Differential Evolution and Agglomerative-Clustering-Based Mutation Strategy for Complex Numerical Optimization Problems

Abstract

Differential evolution is an evolutionary algorithm that is used to solve complex numerical optimization problems. Differential evolution balances exploration and exploitation to find the best genes for the objective function. However, finding this balance is a challenging task. To overcome this challenge, we propose a clustering-based mutation strategy called Agglomerative Best Cluster Differential Evolution (ABCDE). The proposed model converges in an efficient manner without being trapped in local optima. It works by clustering the population to identify similar genes and avoids local optima. The adaptive crossover rate ensures that poor-quality genes are not reintroduced into the population. The proposed ABCDE is capable of generating a population efficiently where the difference between the values of the trial vector and objective vector is even less than 1% for some benchmark functions, and hence it outperforms both classical mutation strategies and the random neighborhood mutation strategy. The optimal and fast convergence of differential evolution has potential applications in the weight optimization of artificial neural networks and in stochastic and time-constrained environments such as cloud computing.