Implementation Strategies for the Cuckoo Search and the African Buffalo Optimization for the Benchmark Rosenbrock Function

Abstract

The introduction of five benchmark global optimization test functions by De Jong has remained prominent in Mathematics and Computer Science for over three decades now. This paper examines the effect of the search population and the number of iterations of the Cuckoo Search and the African Buffalo Optimization in providing solutions to one of Dejong function, the Rosenbrock function, sometimes called Dejong2 function which is a unimodal non-separable function. The Rosenbrock function because of its deceptive flat landscape has proven to be a good test case for optimization algorithms since the flat surface provides very misleading information to search agents. After a number of experimental investigations using different iteration numbers and population, this study concludes that the CS provides better solutions but at a cost of more computer resources than the ABO. As a result, this study in harmony with the No Free Lunch Theorem concludes that if speed is the main consideration, the ABO is a better algorithm in solving the Rosenbrock (or a similar function), otherwise, the CS is a better choice.  

Keywords

• African buffalo optimization,Cuckoo search,Iteration,Rosenbrock,Search

References

1. Agrawal, S., Panda, R., Bhuyan, S. and Panigrahi, B. K. (2013) 'Tsallis entropy based optimal multilevel thresholding using cuckoo search algorithm', Swarm and Evolutionary Computation, 11, pp. 16-30. Casini, F., Vaunat, J., Romero, E. and Desideri, A. (2012) 'Consequences on water retention properties of double-porosity features in a compacted silt', Acta Geotechnica, 7(2), pp. 139-150. De Jong, K. A. (1975) 'Analysis of the behavior of a class of genetic adaptive systems'. function, S. (Accessed on 30th January, 2017a) 'http://www-optima.amp.i.kyoto-u.ac.jp/member/student/hedar/Hedar_files/TestGO_files/Page1113.htm'. Function, S. (Accessed on 30th January, 2017b) 'http://www.al-roomi.org/benchmarks/unconstrained/n-dimensions/192-step-function-no-1'. Kamat, S. and Karegowda, A. (2014) 'A brief survey on cuckoo search applications', Int. J. Innovative Res. Comput. Commun. Eng, 2(2). Khompatraporn, C., Pintér, J. D. and Zabinsky, Z. B. (2005) 'Comparative assessment of algorithms and software for global optimization', Journal of Global Optimization, 31(4), pp. 613-633. Kunna, M. A., Kadir, T. A. A., Jaber, A. S. and Odili, J. B. (2015) 'Large-Scale Kinetic Parameter Identification of Metabolic Network Model of E. coli Using PSO', Advances in Bioscience and Biotechnology, 6(02), pp. 120. Odili, J. B. and Kahar, M. N. M. (2015a) 'African Buffalo Optimization (ABO): a New Meta-Heuristic Algorithm', Journal of Advanced & Applied Sciences, pp. 101-106. Odili, J. B. and Kahar, M. N. M. (2015b) 'Numerical Function Optimization Solutions Using the African Buffalo Optimization Algorithm (ABO)', British Journal of Mathematics & Computer Science, 10(1), pp. 1-12. Odili, J. B., Kahar, M. N. M., Anwar, S. and Azrag, M. A. K. 'A comparative study of African Buffalo Optimization and Randomized Insertion Algorithm for asymmetric Travelling Salesman's Problem'. Software Engineering and Computer Systems (ICSECS), 2015 4th International Conference on: IEEE, 90-95. Odili, J. B. and Mohmad Kahar, M. N. (2016a) 'African Buffalo Optimization Approach to the Design of PID Controller in Automatic Voltage Regulator System', National Conference for Postgraduate Research, Universiti Malaysia Pahang, September, 2016, pp. 641-648. Odili, J. B. and Mohmad Kahar, M. N. (2016b) 'Solving the Traveling Salesman's Problem Using the African Buffalo Optimization', Computational intelligence and neuroscience, 2016, pp. 1-12. Problems, B. (Accessed on 11th February, 2017) 'Benchmark Problems', https://www.cs.cmu.edu/afs/cs/project/jair/pub/volume24/ortizboyer05a-html/node6.html. Rosenbrock (Accessed on 30th Janauary, 2017) 'http://www.cs.unm.edu/~neal.holts/dga/benchmarkFunction/rosenbrock.html'. Sackton, T. B. and Hartl, D. L. (2016) 'Genotypic context and epistasis in individuals and populations', Cell, 166(2), pp. 279-287. Shi, Y. and Eberhart, R. C. 'Empirical study of particle swarm optimization'. Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress on: IEEE, 1945-1950. Sörensen, K. (2015) 'Metaheuristics—the metaphor exposed', International Transactions in Operational Research, 22(1), pp. 3-18. Visintin, A. (2012) Models of phase transitions. Springer Science & Business Media. Yang, X.-S. and Deb, S. 'Cuckoo search via Lévy flights'. Nature & Biologically Inspired Computing, 2009. NaBIC 2009. World Congress on: IEEE, 210-214.