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.

Optimizing multiple conflicting black-box objectives simultaneously is a prevalent occurrence in many real-world applications, such as neural architecture search, and machine learning. These problems are known as expensive multi-objective optimization problems (EMOPs) when the function evaluations are computationally or financially costly. Multi-objective Bayesian optimization (MOBO) offers an efficient approach to discovering a set of Pareto optimal solutions. However, the data deficiency issue caused by limited function evaluations has posed a great challenge to current optimization methods. Moreover, most current methods tend to prioritize the quality of candidate solutions, while ignoring the quantity of promising samples. In order to tackle these issues, our paper proposes a novel multi-objective Bayesian optimization algorithm with a data augmentation strategy that provides ample high-quality samples for Pareto set learning (PSL). Specifically, it utilizes Generative Adversarial Networks (GANs) to enrich data and a dominance prediction model to screen out high-quality samples, mitigating the predicament of limited function evaluations in EMOPs. Additionally, we adopt the regularity model to expensive multi-objective Bayesian optimization for PSL. Experimental results on both synthetic and real-world problems demonstrate that our algorithm outperforms several state-of-the-art and classical algorithms.

Due to computationally and/or financially costly evaluation, tackling expensive multi-objective optimization problems is quite challenging for evolutionary algorithms. One popular approach to these problems is building cheap surrogate models to replace the expensive real function evaluations. To this end, various kinds of surrogate-assisted evolutionary algorithms (SAEAs) have been proposed, building surrogate models which predict the fitness values, classifications, or relation of the candidate solutions. However, off-spring generation, despite its important role in evolutionary optimization, has not received enough attention in these SAEAs. In this paper, a regularity model based framework, namely RM-SAEA, is proposed for better offspring generation in expensive multi-objective optimization. To be specific, RM-SAEA is featured with a heterogeneous offspring generation module, which is composed of a regularity model and a general genetic operator. Moreover, in order to alleviate the data deficiency issue in the expensive optimization scenario, a data augmentation strategy is employed while training the regularity model. Finally, two representative SAEAs are embedded into RM-SAEA in order to instantiate the proposed framework. Experimental results on benchmark multi-objective problems with up to 10 objectives demonstrate that RM-SAEA achieves the best overall performance compared with 6 state-of-the-art algorithms.