Multi-Objective Bayesian Optimization via Adaptive \varepsilon-Constraints Decomposition

Existing Meta-Black-Box Optimization (MetaBBO) methods focus on how to search when controlling optimizers, but largely overlook where to search. We propose MetaSG-SAEA, a bi-level MetaBBO framework for expensive constrained multi-objective optimization problems (ECMOPs), in which a meta-policy provides search guidance to the low-level Surrogate-Assisted Evolutionary Algorithm (SAEA). To achieve this, we introduce Max-Min Constraint-Calibrated Inequality (MM-CCI), a compact, problem-agnostic region abstraction that maps heterogeneous constraint evaluations to an ordered scalar level; we further provide a theoretical analysis of its fundamental properties. Building on this region abstraction, we adopt diffusion-based population initialization to translate the meta-policy's region-level guidance into solution-level priors for the SAEA. To make MetaSG-SAEA scalable, we construct an attention-based state representation across varying problem dimensions, population sizes, and numbers of objectives and constraints. Experimental results demonstrate that MetaSG-SAEA outperforms state-of-the-art baselines across diverse benchmarks and exhibits the ability to generalize across problem distributions.

Multi-objective Bayesian optimization (MOBO) is effective in identifying the Pareto fronts for expensive black-box problems. However, most current MOBO approaches are limited to low-dimensional decision space due to its exponential sampling complexity. This paper presents decision variable interaction analysis-based MOBO, ViaMOBO, a generic framework for expensive multi-objective problems with high-dimensional decision space. The key idea of ViaMOBO is that it utilizes a variable interaction analysis model to determine whether the decision space can be completely or partially divided, and then performs local Bayesian optimization in the divided decision subspaces. Through the variable analysis model, it can be derived whether the objectives in black-box problems are separable, partially separable, or non-separable based on the potential independent or interdependent relationships among decision variables without any strong assumptions. We compare ViaMOBO with the state-of-the-art MOBO methods on both synthetic and real-world benchmarks. The experimental results demonstrate that ViaMOBO outperforms other related MOBO baselines in approximating the Pareto front of high-dimensional expensive multi-objective problems.

This paper presents a general acceleration mechanism for multi-objective Bayesian optimisation (MOBO) that leverages Gaussian process predictive gradients as auxiliary signals. Rather than replacing existing Pareto-compliant acquisition functions, the proposed approach augments them with local stationarity information derived from surrogate-derived gradients, enabling faster convergence toward the global Pareto set under limited evaluation budgets. Two catalyst instantiations are investigated: an adaptive Multiple-Gradient Descent Algorithm-Based Catalyst (MGDA) and a predefined-weight variant that enables focused exploration when budgets are tight. Experiments on the DTLZ benchmark suite (using 2 objectives and 10 decision variables) show that predictive gradient catalysis can deliver significant acceleration compared to other acquisition functions (EHVI, AugTch, tMPoI, SAF) when surrogates are accurate, particularly for stationary problems.