Dual-Stage Self-Adaptive Differential Evolution with Complementary and Ensemble Mutation Strategies for Solving Global Optimization Problems

Differential Evolution (DE) algorithm is widely employed in tackling various real-world optimization problems due to its remarkable performance. Nonetheless, there is a need for further research to address issues such as high parameter sensitivity and the tendency of optimization capabilities to favour specific applications. This paper introduces a novel DE variant known as LSHADE-Code, designed for solving global optimization problems. This approach incorporates a novel mean calculation mode inspired by the Lehmer mean and leverages linear interpolation to ensure a smooth transition during parameter adjustments. By doing so, it mitigates the issue of premature convergence, which is often encountered in adaptive schemes reliant solely on the weighted Lehmer mean. LSHADE-Code also introduces a novel mutation strategy to enhance search efficiency. It utilizes symmetric complementary mechanisms and leverages the characteristics of Gaussian probability distributions, making it highly adaptable for exploration during the evolutionary phases. Furthermore, we combine this strategy with two other mutation strategies to create a composite approach, enabling the algorithm to dynamically select the most suitable method for individuals. Moreover, by reinforcing the population reduction scheme from LSHADE, LSHADE-Code experiences a faster reduction in population size, thereby improving its capacity for local exploration in the later stages of evolution. This new variant has been thoroughly validated on CEC 2011 and CEC 2020 test suites, with results showcasing LSHADE-Code's strong competitiveness when compared to state-of-the-art algorithms.