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Please use this identifier to cite or link to this item: http://hdl.handle.net/123456789/3932

Title: Using Natural Reproduction Processes (Crossover, Mutation And Evolution) To Solve Some Special Complex Functions
Authors: Sarkodie Adabor, Emmanuel
Issue Date: 14-Jun-2012
Abstract: In recent years, Genetic Algorithms (GAs) have become increasingly robust and easy to use. Current knowledge and many successful experiments suggest that the application of GAs is not limited to easy-to-optimize unimodal functions. This work has as its objective to demonstrate the suitability of Genetic Algorithms in optimizing complex, multivariable and multimodal functions. In the quest to establish this objective, a Genetic Algorithm was used to solve three standard complicated functions namely Rosenbrock’s function, Schwefel’s function and the Rastrigin’s function. These functions are classified as standard/benchmark to test the quality of an optimization procedure based on the difficulty of the techniques to obtain the global minimum. A MATLAB function for the Genetic Algorithm was implemented to establish the general solutions and then consequently the conclusion. It was found after simulations that the global minimum for the two dimension Rosenbrock’s function was 0.0000496 which occurred at the point (1.0070, 1.0140); global minimum of the one dimension Rastrigin’s function was 0.00000000239 which occurred at the point 0.00000347; and the global minimum of the Schwefel’s function of a single variable was -418.9829 and it occurred at the point 420.9618. Similar results were also obtained for the Rastrigin’s function with five variables. The GA was recommended for the optimization of multimodal functions with huge number of local extremes and other problems with the behaviour of the Rosenbrock’s function, Rastrigin’s function or the Schwefel’s function.
Description: A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology in partial fulfillment of the Requirements for the Degree of Master Of Philosophy (Applied Mathematics)June 2012
URI: http://hdl.handle.net/123456789/3932
Appears in Collections:College of Science

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