Clustering-Based Monarch Butterfly Optimization for Constrained Optimization

Monarch butterfly optimization (MBO) algorithm is a newly-developed metaheuristic approach that has shown striking performance on several benchmark problems. In order to enhance the performance of MBO, many scholars proposed various strategies for benchmark evaluation and practical applications. As an application of artificial intelligence (AI), machine learning (ML) developed fast and succeeded in dealing with so many complicated problems. However, up to now, ML did not use to improve the performance of MBO algorithm. In this paper, one of ML techniques, clustering, is introduced into the basic MBO algorithm, so an improved clustering-based MBO namely CBMBO is proposed. In CBMBO algorithm, the whole population is divided into two subpopulations according to k-means clustering. Also, only the individuals having better fitness can be passed to the next generation instead of accepting all the updated individuals used in the basic MBO algorithm. In order to improve the diversity of the population, few individuals having worse fitness are accepted as new individuals. In order to verify the performance of our proposed CBMBO algorithm, CBMBO is compared with six basic and four improved metaheuristic algorithms on twenty-eight CEC 2017 constrained problems with dimension of 30, 50, and 100, respectively. The experimental results suggest a significant addition to the portfolio of computational intelligence techniques.