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.
Surrogate-assisted evolutionary algorithms (SAEAs) have been widely used for expensive black-box optimization problems. However, their reliance on rigid and manually designed components limits their flexibility and generalization across tasks. Meta-black-box optimization (MetaBBO) provides a promising paradigm for adaptively configuring algorithmic components. Nevertheless, existing MetaBBO methods usually control only a single component, and few studies have investigated the unified control of multi-component optimizers such as SAEAs. Moreover, the robustness-accuracy trade-off in surrogate modeling, which is crucial for stable early-stage exploration and accurate late-stage exploitation, has rarely been explicitly considered. To address these issues, we propose AdaE-SAEA, an adaptive ensemble surrogate-assisted evolutionary algorithm for expensive multi-objective optimization. AdaE-SAEA embeds SAEA as the low-level optimizer within the MetaBBO framework and jointly controls the infill criterion and ensemble-based surrogate modeling. Specifically, bagging and boosting are designed as surrogate modeling modules to adaptively balance robustness and accuracy across different search phases, while the meta-policy simultaneously selects the infill criterion to enable adaptive sampling decisions. The meta-policy is trained through reinforcement learning with parallel sampling and centralized training, improving both training efficiency and transferability. Experiments on synthetic and real-world problems demonstrate that AdaE-SAEA outperforms state-of-the-art baselines and MetaBBO-based methods. We further verify the effectiveness of TabPFN as the base surrogate model for ensemble learning. To the best of our knowledge, this is the first work to unify the control of surrogate modeling and infill criteria in SAEAs while explicitly addressing the robustness--accuracy trade-off.
Multi-objective Bayesian optimization (MOBO) provides a principled framework for optimizing multiple expensive black-box functions. However, existing MOBO methods often struggle with coverage, scalability, and handling constraints and preferences. In this work we propose STAGE-BO, Sequential Targeting Adaptive Gap-Filling ε-Constraint Bayesian Optimization: by analyzing the coverage of the surrogate Pareto front, our method identifies the Pareto front point with the largest uncovered gap, and uses its coordinates to define adaptive constraints in ε-constraint method, which transforms the problem into a sequence of inequality-constrained subproblems, efficiently solved via constrained expected improvement acquisition. Our approach provides uniform Pareto coverage without hypervolume computation and naturally handles constraints and preferences. Experiments on synthetic and real-world benchmarks demonstrate superior coverage and competitive hypervolume performance against state-of-the-art baselines. Our code implementation can be found at https://github.com/YangYaohong1/STAGE-BO.
Expensive black-box optimization is ubiquitous in science and engineering, where function evaluations are costly and the evaluation budget is limited. Traditional evolutionary algorithms and Meta-BlackBox Optimization (MetaBBO) approaches typically consume most evaluations on candidate selection, often wasting precious budget on inferior solutions. Although surrogate-assisted evolution and Bayesian optimization aim to reduce evaluations through surrogate models, constructing an accurate global model from limited data remains challenging, and model bias can easily trap the search in local optima. To overcome these limitations, we propose NeurGO, a generative MetaBBO framework that directly synthesizes elite candidates from historical population states. Specifically, we employ an attention-based encoder to capture the population-level search trend and condition a decoder on this representation to generate high-quality candidates, avoiding the expensive evaluation of large offspring pools. We then design a quality-diversity loss to maintain solution quality and population diversity throughout the search. Through extensive benchmarking on CEC 2008 and the COCO BBOB test suites, our method achieves better optimization performance under the same evaluation budget and exhibits faster convergence.