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

Yukun Du, Haiyue Yu, Jiang Jiang, Shuaiwen Tang, Xiaotong Xie, Haobo Liu, Chongshuang Hu, Shengkun Chang
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:26833-26850, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-du26r, title = {Meta-Black-Box Optimization Can Do Search Guidance for Expensive Constrained Multi-Objective Optimization}, author = {Du, Yukun and Yu, Haiyue and Jiang, Jiang and Tang, Shuaiwen and Xie, Xiaotong and Liu, Haobo and Hu, Chongshuang and Chang, Shengkun}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {26833--26850}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/du26r/du26r.pdf}, url = {https://proceedings.mlr.press/v306/du26r.html}, 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.} }
Endnote
%0 Conference Paper %T Meta-Black-Box Optimization Can Do Search Guidance for Expensive Constrained Multi-Objective Optimization %A Yukun Du %A Haiyue Yu %A Jiang Jiang %A Shuaiwen Tang %A Xiaotong Xie %A Haobo Liu %A Chongshuang Hu %A Shengkun Chang %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-du26r %I PMLR %P 26833--26850 %U https://proceedings.mlr.press/v306/du26r.html %V 306 %X 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.
APA
Du, Y., Yu, H., Jiang, J., Tang, S., Xie, X., Liu, H., Hu, C. & Chang, S.. (2026). Meta-Black-Box Optimization Can Do Search Guidance for Expensive Constrained Multi-Objective Optimization. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:26833-26850 Available from https://proceedings.mlr.press/v306/du26r.html.

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