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

TL;DR

This paper introduces MetaSG-SAEA, a novel bi-level MetaBBO framework that guides expensive constrained multi-objective optimization using a meta-policy and innovative region abstraction, improving search efficiency and generalization.

Contribution

It proposes a new MetaBBO framework with a problem-agnostic region abstraction and diffusion-based initialization, enhancing search guidance and scalability for ECMOPs.

Findings

MetaSG-SAEA outperforms state-of-the-art methods on diverse benchmarks.

The region abstraction effectively maps constraint evaluations to scalar levels.

The approach generalizes well across different problem distributions.

Abstract

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.