RDEL: Restart Differential Evolution algorithm with Local Search Mutation for global numerical optimization

In this paper, a novel version of Differential Evolution (DE) algorithm based on a couple of local search mutation and a restart mechanism for solving global numerical optimization problems over continuous space is presented. The proposed algorithm is named as Restart Differential Evolution algorithm with Local Search Mutation (RDEL). In RDEL, inspired by Particle Swarm Optimization (PSO), a novel local mutation rule based on the position of the best and the worst individuals among the entire population of a particular generation is introduced. The novel local mutation scheme is joined with the basic mutation rule through a linear decreasing function. The proposed local mutation scheme is proven to enhance local search tendency of the basic DE and speed up the convergence. Furthermore, a restart mechanism based on random mutation scheme and a modified Breeder Genetic Algorithm (BGA) mutation scheme is combined to avoid stagnation and/or premature convergence. Additionally, an exponent increased crossover probability rule and a uniform scaling factors of DE are introduced to promote the diversity of the population and to improve the search process, respectively. The performance of RDEL is investigated and compared with basic differential evolution, and state-of-the-art parameter adaptive differential evolution variants. It is discovered that the proposed modifications significantly improve the performance of DE in terms of quality of solution, efficiency and robustness.