Landscape Features in Single-Objective Continuous Optimization: Have We Hit a Wall in Algorithm Selection Generalization?

2025-01-29

AI Summary

This work addresses the algorithm selection (AS) problem in single-objective continuous optimization by systematically evaluating the out-of-distribution (OOD) generalization capability of mainstream landscape features—including Exploratory, Topological, DeepELA, TransOptAS, and Doe2Vec. Through extensive empirical analysis, we find that all feature-based AS models fail to significantly outperform the single-best-solver baseline on previously unseen problems—an observation that reveals a fundamental generalization bottleneck in current AS paradigms. Our study challenges the prevailing reliance on handcrafted or deep-learning-derived landscape features for building generalizable AS models. Crucially, it provides a key negative empirical result for the AS community: OOD generalization performance has not yet surpassed the “single-best-solver ceiling.” This finding underscores the urgent need for novel methodological frameworks beyond feature engineering—such as foundation models, meta-learning, or problem-agnostic representations—to achieve robust cross-problem algorithm selection.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

%% Text of abstract The process of identifying the most suitable optimization algorithm for a specific problem, referred to as algorithm selection (AS), entails training models that leverage problem landscape features to forecast algorithm performance. A significant challenge in this domain is ensuring that AS models can generalize effectively to novel, unseen problems. This study evaluates the generalizability of AS models based on different problem representations in the context of single-objective continuous optimization. In particular, it considers the most widely used Exploratory Landscape Analysis features, as well as recently proposed Topological Landscape Analysis features, and features based on deep learning, such as DeepELA, TransOptAS and Doe2Vec. Our results indicate that when presented with out-of-distribution evaluation data, none of the feature-based AS models outperform a simple baseline model, i.e., a Single Best Solver.

Problem

• Algorithm Selection
• Single Objective Optimization
• Adaptability

Innovation

• Terrain Features
• Deep Learning
• Algorithm Selection