ADE: advanced differential evolution

This paper proposes a metaheuristic algorithm, called advanced differential evolution (ADE), by improving the DE algorithm. The ADE algorithm was developed with the goal of creating an optimization framework that addresses the challenges of exploration and exploitation balance, avoiding local minima, utilizing chaos theory for diverse initialization, and improving solution quality and convergence speed. By incorporating these features, ADE aims to enhance the effectiveness of optimization processes. The proposed algorithm utilizes chaos theory to generate the initial population, which is subsequently divided into two sub-populations with adaptive sizes. The size of each sub-population is determined using a formula based on the number of iterations during the algorithm’s execution. The first sub-population has a larger size in the beginning and the second one has a smaller size, but the total size of these two populations is always constant. The main contribution of this paper is the proposal of two novel improved differential evolution algorithms, namely MDE1 and MDE2, which are utilized for exploration within these sub-populations. The proposed ADE is tested on 29 well-known benchmarks and six engineering problems, and the results are compared with seven other algorithms. Various statistical experiments are carried out showing that the proposed algorithm provides significant superiority over other well-known algorithms.