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A novel differential evolution algorithm for binary optimization

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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.

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References

  1. Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341–359 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  2. Qian, B., Wang, L., Hu, R., Wang, W.L., Huang, D.X., Wang, X.: A hybrid differential evolution method for permutation flow-shop scheduling. Int. J. Adv. Manuf. Technol. 38, 1433–3015 (2007)

    Google Scholar 

  3. Yang, Q.: A comparative study of discrete differential evolution on binary constraint satisfaction problems. In: Proceeding of the IEEE Congress on Evolutionary Computation, pp. 330–335 (2008)

    Google Scholar 

  4. Pampará, G., Engelbrecht, A.P., Franken, N.: Binary differential evolution. In: Proceeding of the IEEE Congress on Evolutionary Computation, pp. 1873–1879 (2006)

    Google Scholar 

  5. Engelbrecht, A.P., Pampara, G.: Binary differential evolution strategies. In: IEEE Congress on Evolutionary Computation, pp. 1942–1947 (2007)

    Google Scholar 

  6. Dillon, W.R., Goldstein, M.: Multivariate Analysis: Methods and Applications. Wiley, New York (1984)

    MATH  Google Scholar 

  7. Finch, H.: Comparison of distance measures in cluster analysis with dichotomous data. J. Data Sci. 3, 85–100 (2005)

    Google Scholar 

  8. Sneath, P.H.A.: Some thoughts on bacterial classification. J. Gen. Microbiol. 17, 184–200 (1957)

    Google Scholar 

  9. Hands, S., Everitt, B.: A Monte Carlo study of the recovery of cluster structure in binary data by hierarchical clustering techniques. Multivar. Behav. Res. 22, 235–243 (1987)

    Article  Google Scholar 

  10. Daskin, M.S., Snyder, L.V., Berger, R.T.: Facility location in supply chain design. Working paper No. 03-010, Lehigh University (2003)

  11. Holmberg, K.: Exact solution methods for uncapacitated location problems with convex transportation costs. Eur. J. Oper. Res. 114, 127–140 (1999)

    Article  MATH  Google Scholar 

  12. Barcelo, J., Hallefjord, A., Fernandez, E., Jrnsten, K.: Lagrengean relaxation and constraint generation procedures for capacitated plant location problems with single sourcing. OR Spectrum 12, 78–79 (1990)

    Article  Google Scholar 

  13. Erlenkotter, D.: A dual-based procedure for uncapacitated facility location. Oper. Res. 26, 992–1009 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  14. Al-Sultan, K.S., Al-Fawzan, M.A.: A tabu search approach to the uncapacitated facility location problem. Ann. Oper. Res. 86, 91–103 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  15. Sun, M.: Solving the uncapacitated facility location problem using tabu search. Comput. Oper. Res. 33, 2563–2589 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  16. Jaramillo, J.H., Bhadury, J., Batta, R.: On the use of genetic algorithms to solve location problems. Comput. Oper. Res. 29, 761–779 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  17. Sevkli, M., Guner, A.R.: A continuous particle swarm optimization algorithm for uncapacitated facility location problem. In: ANTS 2006, pp. 316–323 (2006)

    Google Scholar 

  18. Wang, D., Wu, C.H., Ip, A., Wang, D., Yan, Y.: Parallel multi-population particle swarm optimization algorithm for the uncapacitated facility location problem using openMP. In: IEEE Congress on Evolutionary Computation, pp. 1214–1218 (2008)

    Google Scholar 

  19. Ghosh, D.: Neighborhood search heuristics for the uncapacitated facility location problem. Eur. J. Oper. Res. 150, 150–162 (2003)

    Article  MATH  Google Scholar 

  20. Beasley, J.E.: OR-library: distributing test problems by electronic mail. J. Oper. Res. Soc. 41, 1069–1072 (1990)

    Google Scholar 

  21. Ahmadieh Khanesar, M., Teshnehlab, M., Aliyari Shoorehdeli, M.: A novel binary particle swarm optimization. In: Proceeding of 2007 Mediterranean Conference on Control and Automation (2007)

    Google Scholar 

  22. Grahl, J., Bosman, P.A.N., Rothlauf, F.: The correlation-triggered adaptive variance scaling IDEA. In: Proceeding of GECCO ’06, Seattle, Washington, USA (2006)

    Google Scholar 

  23. Husseinzadeh Kashan, A.: League championship algorithm: a new algorithm for numerical function optimization. In: Proceeding of IEEE International Conference of Soft Computing and Pattern Recognition, SoCPaR 2009, pp. 43–48 (2009)

    Chapter  Google Scholar 

  24. Husseinzadeh Kashan, A.: An efficient algorithm for constrained global optimization and application to mechanical engineering design: league championship algorithm (LCA). Comput. Aided Des. 43, 1769–1792 (2011)

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Engineering, Tarbiat Modares University, P.O. Box: 14115-111, Tehran, Iran

    Mina Husseinzadeh Kashan & Nasim Nahavandi

  2. Department of Systems & Industrial Engineering, Faculty of Engineering, Islamic Azad University, Science & Research Branch, Tehran, Iran

    Ali Husseinzadeh Kashan

Authors
  1. Mina Husseinzadeh Kashan
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  2. Ali Husseinzadeh Kashan
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  3. Nasim Nahavandi
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Correspondence to Ali Husseinzadeh Kashan.

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Husseinzadeh Kashan, M., Husseinzadeh Kashan, A. & Nahavandi, N. A novel differential evolution algorithm for binary optimization. Comput Optim Appl 55, 481–513 (2013). https://doi.org/10.1007/s10589-012-9521-8

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  • DOI: https://doi.org/10.1007/s10589-012-9521-8

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