Global optimization of some difficult benchmark functions by cuckoo-hostco-evolution meta-heuristics

Mishra, SK (2012): Global optimization of some difficult benchmark functions by cuckoo-hostco-evolution meta-heuristics.

Abstract

This paper proposes a novel method of global optimization based on cuckoo-host co-evaluation. It also develops a Fortran-77 code for the algorithm. The algorithm has been tested on 96 benchmark functions (of which the results of 30 relatively harder problems have been reported). The proposed method is comparable to the Differential Evolution method of global optimization.

• Item Type: MPRA Paper
• Language: English
• Keywords: Cuckoo-Host Co-Evolution; Cuckoo Search; Global Optimization; Differential Evolution; Levy flight; Benchmark functions
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C87 - Econometric Software; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

References

Box, G.E.P. (1957) “Evolutionary Operation: A Method for Increasing Industrial Productivity”, Applied Statistics, 6 :81-101.

Box, M.J. (1965) “A New Method of Constrained Optimization and a Comparison with Other Methods”, Comp. Journal, 8: 42-52.

Brown, C., Liebovitch, L. S., Glendon, R. (2007) “Lévy flights in Dobe Ju/’hoansi foraging patterns”, Human Ecol., 35(129-138).

Cerny, V. (1985) "Thermodynamical Approach to the Traveling Salesman Problem: An Efficient Simulation Algorithm", J. Opt. Theory Appl., 45(1):41-51.

Civicioglu, P. and Besdok, E. (2011) “A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms”, Artificial Intelligence Review, DOI 10.1007/s10462-011-9276-0

Davies, N.B. and Brooke, M. de L. (1989a) “An experimental study of co-evolution between the cuckoo, Cuculus canorus, and its hosts. I. Host egg discrimination”. J. Anim. Ecol., 58: 207-224.

Davies, N.B. and Brooke, M. de L. (1989b) An experimental study of co-evolution between the cuckoo, Cuculus canorus, and its hosts. II. Host egg markings, chick discrimination and general discussion”, J. Anim. Ecol., 58:225-236.

Dawkins, R. and Krebs, J. R. (1979) “Arms races between and within species”, Proc. R. Soc. Lond. Ser. B., 205:489–511.

Dorigo, M. (1992) Optimization, Learning and Natural Algorithms, PhD thesis, Politecnico di Milano, Italie, 1992.

Eberhart R.C. and Kennedy J. (1995) “A New Optimizer using Particle Swarm Theory”, in Proceedings Sixth Symposium on Micro Machine and Human Science, pp. 39–43. IEEE Service Center, Piscataway, NJ, 1995.

Geem, Z.W., Kim, J.H. and Loganathan, G.V. (2001) “A New Heuristic Optimization Algorithm: Harmony Search”, Simulation, 76(2):60-68.

Glover F. (1986) "Future Paths for Integer Programming and Links to Artificial Intelligence", Computers and Operations Research, 5:533-549.

Gutowski, M. (2001) “Lévy flights as an underlying mechanism for global optimization algorithms”, arXiv:math-ph/0106003v1[4 Jun 2001]. http://arxiv.org/abs/math-ph/0106003v1.

Holland, J. (1975) Adaptation in Natural and Artificial Systems, Univ. of Michigan Press, Ann Arbor, 1975.

Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization, Technical Report-TR06, Computer Engineering Department. Erciyes University, Turkey.

Karaboga, D. & Basturk, B. (2007). A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization, 39 (3), 459-471.

Kirkpatrick, S., Gelatt, C.D. Jr., and Vecchi, M.P. (1983) "Optimization by Simulated Annealing", Science, 220 (4598):671-680.

Lotem, A., Nakamura, H. and Zahavi, A. (1995) “Constraints on egg discrimination and cuckoo–host co-evolution”, Animal Behav., 49(5): 1185–1209

Lŭcíc, P. and Teodorovíc, D. (2001) “Bee system: modeling combinatorial optimization transportation engineering problems by swarm intelligence”, in Preprints of the TRISTAN IV Triennial Symposium on Transportation Analysis. Sao Miguel, Azores Islands: 441–445.

Mishra, S.K. (2010) "Performance of Differential Evolution and Particle Swarm Methods on Some Relatively Harder Multi-modal Benchmark Functions", The IUP Journal of Computational Mathematics, III(1): 7-18.

Mishra, S.K. (2006a) "Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions", Working Paper Series, Munich Personal RePEc Archive. http://mpra.ub.uni-muenchen.de/1005/1/MPRA_paper_1005.pdf.

Mishra, S.K. (2006b) “Some New Test Functions for Global Optimization and Performance of Repulsive Particle Swarm Method”, Social Science Research Network (SSRN) Working Papers Series, http://ssrn.com/abstract=927134.

Nelder, J.A. and Mead, R. (1964) “A Simplex Method for Function Minimization” Computer Journal, 7: 308-313.

Pavlyukevich, I. (2007) “Lévy flights, non-local search and simulated annealing”, J. Computational Physics, 226(1830-1844).

Rajabioun, R. (2011) “Cuckoo Optimization Algorithm”, Applied Soft Computing, 11: 5508–5518.

Storn, R. and Price, K. (1995) "Differential Evolution - A Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces": Technical Report, International Computer Science Institute, Berkley.

Rothstein, S. I. (1990) “A model system for co-evolution: avian brood parasitism”, A. Rev. Ecol. Syst., 21:481–508.

Teodorović, D., Davidović, T. and Šelmić, M. (2011) “Bee Colony Optimization: The Applications Survey”, http://www.mi.sanu.ac.rs/~tanjad/BCO-ACM-Trans-Ver2.pdf

Törn, A.A and Viitanen, S. (1994) “Topographical Global Optimization using Presampled Points”, J. of Global Optimization, 5:267-276.

Tsallis, C. and Stariolo, D.A. (1995) “Generalized Simulated Annealing”, ArXive condmat/9501047 v1 12 Jan, 1995.

Valian, E., Mohanna, E. and Tavakoli, S. (2011) “Improved Cuckoo Search Algorithm for Global Optimization”, Int. J. Communications and Information Technology, 1(1): 31-44.

Viswanathan, G. M., Afanasyev, V., Buldyrev, S. V., Murphy, E. J., Prince, P. A., and Stanley, H. E. (1996) “Lévy Flight Search Patterns of Wandering Albatrosses”, Nature 381: 413–415.

Viswanathan, G. M., Buldyrev, S. V., Havlin, S., da Luz, M. G. E., Raposo, E. P., and Stanley, H. E. (1999) “Optimizing the Success of Random Searches”, Nature 401: 911–914.

Viswanathan, G. M., Bartumeus, F., Buldyrev, S. V., Catalan, J.,Fulco, U. L., Havlin, S., da Luz, M. G. E., Lyra, M. L., Raposo,E. P., and Stanley, H. E. (2002) “Lévy Flight Random Searches in Biological Phenomena”, Physica A 314: 208–213.

Yang, X. S. and Deb, S. (2009) “Cuckoo search via Lévy flights”, Proceeings of World Congress on Nature & Biologically Inspired Computing (NaBIC 2009, India), IEEE Publications, USA: 210-214.

Yang, X.S. and Deb, S. (2010) “Engineering Optimisation by Cuckoo Search”, Int. J. Mathematical Modelling and Numerical Optimisation, 1(4): 330–343.