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

2026-05-11

AI Summary

This work addresses the lack of effective search-region guidance in existing meta black-box optimization methods for expensive constrained multi-objective problems. The authors propose MetaSG-SAEA, a novel bi-level framework that, for the first time, enables cross-problem, region-level search guidance and generalization. The approach introduces a problem-agnostic MM-CCI region abstraction and a scalable attention-based state representation, leveraging a diffusion model for initialization and employing MM-CCI-constrained calibration inequalities to guide a surrogate-assisted evolutionary algorithm. Experimental results demonstrate that MetaSG-SAEA significantly outperforms state-of-the-art methods across multiple benchmarks, achieving superior optimization performance while exhibiting strong generalization across diverse 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.

Problem

• Meta-Black-Box Optimization
• Expensive Constrained Multi-Objective Optimization
• Search Guidance
• Surrogate-Assisted Evolutionary Algorithm
• Region Abstraction

Innovation

• Meta-Black-Box Optimization
• Surrogate-Assisted Evolutionary Algorithm
• Constraint-Calibrated Inequality
• Diffusion-based Initialization
• Attention-based Representation