Expensive Multiobjective Optimization Guided by Attention-Enhanced Generative Models

Surrogate-assisted evolutionary algorithms (SAEAs) have garnered significant attention for addressing expensive multiobjective optimization problems. Most existing SAEAs, however, still rely on conventional genetic operators in reproduction, which is inefficient in generating promising candidate solutions. To address the above issue, this article presents a learning-based generative model that replaces crossover and mutation and learns to conduct multiobjective search for expensive multiobjective optimization problems. The key idea is to design an attention-enhanced convolutional residual network with the assistance of surrogate model for offspring generations. The proposed framework employs a generative model to produce promising solutions for each decomposed subproblem based on the Tchebycheff metric, while a surrogate model assists in optimizing the generative model's hyperparameters through an online learning process. We demonstrate the efficacy of our learning-based multiobjective generative model (LMOGM) on DTLZ, ZDT, and WFG benchmark function suites, varying in dimensions from 30 to 200, as well as through a practical application involving the geothermal energy extraction design optimization. Experimental results highlight the superior performance of the proposed approach when compared to traditional evolutionary algorithms and state-of-the-art surrogate-assisted multiobjective evolutionary algorithms (MOEAs).