Meta-Black-Box Optimization Can Do Search Guidance for Expensive Constrained Multi-Objective Optimization

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.

Many important optimization problems are difficult because each candidate solution is costly to evaluate, and acceptable solutions must satisfy multiple constraints. In these settings, an optimizer should not only decide how to improve solutions, but also learn which regions of the search space are worth exploring. Our paper proposes MetaSG-SAEA, a learning-based framework that guides an optimization algorithm toward more useful regions. A key idea is to give the algorithm a simple “map” of constraint satisfaction. Instead of treating all infeasible solutions alike, our method converts different kinds of constraint violations into a common ordered score, helping the algorithm recognize which regions are closer to feasibility and therefore more promising. We then use a diffusion-based generation method to turn this high-level guidance into concrete candidate solutions, giving the optimizer a better starting point. The framework can also handle problems with different numbers of variables, objectives, and constraints. Experiments show that MetaSG-SAEA outperforms strong existing methods and can transfer to new problem settings.