Global Optimization of Some Difficult Benchmark Functions by Cuckoo-Host Co-Evolution Meta-Heuristics

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.

[1]  J. Krebs,et al.  Arms races between and within species , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[2]  George E. P. Box,et al.  Evolutionary Operation: a Method for Increasing Industrial Productivity , 1957 .

[3]  G. Hogg,et al.  UNCONSTRAINED DISCRETE NONLINEAR PROGRAMMING , 1979 .

[4]  Aimo A. Törn,et al.  Topographical global optimization using pre-sampled points , 1994, J. Glob. Optim..

[5]  Clifford T. Brown,et al.  Lévy Flights in Dobe Ju/’hoansi Foraging Patterns , 2007 .

[6]  P. A. Prince,et al.  Lévy flight search patterns of wandering albatrosses , 1996, Nature.

[7]  M. J. Box.  A New Method of Constrained Optimization and a Comparison With Other Methods , 1965, Comput. J..

[8]  C. Tsallis,et al.  Generalized simulated annealing , 1995, cond-mat/9501047.

[9]  Zong Woo Geem,et al.  A New Heuristic Optimization Algorithm: Harmony Search , 2001, Simul..

[10]  N. Davies,et al.  AN EXPERIMENTAL STUDY OF CO-EVOLUTION BETWEEN THE CUCKOO, CUCULUS CANORUS, AND ITS HOSTS. I. HOST EGG DISCRIMINATION , 1989 .

[11]  John A. Nelder,et al.  A Simplex Method for Function Minimization , 1965, Comput. J..

[12]  Xin-She Yang,et al.  Engineering optimisation by cuckoo search , 2010 .

[13]  N. Davies,et al.  AN EXPERIMENTAL STUDY OF CO-EVOLUTION BETWEEN THE CUCKOO, CUCULUS CANORUS, AND ITS HOSTS. II. HOST EGG MARKINGS, CHICK DISCRIMINATION AND GENERAL DISCUSSION , 1989 .

[14]  Dervis Karaboga,et al.  A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm , 2007, J. Glob. Optim..

[15]  Ilya Pavlyukevich.  Lévy flights, non-local search and simulated annealing , 2007, J. Comput. Phys..

[16]  Ramin Rajabioun,et al.  Cuckoo Optimization Algorithm , 2011, Appl. Soft Comput..

[17]  H. Stanley,et al.  Lévy flight random searches in biological phenomena , 2002 .

[18]  S. Rothstein.  A Model System for Coevolution: Avian Brood Parasitism , 1990 .

[19]  Saeed Tavakoli,et al.  Improved Cuckoo Search Algorithm for Global Optimization , 2011 .

[20]  Sudhanshu K. Mishra,et al.  Some New Test Functions for Global Optimization and Performance of Repulsive Particle Swarm Method , 2006 .

[21]  Xin-She Yang,et al.  Cuckoo Search via Lévy flights , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[22]  Andrew M. Sutton,et al.  The Impact of Global Structure on Search , 2008, PPSN.

[23]  Johannes M. Dieterich,et al.  Empirical review of standard benchmark functions using evolutionary global optimization , 2012, ArXiv.

[24]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[25]  Fred W. Glover,et al.  Future paths for integer programming and links to artificial intelligence , 1986, Comput. Oper. Res..

[26]  Sudhanshu K. Mishra.  Performance of Differential Evolution and Particle Swarm Methods on Some Relatively Harder Multi-Modal Benchmark Functions , 2006 .

[27]  Marek Gutowski.  L\'evy flights as an underlying mechanism for global optimization algorithms , 2001 .

[29]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[30]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[31]  A. Zahavi,et al.  Constraints on egg discrimination and cuckoo-host co-evolution , 1995, Animal Behaviour.

[32]  Marco Dorigo,et al.  Optimization, Learning and Natural Algorithms , 1992 .

[33]  H. Stanley,et al.  Optimizing the success of random searches , 1999, Nature.

[34]  Xin Yao,et al.  Fast Evolutionary Programming , 1996, Evolutionary Programming.

[35]  Fabrizio Lillo,et al.  Correlation, Hierarchies, and Networks in Financial Markets , 2008, 0809.4615.

[36]  SK Mishra,et al.  Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions , 2006 .

[37]  Pinar Civicioglu,et al.  A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms , 2013, Artificial Intelligence Review.

[38]  S. Dreyfus,et al.  Thermodynamical Approach to the Traveling Salesman Problem : An Efficient Simulation Algorithm , 2004 .

[39]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[40]  Dervis Karaboga,et al.  AN IDEA BASED ON HONEY BEE SWARM FOR NUMERICAL OPTIMIZATION , 2005 .