during the construction of the new solution. To verify effectiveness of our approach, we choose the uncapacitated facility location problem (UFLP)—one of the most frequently encountered binary optimization problems—and solve benchmark suites collected from OR-Library. Extensive computational experiments are carried out to find out the behavior of our algorithm under various setting of the control parameters and also to measure how well it competes with other state of the art binary optimization algorithms. Beside UFLP, we also investigate the suitably of our approach for optimizing numerical functions. We select a number of well-known functions on which we compare the performance of our approach with different binary optimization algorithms. Results testify that our approach is very efficient and can be regarded as a promising method for solving wide class of binary optimization problems. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Mina Husseinzadeh Kashan & Ali Husseinzadeh Kashan & Nasim Nahavandi, 2013. "A novel differential evolution algorithm for binary optimization," Computational Optimization and Applications, Springer, vol. 55(2), pages 481-513, June.
    • Handle: RePEc:spr:coopap:v:55:y:2013:i:2:p:481-513
    DOI: 10.1007/s10589-012-9521-8
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    References listed on IDEAS

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    1. Ghosh, Diptesh, 2003. "Neighborhood search heuristics for the uncapacitated facility location problem," European Journal of Operational Research, Elsevier, vol. 150(1), pages 150-162, October.
    2. K.S. Al‐Sultan & M.A. Al‐Fawzan, 1999. "A tabu search approach to the uncapacitated facility location problem," Annals of Operations Research, Springer, vol. 86(0), pages 91-103, January.
    3. Holmberg, Kaj, 1999. "Exact solution methods for uncapacitated location problems with convex transportation costs," European Journal of Operational Research, Elsevier, vol. 114(1), pages 127-140, April.
    4. Donald Erlenkotter, 1978. "A Dual-Based Procedure for Uncapacitated Facility Location," Operations Research, INFORMS, vol. 26(6), pages 992-1009, December.
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    Cited by:

    1. Maliheh Khorsi & Seyed Kamal Chaharsooghi & Ali Husseinzadeh Kashan & Ali Bozorgi-Amiri, 2021. "Pareto-based grouping meta-heuristic algorithm for humanitarian relief logistics with multistate network reliability," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(2), pages 327-365, June.

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