Solving multimodal optimization problems based on efficient partitioning of genotypic search space

Authors: ATABAK MASHHADI KASHTIBAN, SOHRAB KHANMOHAMMADI, KAYVAN ASGHARI

Abstract: Enhancing the exploration and exploitation of multimodal optimization is still an interesting and challenging problem in optimization. Here we present a new population-based evolutionary algorithm for multiple optimal determinations. The approach is simply based on partitioning the genotypic search space and running a simple genetic algorithm with a small population within each partition. To increase the efficiency of the algorithm, the first-order discrete derivative of the fitness function for elite solutions was used to omit extra solutions. If the derivative of the fitness function is larger than a specified gradient threshold, no optimum exists within a given partition, and no population is created there after the first iteration. Except the adjusted gradient threshold, the proposed algorithm requires no other parameters rather than those of classical genetic algorithms. Moreover, unlike the other well-known algorithms, the proposed algorithm is not sensitive to the niche radius, and it needs no prior knowledge about the fitness function. The algorithm was tested for 10 multimodal benchmark functions, and its results were compared with the other related algorithms considering 4 commonly performance criteria. Our results show that the proposed algorithm is not only acceptable in terms of diversification and function evaluation number, but also has improved efficiency as compared to the others.

Keywords: Evolutionary algorithms, multimodal optimization problem, genotypic search space partitioning

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