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In this article, we propose a new hybrid Honey Bee Mating Optimization (HBMO) algorithm with simplex Nelder-Mead method in order to solve constrained optimization, integer programming and minimax problems. We call the proposed algorithm a hybrid Honey Bee Mating Optimization(HBMONM) algorithm. In the the proposed algorithm, we combine HBMO algorithm with Nelder-Mead method in order to refine the best obtained solution from the standard HBMO algorithm.We perform several experiments on a wide variety of well known test functions, 6 constrained optimization problems, 7 integer programming and 7 minimax benchmark problems.We compare the performance of HBMONMagainst standard HBMO algorithm and Genetic Algorithm (GA). In the majority of tests, HBMONM is shown to converge faster, and reach a better solution than both HBMO and GA in reasonable time.

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