Surrogate and Autoencoder-Assisted Multitask Particle Swarm Optimization for High-Dimensional Expensive Multimodal Problems

In practice, some optimization problems require expensive calculation and exhibit multimodal characteristics simultaneously. These problems are called high-dimensional expensive multimodal optimization problems. When addressing such problems, existing surrogate-assisted evolutionary algorithms (SAEAs) encounter the “curse of dimensionality," which severely affects their capability to search optimal solutions. Therefore, this study proposed a surrogate and autoencoder-assisted multitask particle swarm optimization algorithm. First, an autoencoder-embedded multitask evolutionary framework was established to transform a high-dimensional multimodal optimization problem into multiple low-dimensional subproblems or subtasks. Further, a multi-level surrogate model management mechanism combining mirror learning was proposed. An appropriate local surrogate model can be rapidly generated for each modality of the problem. Moreover, a dual-mode local exploitation strategy was developed to improve the capability of swarm to exploit each subtask. The proposed algorithm was compared with seven existing SAEAs on 33 benchmark functions and the aeroengine aerodynamic design optimization problem. Experimental results revealed that the proposed algorithm can obtain multiple highly competitive optimal solutions, including global optimal solutions.