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ACM-DE: Adaptive p-best Cauchy Mutation with linear failure threshold reduction for Differential Evolution in numerical optimization

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Authors: Tae Jong Choi,Julian Togelius,Yun-Gyung Cheong
ArXiv: 1907.01095
Document:  PDF  DOI 
Abstract URL: https://arxiv.org/abs/1907.01095v2


A new Cauchy mutation for improving the convergence of differential evolution (DE) is proposed in this paper. DE is an efficient evolutionary algorithm for optimizing multidimensional real-valued functions, which has been successfully applied to various real-world problems. To improve convergence a Cauchy mutation-based DE variant called modified DE was proposed, but it has serious limitations of 1) controlling the balance between exploration and exploitation; 2) adjusting the algorithm to a given problem; 3) having less reliable performance on multimodal problems. In this paper, we propose a new adaptive Cauchy mutation-based DE variant called ACM-DE (Adaptive Cauchy Mutation Differential Evolution), which removes all of these limitations. Specifically, two popular parameter controls are employed for the exploration and exploitation scheme and robust performance. Also, a less greedy approach is employed, which uses any of the top p% individuals in the phase of the Cauchy mutation. Experimental results on a set of 58 benchmark problems show that ACM-DE is capable of finding more accurate solutions than modified DE, especially for multimodal problems. In addition, we applied ACM to two state-of-the-art DE variants, and similar to the previous results, ACM based variants exhibit significantly improved performance.

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