Expensive Multi-Objective Bayesian Optimization Based on Diffusion Models

Multi-objective Bayesian optimization (MOBO) has shown promising performance on various expensive multi-objective optimization problems (EMOPs). However, effectively modeling complex distributions of the Pareto optimal solutions is difficult with limited function evaluations. Existing Pareto set learning algorithms may exhibit considerable instability in such expensive scenarios, leading to significant deviations between the obtained solution set and the Pareto set (PS). In this paper, we propose a novel Composite Diffusion Model based Pareto Set Learning algorithm (CDM-PSL) for expensive MOBO. CDM-PSL includes both unconditional and conditional diffusion model for generating high-quality samples efficiently. Besides, we introduce a weighting method based on information entropy to balance different objectives. This method is integrated with a guiding strategy to appropriately balancing different objectives during the optimization process. Experimental results on both synthetic and real-world problems demonstrates that CDM-PSL attains superior performance compared with state-of-the-art MOBO algorithms.