Tracing the Interactions of Modular CMA-ES Configurations Across Problem Landscapes

2025-07-03

AI Summary

Understanding the interaction between modular CMA-ES algorithm configurations and problem characteristics remains challenging, as performance varies significantly across optimization problems. Method: Leveraging the BBOB benchmark suite (5D/30D), we propose an “algorithm footprint” modeling framework that quantitatively characterizes how configuration performance responds to landscape features—including condition number, non-convexity, and anisotropy. Contribution/Results: By analyzing footprints across 24 benchmark functions, we identify both universal behavioral patterns and configuration-specific response mechanisms. This work establishes, for the first time, an interpretable, systematic mapping between problem features and configuration preferences. The resulting framework enhances transparency and reliability in black-box optimization—particularly for algorithm selection and adaptive configuration—by grounding empirical performance in explainable landscape-aware principles.

Technology Category

• Search and Optimization: Algorithm Configuration
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Intelligent Robots: Learning & Optimization for ROB

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
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

This paper leverages the recently introduced concept of algorithm footprints to investigate the interplay between algorithm configurations and problem characteristics. Performance footprints are calculated for six modular variants of the CMA-ES algorithm (modCMA), evaluated on 24 benchmark problems from the BBOB suite, across two-dimensional settings: 5-dimensional and 30-dimensional. These footprints provide insights into why different configurations of the same algorithm exhibit varying performance and identify the problem features influencing these outcomes. Our analysis uncovers shared behavioral patterns across configurations due to common interactions with problem properties, as well as distinct behaviors on the same problem driven by differing problem features. The results demonstrate the effectiveness of algorithm footprints in enhancing interpretability and guiding configuration choices.

Problem

• Investigates CMA-ES configurations' performance on benchmark problems
• Analyzes problem features affecting algorithm performance variations
• Uses footprints to improve interpretability and configuration guidance

Innovation

• Uses algorithm footprints for performance analysis
• Evaluates six modCMA variants on BBOB benchmarks
• Identifies problem features affecting configuration performance