A Nonlinear Dimensionality Reduction Search Improved Differential Evolution for large-scale optimization

Large-scale optimization problems present significant challenges due to the high dimensionality of the search spaces and the extensive computational resources required. This paper introduces a novel algorithm, Nonlinear Dimensionality Reduction Enhanced Differential Evolution (NDRDE), designed to address these challenges by integrating nonlinear dimensionality reduction techniques with differential evolution. The core innovation of NDRDE is its stochastic dimensionality reduction strategy, which enhances population diversity and improves the algorithm's exploratory capabilities. NDRDE also employs a spherical search method to maximize the obliteration of directional information, thus increasing randomness and improving the exploration phase. The algorithm dynamically adjusts the dimensionality of the search space, leveraging a combination of high-dimensional precision search and low-dimensional exploratory search. This approach not only reduces the computational burden but also maintains a high level of accuracy in finding optimal solutions. Extensive experiments on the IEEE CEC large-scale global optimization benchmark problems, including CEC2010 and CEC2013, demonstrate that NDRDE significantly outperforms several state-of-the-art algorithms, showcasing its superiority in tackling large-scale optimization problems. The code for NDRDE will be made publicly available at https://github.com/louiseklocky.