Differential Evolution with Self-Adaptive Mutation and Population Improvement Strategy for Optimization Problems

Abstract

Differential Evolution (DE) algorithms are widely recognized as effective metaheuristic techniques used to solve continuous optimization problems. However, DE algorithms encounter limitations in exploration and exploitation due to their sensitivity to parameter settings and reliance on mutation strategies. To overcome these drawbacks, we introduced a self-adaptive mutation and population improvement strategy in differential evolution, SAMPIDE. The algorithm adjusts the mutation operator automatically according to the successful mutation operator value from the previous generation. Additionally, to enhance the algorithm's convergence, we adopted a random learning mechanism to update the population. SAMPIDE was compared with nine state-of-the-art DE variants and four other metaheuristic algorithms across thirty-two benchmark functions. SAMPIDE consistently outperformed others on unimodal, step and noisy functions, while maintaining competitive performance on multimodal functions. Additionally, when tested on five real-world problems, SAMPIDE outperformed other metaheuristic algorithms. Thus, the self-adaptive mutation and population improvement strategy incorporated into SAMPIDE positioned it as a promising solution for a wide range of optimization problems.