Meta-Black-Box Optimization with Ensemble Surrogate Modeling for Robustness-Accuracy Trade-off within SAEA

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.

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.