Affiliations: [a] Department of Computer Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt | [b] Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, Kamloops, BC, Canada | [c] Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt
Correspondence:
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Corresponding author: Mohamed A. Tawhid, Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, Kamloops, BC, Canada. E-mail: Mtawhid@tru.ca.
Abstract: The aim of this paper is to produce a new hybrid algorithm to solve minimax problems by combining the bat algorithm with direct search methods. The proposed algorithm is called hybrid bat direct search algorithm (HBATDS). In HBATDS, the global exploration and the local exploitation process are balanced. The bat algorithm has a good ability to make exploration and exploitation search. The exploitation capability of the proposed algorithm is increased by invoking the pattern search method as a local search method instead of the random walk method in the standard bat algorithm. In the final stage of the algorithm, the Nelder-Mead method is applied in order to refine the best found solution from the bat and pattern search method instead of running the algorithm more iterations without any improvements in the fitness function value. The performance of the HBATDS algorithm is investigated by applying it on 10 minimax problems and comparing it against 8 benchmark algorithms. The experimental results indicate that HBATDS is a promising algorithm and outperforms the other algorithms in most cases.
Keywords: Bat algorithm, direct search methods, pattern search, Nelder-Mead method, minimax problemsMathematics Subject Classification. 90C47, 90C30, 49K35, 68U20, 68W01.
