Applied Mathematics & Information Sciences

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In this paper, we propose a new hybrid algorithm for solving global optimization problems, namely, integer programming and minimax problems. The main idea of the proposed algorithm, Direct Search Firefly Algorithm (DSFFA), is to combine the firefly algorithm with direct search methods such as pattern search and Nelder-Mead methods. In the proposed algorithm, we try to balance between the global exploration process and the local exploitation process. The firefly algorithm has a good ability to make a wide exploration process while the pattern search can increase the exploitation capability of the proposed algorithm. In the final stage of the proposed algorithm, we apply a final intensification process by applying the Nelder-Mead method on the best solution found so far, in order to accelerate the search instead of letting the algorithm running with more iterations without any improvement of the results. Moreover, we investigate the general performance of the DSFFA algorithm on 7 integer programming problems and 10 minimax problems, and compare it against 5 benchmark algorithms for solving integer programming problems and 4 benchmark algorithms for solving minimax problems. Furthermore, the experimental results indicate that DSFFA is a promising algorithm and outperforms the other algorithms in most cases.

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