• Samuel O. Obadan
  • Zenghui Wang




Simulated Annealing, Particle Swarm Optimization, Genetic Algorithm, Cuckoos-Search Algorithm, Hybridization.


With respect to the ‘no free launch’ theorem, no single algorithm has a better performance when tested against a completely stochastic algorithm on all objective functions. Consequently, choosing the best algorithm for a particular problem is often more of an art than science. The complexity of an objective function can be determined by certain features such as the modality, the basins, the valleys, the separability, and the dimensionality of the objective function. While the separability and modality contribute to the complexity of the function, the dimensionality and domain range increases the function’s search space exponentially. In this paper, the authors analyze the algorithmic constructs of Simulated Annealing (SA), Cuckoo-search (CK), Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) along with two hybrid paradigms. In addition, an extensive comparative study was conducted using 30 standard bench mark functions to demonstrate how an ingenious hybrid algorithm could significantly shorten the amount of function calls (generations) needed to attain the optimal or rather near optimal solution for almost any complex objective function. Results from empirical analysis unveil the precision, robustness and success of the hybrid algorithm (without compromising run-time complexity) over its counterparts.


A. Prügel-Bennett, “Benefits of a population: five mechanisms that advantage population-based algorithms,” IEEE Trans. Evol. Comput., Vol. 14, No. 4, pp. 500-517, 2010.

R. L. Haupt, S. E. Haupt, Practical Genetic Algorithms, John Wiley and Sons Inc. 2004.

M. Jamil and X.-S. Yang, “A literature survey of benchmark functions for global optimization problems,” Int. Journal of Mathematical Modelling and Numerical Optimisation, Vol. 4, No. 2, pp. 150–194 2013.

D. H. Ackley, A Connectionist Machine for Genetic Hill-Climbing, Kluwer, 1987.

I. O. Bohachevsky, M. E. Johnson, M. L. Stein, “General Simulated Annealing for Function Optimization,” Technometrics, Vol. 28, No. 3, pp. 209-217, 1986.

C. Muntenau, V. Lazarescu, “Global search using a new evolutionay framework: the adaptive reservoir genetic algorithm,” Complexity International, vol. 5, 1998.

F. H. Branin Jr., “Widely convergent method of finding multiple solutions of simultaneous nonlinear equations,” IBM Journal of Research and Development, vol. 16, no. 5, pp. 504-522, 1972.

A. Lavi, T. P. Vogel (eds), Recent Advances in Optimization Techniques,” JohnWliley & Sons, 1966.

M. M. Ali, C. Khompatraporn, Z. B. Zabinsky, “A numerical evaluation of several stochastic algorithms on selected continuous global optimization test problems,” Journal of Global Optimization, vol. 31, pp. 635-672, 2005.

C. J. Chung, R. G. Reynolds, “CAEP: an evolution-based tool for real-valued function optimization using cultural algorithms,” International Journal on Artificial Intelligence Tool, vol. 7, no. 3, pp. 239-291, 1998.

S. S. Rao, Engineering Optimization: Theory and Practice, John Wiley & Sons, 2009.

A. A. Goldstein, J. F. Price, “On descent from local minima,” Mathematics and Comptutaion, vol. 25, no. 115, pp. 569-574, 1971.

H. H. Rosenbrock, “An automatic method for finding the greatest or least value of a function,” Computer Journal, vol. 3, no. 3, pp. 175-184, 1960.

S. K. Mishra, “Some new test functions for global optimization and performance of repulsive particle swarm method,” http://mpra.ub.uni-muenchen.de/2718/

S. K. Mishra, “Global optimization by differential evolution and particle swarm methods: evaluation on some benchmark functions,” Munich Research Papers in Economics: http://mpra.ub.uni-muenchen.de/1005/

E. P. Adorio, U. P. Dilman, “MVF – multivariate test function library in C for unconstrained global optimization methods,” http://www.geocities.ws/eadorio/mvf.pdf

C. S. Adjiman, S. Sallwig, C. A. Flouda, A. Neumaier, “A global optimization method, aBB for general twice-differentiable NLPs-1, theoretical advances,” Computers Chemical Engineering, vol. 22, no. 9, pp. 1137-1158, 1998.

N. Damavandi, S. Safavi-Naeini, “A hybrid evolutionary programming method for circuit optimization,” IEEE Transaction on Circuit and Systems I, vol. 52, no. 5, pp. 902-910, 2005.

M. Negnevitsky, Artificial Intelligence: A Guide to Intelligent Systems, second edition, Pearson Education Limited, Edinburgh Gate, Harlow, 2005.

S. Kirkpatrick, C.D. Gelatt Jr., and M.P Vecchi, “Optimization by simulated annealing,” Science, Vol. 220, Issue 4598, pp. 671-680, 1983.

J. Kennedy and R.C. Eberhart, “Particle swarm optimization,” Proceedings of the IEEE International Conference on Neural Networks, 1995.

X.-S. Yang, S. Deb, “Cuckoo search via Lévy flights,” Proceedings of the IEEE World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), India, 1999, pp. 210-214.

S.A. Kazarlis, et al., “Micro-genetic algorithms as generalized hill climbing operators for GA optimization,” IEEE Trans. Evol. Comp., Vol. 5, No. 3, pp. 204-217, 2001.

K. A. De Jong, An Analysis of a Class of Genetic Adaptive Systems, Ph.D. thesis, University of Michigan, 1975.

D. E. Goldberg and J. Richardson, “Genetic algorithm with sharing for multimodal function optimization,” Proceedings of the second International Conference on Genetic Algorithms and their Applications, Cambridge, Massachusetts, USA, 1987, pp. 41-49.

I. J Eshelman and J. D. Schaffer, “Preventing premature convergence in genetic algorithms by preventing incest,” In: R.Belew, L.B. Booker, (eds), Proc. of the Fourth Int. Conf. on Genetic Algorithms. Morgan Kaufmann, San Mateo, CA, 1991, pp. 115-122.

J. H. Holland, Adaptation in Neural and Artificial Systems, second edition, University of Michigan press, 1975.

P. Civicioglue, E. Besdok, “A conceptual comparison of the Cuckoo-search, particle Swarm optimization, differential evolution and artificial bee colony algorithms,” Artificial Intelligence Review, Vol. 39, Issue 4, pp. 315-346, 2013. DOI 10.1007/s10462-011-9276-0.

N. Barton and T. Paixão, “Can quantitative and population genetics help us understand evolutionary computation?,” Proceedings of the 15th annual conference on Genetic and evolutionary computation GECCO ’13, July 6-10’2013, pp. 1573–1580.

B. Doerr, C. Doerr and F. Ebel, “From black-box complexity to designing new genetic algorithms”, Theor. Comput. Sci., Vol. 567, pp. 87–104, 2015.




How to Cite

Obadan, S. O., & Wang, Z. (2018). A HYBRID OPTIMIZATION APPROACH FOR COMPLEX NONLINEAR OBJECTIVE FUNCTIONS. International Journal of Computing, 17(2), 102-112. https://doi.org/10.47839/ijc.17.2.996