Differential evolution based on two-stage mutation strategy and multi-stage parameter control

Abstract

The Differential Evolution (DE) algorithm is an advanced evolutionary method for tackling global optimization challenges, yet designing effective parameter control generation methods and mutation strategies remains a significant challenge. In response, this paper introduces a differential evolution based on Two-Stage Mutation Strategy and Multi-Stage Parameter Control (TSMS-DE). Firstly, a multi-stage parameter control is proposed, in the early stage, a larger step size is used to enhance exploration, in the mid stage, the scaling factor is dynamically adjusted based on individual ranking, and in the late stage, a Cauchy distribution is applied to improve parameter adaptability. Secondly, an external archive optimization method utilizing a Two-Stage Mutation Strategy is developed to effectively eliminate individuals with suboptimal fitness values, ensuring the archive consistently retains high-quality individuals. Third, TSMS-DE employs an Opposite-Based Learning Strategy to generate sample points in the solution space, enabling more comprehensive coverage of the search space and enhancing overall search performance. We conducted comparative experiments on 100 benchmark test suites from the Congress on Evolutionary Computation (CEC) competitions, including CEC2013, CEC2014, CEC2017 and CEC2022. In order to rigorously evaluate the performance of the algorithms, statistical validation was carried out using a variety of tests. Compared to several advanced Differential Evolution variants and heuristic algorithms, the results demonstrate that our algorithm exhibits significant advantages in convergence, diversity, and accuracy.