Multispace Dimensionality Reduction Based on Extreme Learning Machine-Assisted Autoencoder for High-Dimensional Expensive Optimization
提出一种多空间降维的高维昂贵优化算法，利用两种极限学习机辅助自编码器分别构建压缩空间，让低质量个体快速探索、中等质量个体加速收敛，高质量个体在原始空间精细搜索，显著提升优化性能。
Faced with high-dimensional expensive optimization problems (HEOPs), existing high-dimensional expensive optimization algorithms (HEOAs) struggle to locate promising areas quickly due to a dramatically expanded search space. Besides, slow convergence is a critical issue causing inefficiency of HEOAs. To address these issues, we propose a multispace dimensionality reduction-based HEOA (MDR-HEOA) where two extreme learning machine-assisted autoencoders (ELM-AEs) are devised. Specifically, an autoencoder with online sequential learning ELM (OSL-ELM-AE) builds a compressed space, where individuals of low quality explore expecting to locate promising areas quickly. Afterwards, the individuals’ positions are reconstructed to the original space by the output layer of OSL-ELM-AE. Online sequential learning ELM continuously updates OSL-ELM-AE’s parameters whenever new individuals arrive, ensuring high generalization performance in reconstructing the positions that approximate the related target ones. In contrast, ELM-AE with an equal number of hidden nodes and the individuals input each time (ELM-EAE) compresses the search space, where medium-quality individuals exploit aiming to expedite convergence. Based on the universal approximation theorem, ELM-EAE can learn these input individuals with zero error, demonstrating high reconstruction capability. Thus, the individuals’ positions with small offsets caused by exploitation can be reconstructed to closely approximate their target ones. Besides, high-quality individuals conduct a refined search in the original space to find the optimal solution of a HEOP. Our experimental results, particularly comprehensive comparisons with nine state-of-the-art HEOAs, validate that MDR-HEOA significantly improves the performance in handling HEOPs.