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Heuristic-based firefly algorithm for bound constrained nonlinear binary optimization. (English) Zbl 1302.90259

Summary: Firefly algorithm (FA) is a metaheuristic for global optimization. In this paper, we address the practical testing of a heuristic-based FA (HBFA) for computing optima of discrete nonlinear optimization problems, where the discrete variables are of binary type. An important issue in FA is the formulation of attractiveness of each firefly which in turn affects its movement in the search space. Dynamic updating schemes are proposed for two parameters, one from the attractiveness term and the other from the randomization term. Three simple heuristics capable of transforming real continuous variables into binary ones are analyzed. A new sigmoid “erf” function is proposed. In the context of FA, three different implementations to incorporate the heuristics for binary variables into the algorithm are proposed. Based on a set of benchmark problems, a comparison is carried out with other binary dealing metaheuristics. The results demonstrate that the proposed HBFA is efficient and outperforms binary versions of differential evolution (DE) and particle swarm optimization (PSO). The HBFA also compares very favorably with angle modulated version of DE and PSO. It is shown that the variant of HBFA based on the sigmoid “erf” function with “movements in continuous space” is the best, in terms of both computational requirements and accuracy.

MSC:

90C59 Approximation methods and heuristics in mathematical programming
90C30 Nonlinear programming
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[1] L. Wang, R. Yang, Y. Xu, Q. Niu, P. M. Pardalos, and M. Fei, “An improved adaptive binary harmony search algorithm,” Information Sciences, vol. 232, pp. 58-87, 2013. · Zbl 06323783 · doi:10.1016/j.ins.2012.12.043
[2] M. A. K. Azad, A. M. A. C. Rocha, and E. M. G. P. Fernandes, “Improved binary artificial fish swarm algorithm for the 0-1 multidimensional knapsack problems,” Swarm and Evolutionary Computation, vol. 14, pp. 66-75, 2014. · Zbl 1314.90067 · doi:10.1016/j.swevo.2013.09.002
[3] A. P. Engelbrecht and G. Pampará, “Binary differential evolution strategies,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC ’07), pp. 1942-1947, September 2007. · doi:10.1109/CEC.2007.4424711
[4] M. H. Kashan, N. Nahavandi, and A. H. Kashan, “DisABC: a new artificial bee colony algorithm for binary optimization,” Applied Soft Computing Journal, vol. 12, no. 1, pp. 342-352, 2012. · doi:10.1016/j.asoc.2011.08.038
[5] M. H. Kashan, A. H. Kashan, and N. Nahavandi, “A novel differential evolution algorithm for binary optimization,” Computational Optimization and Applications, vol. 55, no. 2, pp. 481-513, 2013. · Zbl 1271.90052 · doi:10.1007/s10589-012-9521-8
[6] J. Kennedy and R. C. Eberhart, “A discrete binary version of the particle swarm algorithm,” in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, vol. 5, pp. 4104-4108, Orlando, Fla, USA, October 1997. · doi:10.1109/ICSMC.1997.637339
[7] T. Liu, L. Zhang, and J. Zhang, “Study of binary artificial bee colony algorithm based on particle swarm optimization,” Journal of Computational Information Systems, vol. 9, no. 16, pp. 6459-6466, 2013. · doi:10.12733/jcisP0675
[8] S. Mirjalili and A. Lewis, “S-shaped versus V-shaped transfer functions for binary particle swarm optimization,” Swarm and Evolutionary Computation, vol. 9, pp. 1-14, 2013. · doi:10.1016/j.swevo.2012.09.002
[9] G. Pampará, A. P. Engelbrecht, and N. Franken, “Binary differential evolution,” in Proceedings of the IEEE Congress on Evolutionary Computation (CEC ’06), pp. 1873-1879, Vancouver, Canada, July 2006. · doi:10.1109/CEC.2006.1688535
[10] G. Pampará and A. P. Engelbrecht, “Binary artificial bee colony optimization,” in Proceedings of the IEEE Symposium on Swarm Intelligence (SIS ’11), pp. 1-8, IEEE Perth, April 2011. · doi:10.1109/SIS.2011.5952562
[11] S. Burer and A. N. Letchford, “Non-convex mixed-integer nonlinear programming: a survey,” Surveys in Operations Research and Management Science, vol. 17, no. 2, pp. 97-106, 2012. · doi:10.1016/j.sorms.2012.08.001
[12] X.-S. Yang, “Firefly algorithms for multimodal optimization,” in Proceedings of the Stochastic Algorithms: Foundations and Applications (SAGA ’09), O. Watanabe and T. Zeugmann, Eds., vol. 5792 of Lecture Notes in Computer Science, pp. 169-178, 2009. · Zbl 1260.90164
[13] X.-S. Yang, “Firefly algorithm, stochastic test functions and design optimization,” International Journal of Bio-Inspired Computation, vol. 2, no. 2, pp. 78-84, 2010. · Zbl 05769361 · doi:10.1504/IJBIC.2010.032124
[14] I. Fister Jr., X.-S. Yang, and J. Brest, “A comprehensive review of firefly algorithms,” Swarm and Evolutionary Computation, vol. 13, pp. 34-46, 2013. · doi:10.1016/j.swevo.2013.06.001
[15] S. Yu, S. Yang, and S. Su, “Self-adaptive step firefly algorithm,” Journal of Applied Mathematics, vol. 2013, Article ID 832718, 8 pages, 2013. · Zbl 1397.90419 · doi:10.1155/2013/832718
[16] S. M. Farahani, A. A. Abshouri, B. Nasiri, and M. R. Meybodi, “A Gaussian firefly algorithm,” International Journal of Machine Learning and Computing, vol. 1, no. 5, pp. 448-453, 2011.
[17] L. Guo, G.-G. Wang, H. Wang, and D. Wang, “An effective hybrid firefly algorithm with harmony search for global numerical optimization,” The Scientific World Journal, vol. 2013, Article ID 125625, 9 pages, 2013. · Zbl 1266.90149 · doi:10.1155/2013/125625
[18] S. M. Farahani, A. A. Abshouri, B. Nasiri, and M. R. Meybodi, “Some hybrid models to improve firefly algorithm performance,” International Journal of Artificial Intelligence, vol. 8, no. 12, pp. 97-117, 2012.
[19] S. L. Tilahun and H. C. Ong, “Modified firefly algorithm,” Journal of Applied Mathematics, vol. 2012, Article ID 467631, 12 pages, 2012. · Zbl 1268.65082 · doi:10.1155/2012/467631
[20] X. Lin, Y. Zhong, and H. Zhang, “An enhanced firefly algorithm for function optimisation problems,” International Journal of Modelling, Identification and Control, vol. 18, no. 2, pp. 166-173, 2013. · doi:10.1504/IJMIC.2013.052298
[21] A. Manju and M. J. Nigam, “Firefly algorithm with fireflies having quantum behavior,” in Proceedings of the International Conference on Radar, Communication and Computing (ICRCC ’12), pp. 117-119, IEEE, Tiruvannamalai, India, December 2012. · doi:10.1109/ICRCC.2012.6450559
[22] X.-S. Yang and X. He, “Firefly algorithm: recent advances and applications,” International Journal of Swarm Intelligence, vol. 1, no. 1, pp. 36-50, 2013. · doi:10.1504/IJSI.2013.055801
[23] S. Arora and S. Singh, “The firefly optimization algorithm: convergence analysis and parameter selection,” International Journal of Computer Applications, vol. 69, no. 3, pp. 48-52, 2013.
[24] X.-S. Yang, S. S. S. Hosseini, and A. H. Gandomi, “Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect,” Applied Soft Computing Journal, vol. 12, no. 3, pp. 1180-1186, 2012. · doi:10.1016/j.asoc.2011.09.017
[25] A. H. Gandomi, X.-S. Yang, and A. H. Alavi, “Mixed variable structural optimization using firefly algorithm,” Computers and Structures, vol. 89, no. 23-24, pp. 2325-2336, 2011. · doi:10.1016/j.compstruc.2011.08.002
[26] X.-S. Yang, “Multiobjective firefly algorithm for continuous optimization,” Engineering with Computers, vol. 29, no. 2, pp. 175-184, 2013. · doi:10.1007/s00366-012-0254-1
[27] A. N. Kumbharana and G. M. Pandey, “Solving travelling salesman problem using firefly algorithm,” International Journal for Research in Science & Advanced Technologies, vol. 2, no. 2, pp. 53-57, 2013.
[28] M. K. Sayadi, A. Hafezalkotob, and S. G. J. Naini, “Firefly-inspired algorithm for discrete optimization problems: an application to manufacturing cell formation,” Journal of Manufacturing Systems, vol. 32, no. 1, pp. 78-84, 2013. · doi:10.1016/j.jmsy.2012.06.004
[29] X.-S. Yang, “Firefly algorithm,” in Nature-Inspired Metaheuristic Algorithms, pp. 81-96, Luniver Press, University of Cambridge, Cambridge, UK, 2nd edition, 2010.
[30] A. R. Jordehi and J. Jasni, “Parameter selection in particle swarm optimisation: a survey,” Journal of Experimental & Theoretical Artificial Intelligence, vol. 25, no. 4, pp. 527-542, 2013. · doi:10.1080/0952813X.2013.782348
[31] M. Mahdavi, M. Fesanghary, and E. Damangir, “An improved harmony search algorithm for solving optimization problems,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1567-1579, 2007. · Zbl 1119.65053 · doi:10.1016/j.amc.2006.11.033
[32] M. Padberg, “Harmony search algorithms for binary optimization problems,” in Operations Research Proceedings 2011, pp. 343-348, Springer, Berlin, Germany, 2012. · Zbl 1306.90096 · doi:10.1007/978-3-642-29210-1_55
[33] M. A. K. Azad, A. M. A. C. Rocha, and E. M. G. P. Fernandes, “A simplified binary artificial fish swarm algorithm for uncapacitated facility location problems,” in Proceedings of World Congress on Engineering, S. I. Ao, L. Gelman, D. W. L. Hukins, A. Hunter, and A. M. Korsunsky, Eds., vol. 1, pp. 31-36, IAENG, London, UK, 2013.
[34] M. Sevkli and A. R. Guner, “A continuous particle swarm optimization algorithm for uncapacitated facility location problem,” in Ant Colony Optimization and Swarm Intelligence, M. Dorigo, L. M. Gambardella, M. Birattari, A. Martinoli, R. Poli, and T. Stützle, Eds., vol. 4150 of Lecture Notes in Computer Sciences, pp. 316-323, Springer, 2006.
[35] L. Wang and C. Singh, “Unit commitment considering generator outages through a mixed-integer particle swarm optimization algorithm,” Applied Soft Computing Journal, vol. 9, no. 3, pp. 947-953, 2009. · Zbl 05739163 · doi:10.1016/j.asoc.2008.11.010
[36] M. M. Ali, C. Khompatraporn, and Z. B. Zabinsky, “A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems,” Journal of Global Optimization, vol. 31, no. 4, pp. 635-672, 2005. · Zbl 1093.90028 · doi:10.1007/s10898-004-9972-2
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