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Differential Evolution with Random Walk Mutation and an External Archive for Multimodal Optimization

Locating multiple optima of a problem is an important and challenging task for many real-world applications. In this paper, a random walk mutation strategy is proposed for differential evolution (DE) to handle multimodal optimization problems. The mutation strategy is able to find a balance between exploitation and exploration. First, the neighborhood and fitness information of individuals is incorporated into mutation to guide the formation of donor vectors. This facilitates the evolution of individuals toward their nearby optima. Second, the exploration ability of the mutation strategy is preserved by simulating a random walk process. Moreover, an archive technique is designed to detect converged subpopulations. The converged individuals are then reinitialized to search for other optima. This enhance the algorithm's exploration ability. Meanwhile, found optima can be maintained throughout the optimization process by using the archive technique. The random walk mutation strategy and the archive technique are integrated with DE to make a competitive multimodal algorithm. The resulting algorithm is tested on a recently proposed benchmark function set. Experimental results show that the proposed algorithm is able to provide better performance than a number of state-of-the-art multimodal algorithms.