Supervised Reconstruction for High-Dimensional Expensive Multiobjective Optimization

With the rising popularity of computationally expensive multiobjective optimization problems (EMOPs) in real-world applications, many surrogate-assisted evolutionary algorithms (SAEAs) have been proposed in the recent decade. Nevertheless, high-dimensional EMOPs remain challenging for existing SAEAs attributed to their requirement in massive fitness evaluations and complex models. We propose an SAEA with a supervised reconstruction strategy, namely SR-SAEA, for solving high-dimensional EMOPs. In SR-SAEA, we first select several well-converged reference solutions to form a set of reference vectors in the decision space. Then each candidate solution is projected onto these reference vectors, reflecting the closeness between the candidate solution and those reference solutions. Each candidate solution is then projected onto these reference vectors, generating a projection vector that reflects its proximity to the reference solutions. This allows the optimization of the high-dimensional decision vector to be approximated by optimizing the low-dimensional projection vector. Subsequently, a supervised autoencoder is employed to reconstruct the optimized low-dimensional projection vector back to the original decision space. Notably, the latency vector of the autoencoder is replaced with the projection vector for supervised reconstruction. An ablation study confirms the effectiveness of the proposed supervised reconstruction strategy. The superiority of SR-SAEA, compared with six state-of-the-art SAEAs, is validated on benchmark problems with up to 200 decision variables.