Self equation based differential evolution for big optimization

Abstract The rapid advancement of technology and the exponential growth of the global population have led to an increasing demand for data-driven solutions, giving rise to Big Data. Extracting meaningful insights from these vast datasets has significantly enhanced decision-making in fields such as healthcare, finance, and e-commerce. In particular, electroencephalography (EEG) signal analysis is crucial for diagnosing complex neurological disorders, including schizophrenia, epilepsy, and psychological conditions. However, EEG signal processing presents a major challenge due to its high dimensionality and large-scale nature, making it a Big Optimization (BigOpt) problem. Evolutionary Algorithms (EAs) have been widely employed to address BigOpt challenges, with Differential Evolution (DE) being one of the most commonly used approaches. Despite its effectiveness, DE struggles with high-dimensional and computationally expensive BigOpt tasks due to its limited exploration and exploitation capabilities. To overcome these challenges, this study proposes Self-Equation-Based Differential Evolution for Big Optimization (SSE-DEP), an enhanced DE variant that integrates three key improvements: (1) Self-Adaptive Mutation Operator: Utilizes a dynamic mutation equation pool to enhance DE’s exploration. (2) Competitive Local Search: Dynamically integrates CMA-ES and Powell’s local search to improve exploitation. (3) oldArchive Strategy: Balances exploration and exploitation to prevent premature convergence and accelerate optimization. The proposed SSE-DEP algorithm was rigorously evaluated using the IEEE Congress on Evolutionary Computation (CEC) 2014 and CEC 2017 benchmark suites for problem dimensions of 30, 50, and 100, as well as the CEC 2019 benchmark set to assess its performance across diverse optimization challenges. Comparative analyses against various self-adaptive DE variants, state-of-the-art metaheuristic algorithms, and EEG-specific optimization approaches demonstrate that SSE-DEP significantly outperforms existing methods in both benchmark and real-world EEG signal decomposition tasks.