High-dimensional expensive problems are often encountered in the design and optimization of complex robotic and automated systems and distributed computing systems, and they suffer from a time-consuming fitness evaluation process. It is extremely challenging and difficult to produce promising solutions in a high-dimensional search space. This work proposes an evolutionary optimization framework with embedded autoencoders that effectively solve optimization problems with high-dimensional search space. Autoencoders provide strong dimension reduction and feature extraction abilities that compress a high-dimensional space to an informative low-dimensional one. Search operations are performed in a low-dimensional space, thereby guiding whole population to converge to the optimal solution more efficiently. Multiple subpopulations coevolve iteratively in a distributed manner. One subpopulation is embedded by an autoencoder, and the other one is guided by a newly proposed Multi-swarm Gray-wolf-optimizer based on Genetic-learning (MGG). Thus, the proposed multi-swarm framework is named Autoencoder-based MGG (AMGG). AMGG consists of three proposed strategies that balance exploration and exploitation abilities, i.e., a dynamic subgroup number strategy for reducing the number of subpopulations, a subpopulation reorganization strategy for sharing useful information about each subpopulation, and a purposeful detection strategy for escaping from local optima and improving exploration ability. AMGG is compared with several widely used algorithms by solving benchmark problems and a real-life optimization one. The results well verify that AMGG outperforms its peers in terms of search accuracy and convergence efficiency.