  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, namely CDM-PSL, for expensive MOBO.
CDM-PSL includes both unconditional and conditional diffusion model for
generating high-quality samples. Besides, we introduce an information entropy
based weighting method to balance different objectives of EMOPs. This method is
integrated with the guiding strategy, ensuring that all the objectives are
appropriately balanced and given due consideration during the optimization
process; Extensive experimental results on both synthetic benchmarks and
real-world problems demonstrates that our proposed algorithm attains superior
performance compared with various state-of-the-art MOBO algorithms.
