Enhancing SHADE and L-SHADE Algorithms Using Ordered Mutation

Differential Evolution (DE) algorithm is an efficient population-based metaheuristic algorithm which has shown satisfactory performance in solving complex real-world optimization problems. A Success-History Based Parameter Adaptation for Differential Evolution (SHADE) is a well-established variant of DE algorithm which employs a historical performance of the successful control parameters. L-SHADE algorithm extends SHADE with a linear population size reduction strategy. The SHADE and L-SHADE algorithms employ current-to-pbest/1 strategy for evolution, whilst the order of candidate solutions is not considered in their schemes. This paper proposes an ordering strategy for SHADE and L-SHADE algorithms which has shown a satisfactory influence on the performance of both algorithms. In the first direction, we propose current-to-3order/1 strategy for SHADE algorithm, which is based on ordering three candidate solutions. In the second direction, L-SHADE algorithm is improved based on ordering two candidate solutions, called current-to-pbest-2order/1. The proposed strategies can improve the performance of SHADE and L-SHADE algorithms without adding any extra significant computational cost. The proposed strategy is evaluated on CEC-2017 benchmark functions and with dimensions 30, 50, and 100. Our experimental results clearly verify the effectiveness of the proposed strategies.