Meta-Black-Box Optimization with Bi-Space Landscape Analysis and Dual-Control Mechanism for SAEA

TL;DR

DB-SAEA introduces a MetaBBO framework for expensive multi-objective optimization that learns a meta-policy to jointly control candidate generation and infill-criterion selection, guided by a bi-space Exploratory Landscape Analysis that fuses true and surrogate evaluation signals. It uses TabPFN as a scalable surrogate model, reducing training cost and providing uncertainty, and is trained through parallel reinforcement learning with centralized replay. The key innovations are a dual-control mechanism enabling simultaneous management of search strategy and evaluation decisions, a bi-space ELA capturing surrogate model information across true and surrogate spaces, and the use of TabPFN to replace Gaussian Processes for scalability. Empirical results show strong performance and zero-shot transfer to unseen higher-dimensional tasks, with TabPFN outperforming GP in predictive accuracy and speed.

Abstract

Surrogate-Assisted Evolutionary Algorithms (SAEAs) are widely used for expensive Black-Box Optimization. However, their reliance on rigid, manually designed components such as infill criteria and evolutionary strategies during the search process limits their flexibility across tasks. To address these limitations, we propose Dual-Control Bi-Space Surrogate-Assisted Evolutionary Algorithm (DB-SAEA), a Meta-Black-Box Optimization (MetaBBO) framework tailored for multi-objective problems. DB-SAEA learns a meta-policy that jointly regulates candidate generation and infill criterion selection, enabling dual control. The bi-space Exploratory Landscape Analysis (ELA) module in DB-SAEA adopts an attention-based architecture to capture optimization states from both true and surrogate evaluation spaces, while ensuring scalability across problem dimensions, population sizes, and objectives. Additionally, we integrate TabPFN as the surrogate model for accurate and efficient prediction with uncertainty estimation. The framework is trained via reinforcement learning, leveraging parallel sampling and centralized training to enhance efficiency and transferability across tasks. Experimental results demonstrate that DB-SAEA not only outperforms state-of-the-art baselines across diverse benchmarks, but also exhibits strong zero-shot transfer to unseen tasks with higher-dimensional settings. This work introduces the first MetaBBO framework with dual-level control over SAEAs and a bi-space ELA that captures surrogate model information.

Figures (6)

• Figure 1: The general workflow of MetaBBO
• Figure 2: The framework of DB-SAEA. (right) DB-SAEA generates candidate solutions using hybrid sampling (NSGA-III, CDM-PSL, qNEHVI), evaluates them with TabPFNs, and extracts landscape-aware features via bi-space ELA. The meta-policy determines whether to perform true evaluation or continue surrogate-assisted search. Upon true evaluation, elite solutions are selected and $\mathcal{P}_\text{true}$ is updated.
• Figure 3: Average reward per true evaluation
• Figure 4: Performance comparison on unseen 30D tasks
• Figure 5: Prediction and uncertainty of surrogate models