Multiple global optima location using differential evolution, clustering, and local search

Multimodal optimization can be divided into two main categories. The first focuses on finding only one global optimum, e.g., one peak, and the second focuses on finding multiple global optima, e.g., multiple peaks, and it is the focus of this work. The first category can be approached by single-solution and population-based metaheuristics, while in the second category, the use of population-based metaheuristics is best suited. Finding multiple global optima is more common in real-world optimization problems where there is no previous information about the number of globally optimal solutions in the search space landscape. Thus, this work proposes a self-adaptive Differential Evolution with DBSCAN algorithm and a two-step exploitation routine, named NCjDE-2LS(ar), applied to multiple global optima multimodal optimization. The jDE algorithm with Michalewicz mutation strategy is employed as a global optimizer. Candidate solutions are grouped in an external archive using the DBSCAN algorithm. External archive solutions represent possible peaks that will feed the Nelder-Mead and Hooke-Jeeves exploitation algorithms. The peak ratio is used as a performance metric. Six state-of-the-art algorithms are used to compare the results obtained by the proposed approach. Results show that the proposed algorithm outperforms the state-of-the-art algorithms concerning the mean absolute value of the peak ratio evaluation metric. The algorithm also achieved the perfect peak ratio (100%) in 10 out of 20 functions. (C) 2021 Published by Elsevier B.V.

Automated summary

The article discusses two main categories of multimodal optimization: finding a single global optimum and finding multiple global optima. It proposes a self-adaptive Differential Evolution with DBSCAN algorithm named NCjDE-2LS(ar) for solving the problem of multiple global optima optimization. Experimental results demonstrate that the proposed algorithm outperforms state-of-the-art algorithms in terms of peak ratio evaluation metric.