DXMODE: A dynamic explorative multi-operator differential evolution algorithm for engineering optimization problems

Traditional methods often struggle with complex, real-world problems, while Differential Evolution (DE) offers more robust and adaptable solutions. However, many DE variants intertwine exploration and exploitation within mutation operators and rely on static or blind population reduction, leading to premature diversity loss. This paper proposes Dynamic Explorative Multi-Operator Differential Evolution (DXMODE), a novel DE variant featuring Error-based Linear Population Decay (ELPD) for adaptive sizing, considering both the error improvement and the iteration count. A decoupled exploration phase is also introduced with two new operators, Aggressive Gaussian Exploration (AGE) and Multiple Nested Chaotic Exploration (MNCE), enhancing diversity and search efficiency. DXMODE is validated on CEC2020/2021 and CEC2022 benchmarks against 30 state-of-the-art algorithms, including advanced DE variants and CEC winners. Statistical analyses indicate that DXMODE consistently outperforms competing methods, securing first place across all tests with statistically significant p-values; it surpasses IMODE with a confidence of 99.29%. DXMODE is also validated on 13 Engineering optimization problems, outperforming all algorithms with significant p-values, proving its superiority across real-world problems. The source code of DXMODE is available at: [GitHub/Mathworks repository link will be provided upon publication].