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Simulated annealing-based krill herd algorithm for global optimization. (English) Zbl 1291.90330

Summary: Recently, Gandomi and Alavi proposed a novel swarm intelligent method, called krill herd (KH), for global optimization. To enhance the performance of the KH method, in this paper, a new improved meta-heuristic simulated annealing-based krill herd (SKH) method is proposed for optimization tasks. A new krill selecting (KS) operator is used to refine krill behavior when updating krill’s position so as to enhance its reliability and robustness dealing with optimization problems. The introduced KS operator involves greedy strategy and accepting few not-so-good solutions with a low probability originally used in simulated annealing (SA). In addition, a kind of elitism scheme is used to save the best individuals in the population in the process of the krill updating. The merits of these improvements are verified by fourteen standard benchmarking functions and experimental results show that, in most cases, the performance of this improved meta-heuristic SKH method is superior to, or at least highly competitive with, the standard KH and other optimization methods.

MSC:

90C59 Approximation methods and heuristics in mathematical programming
90C26 Nonconvex programming, global optimization

Software:

ABC; Krill herd
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References:

[1] Wang, G.; Guo, L., A novel hybrid bat algorithm with harmony search for global numerical optimization, Journal of Applied Mathematics, 2013 (2013) · Zbl 1266.90149 · doi:10.1155/2013/696491
[2] Wang, G.; Guo, L.; Gandomi, A. H.; Cao, L.; Alavi, A. H.; Duan, H.; Li, J., Lévy-flight krill herd algorithm, Mathematical Problems in Engineering, 2013 (2013) · doi:10.1155/2013/682073
[3] Yang, X. S., Nature-Inspired Metaheuristic Algorithms (2010), Frome, UK: Luniver Press, Frome, UK
[4] Chen, R.-M.; Wang, C.-M., Project scheduling heuristics-based standard PSO for task-resource assignment in heterogeneous grid, Abstract and Applied Analysis, 2011 (2011) · Zbl 1214.90051 · doi:10.1155/2011/589862
[5] Zhang, W. Y.; Xu, S.; Li, S. J., Necessary conditions for weak sharp minima in cone-constrained optimization problems, Abstract and Applied Analysis, 2012 (2012) · Zbl 1242.49052 · doi:10.1155/2012/909520
[6] Duan, H.; Zhao, W.; Wang, G.; Feng, X., Test-sheet composition using analytic hierarchy process and hybrid metaheuristic algorithm TS/BBO, Mathematical Problems in Engineering, 2012 (2012) · doi:10.1155/2012/712752
[7] Yang, X. S.; Gandomi, A. H.; Talatahari, S.; Alavi, A. H., Metaheuristics in Water, Geotechnical and Transport Engineering (2013), Waltham, Mass, USA: Elsevier, Waltham, Mass, USA
[8] Gandomi, A. H.; Yang, X. S.; Talatahari, S.; Alavi, A. H., Metaheuristic Applications in Structures and Infrastructures (2013), Waltham, Mass, USA: Elsevier, Waltham, Mass, USA
[9] Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning (1998), New York, NY, USA: Addison-Wesley, New York, NY, USA
[10] Yang, X. S.; Gandomi, A. H., Bat algorithm: a novel approach for global engineering optimization, Engineering Computations, 29, 5, 464-483 (2012)
[11] Chen, H.; Zhu, Y.; Hu, K., Adaptive bacterial foraging optimization, Abstract and Applied Analysis, 2011 (2011) · Zbl 1220.90167
[12] Simon, D., Biogeography-based optimization, IEEE Transactions on Evolutionary Computation, 12, 6, 702-713 (2008) · doi:10.1109/TEVC.2008.919004
[13] Laseetha, T. S. J.; Sukanesh, R., Investigations on the synthesis of uniform linear antenna array using biogeography-based optimisation techniques, International Journal of Bio-Inspired Computation, 4, 2, 119-130 (2012)
[14] Lohokare, M. R.; Devi, S.; Pattnaik, S. S.; Panigrahi, B. K.; Joshi, J. G., Modified biogeography-based optimisation (MBBO), International Journal of Bio-Inspired Computation, 3, 4, 252-266 (2011)
[15] Hamdi, A.; Mukheimer, A. A., Modified Lagrangian methods for separable optimization problems, Abstract and Applied Analysis, 2012 (2012) · Zbl 1243.49038 · doi:10.1155/2012/471854
[16] Cai, X.; Fan, S.; Tan, Y., Light responsive curve selection for photosynthesis operator of APOA, International Journal of Bio-Inspired Computation, 4, 6, 373-379 (2012)
[17] Xie, L.; Zeng, J.; Formato, R. A., Selection strategies for gravitational constant G in artificial physics optimisation based on analysis of convergence properties, International Journal of Bio-Inspired Computation, 4, 6, 380-391 (2012)
[18] Storn, R.; Price, K., Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces, Journal of Global Optimization, 11, 4, 341-359 (1997) · Zbl 0888.90135 · doi:10.1023/A:1008202821328
[19] Gao, Y.; Liu, J., Multiobjective differential evolution algorithm with multiple trial vectors, Abstract and Applied Analysis, 2012 (2012) · Zbl 1253.90205
[20] Gandomi, A. H.; Alavi, A. H., Multi-stage genetic programming: a new strategy to nonlinear system modeling, Information Sciences, 181, 23, 5227-5239 (2011)
[21] Kennedy, J.; Eberhart, R., Particle swarm optimization, Proceedings of the IEEE International Conference on Neural Networks
[22] Gholizadeh, S.; Fattahi, F., Design optimization of tall steel buildings by a modified particle swarm algorithm, The Structural Design of Tall and Special Buildings (2012) · doi:10.1002/tal.1042
[23] Talatahari, S.; Kheirollahi, M.; Farahmandpour, C.; Gandomi, A. H., A multi-stage particle swarm for optimum design of truss structures, Neural Computing and Applications (2012) · doi:10.1007/s00521-012-1072-5
[24] Yang, C.; Simon, D., A new particle swarm optimization technique, Proceedings of the 18th International Conference on Systems Engineering (ICSEng ’05) · doi:10.1109/ICSENG.2005.9
[25] Selvakumar, A. I.; Thanushkodi, K., A new particle swarm optimization solution to nonconvex economic dispatch problems, IEEE Transactions on Power Systems, 22, 1, 42-51 (2007) · doi:10.1109/TPWRS.2006.889132
[26] Gandomi, A. H.; Yang, X.-S.; Alavi, A. H., Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems, Engineering with Computers, 29, 1, 17-35 (2013) · doi:10.1007/s00366-011-0241-y
[27] Gandomi, A. H.; Alavi, A. H., Krill herd: a new bio-inspired optimization algorithm, Communications in Nonlinear Science and Numerical Simulation, 17, 12, 4831-4845 (2012) · Zbl 1266.65092 · doi:10.1016/j.cnsns.2012.05.010
[28] Wang, G.; Guo, L.; Wang, H.; Duan, H.; Liu, L.; Li, J., Incorporating mutation scheme into krill herd algorithm for global numerical optimization, Neural Computing and Applications (2012) · doi:10.1007/s00521-012-1304-8
[29] Kirkpatrick, S.; Gelatt,, C. D.; Vecchi, M. P., Optimization by simulated annealing, Science, 220, 4598, 671-680 (1983) · Zbl 1225.90162 · doi:10.1126/science.220.4598.671
[30] Chen, S. M.; Sarosh, A.; Dong, Y. F., Simulated annealing based artificial bee colony algorithm for global numerical optimization, Applied Mathematics and Computation, 219, 8, 3575-3589 (2012) · Zbl 1311.65068 · doi:10.1016/j.amc.2012.09.052
[31] Tawhid, M. A., Solution of nonsmooth generalized complementarity problems, Journal of the Operations Research Society of Japan, 54, 1, 12-24 (2011) · Zbl 1228.90131
[32] Yao, X.; Liu, Y.; Lin, G., Evolutionary programming made faster, IEEE Transactions on Evolutionary Computation, 3, 2, 82-102 (1999) · doi:10.1109/4235.771163
[33] Li, X.; Wang, J.; Zhou, J.; Yin, M., A perturb biogeography based optimization with mutation for global numerical optimization, Applied Mathematics and Computation, 218, 2, 598-609 (2011) · Zbl 1226.65055 · doi:10.1016/j.amc.2011.05.110
[34] Karaboga, D.; Basturk, B., A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm, Journal of Global Optimization, 39, 3, 459-471 (2007) · Zbl 1149.90186 · doi:10.1007/s10898-007-9149-x
[35] Yang, X. S.; Deb, S., Engineering optimisation by cuckoo search, International Journal of Mathematical Modelling and Numerical Optimisation, 1, 4, 330-343 (2010) · Zbl 1279.90204
[36] Beyer, H.-G., The Theory of Evolution Strategies (2001), Berlin, Germany: Springer, Berlin, Germany · Zbl 1001.68186
[37] Geem, Z. W.; Kim, J. H.; Loganathan, G. V., A new heuristic optimization algorithm: harmony search, Simulation, 76, 2, 60-68 (2001)
[38] Shumeet, B., Population-based incremental learning: a method for integrating genetic search based function optimization and competitive learning, CMU-CS-94-163 (1994), Pittsburgh, Pa, USA: Carnegie Mellon University, Pittsburgh, Pa, USA
[39] Cui, Z.; Gao, F.; Cui, Z.; Qu, J., A second nearest-neighbor embedded atom method interatomic potential for Li-Si alloys, Journal of Power Sources, 207, 150-159 (2012)
[40] Cui, Z.; Gao, F.; Cui, Z.; Qu, J., Developing a second nearest-neighbor modified embedded atom method interatomic potential for lithium, Modelling and Simulation in Materials Science and Engineering, 20, 1 (2011) · doi:10.1088/0965-0393/20/1/015014
[41] Wang, G.; Guo, L., Hybridizing harmony search with biogeography based optimization for global numerical optimization
[42] Tang, K.; Li, X.; Suganthan, P. N.; Yang, Z.; Weise, T., Benchmark functions for the CEC 2010 special session and competition on large scale global optimization (2010), Hefei, China: Nature Inspired Computation and Applications Laboratory, USTC, Hefei, China
[43] Mallipeddi, R.; Suganthan, P., Problem definitions and evaluation criteria for the CEC 2010 competition on constrained real-parameter optimization (2010), Singapore: Nanyang Technological University, Singapore
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