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A HYBRID OPTIMIZATION APPROACH FOR COMPLEX NONLINEAR OBJECTIVE FUNCTIONS

Samuel O. Obadan, Zenghui Wang

Abstract


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.

Keywords


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

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References


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