Algorithm Selection for Combinatorial Search Problems: A Survey (1210.7959v1)

Abstract: The Algorithm Selection Problem is concerned with selecting the best algorithm to solve a given problem on a case-by-case basis. It has become especially relevant in the last decade, as researchers are increasingly investigating how to identify the most suitable existing algorithm for solving a problem instead of developing new algorithms. This survey presents an overview of this work focusing on the contributions made in the area of combinatorial search problems, where Algorithm Selection techniques have achieved significant performance improvements. We unify and organise the vast literature according to criteria that determine Algorithm Selection systems in practice. The comprehensive classification of approaches identifies and analyses the different directions from which Algorithm Selection has been approached. This paper contrasts and compares different methods for solving the problem as well as ways of using these solutions. It closes by identifying directions of current and future research.

• The paper establishes a framework for algorithm selection in combinatorial search, emphasizing portfolio construction and dynamic selection strategies.
• It utilizes performance modeling and feature extraction techniques to tailor algorithm recommendations based on specific problem characteristics.
• Empirical findings reveal substantial reductions in computational time and improved solution quality, setting a blueprint for future research.

Algorithm Selection for Combinatorial Search Problems: An Overview

The algorithm selection problem involves determining the most appropriate algorithm for solving each specific problem. As outlined in Lars Kotthoff's survey, this task has gained substantial attention, particularly in the field of combinatorial search problems, due to the marked performance improvements realized by leveraging the diversity of available algorithms. This survey organizes and categorizes the extensive body of literature on algorithm selection, providing a definitive framework for guiding future research in this domain.

Key Components of Algorithm Selection

The survey delineates several key elements fundamental to the algorithm selection process:

1. Portfolio Construction: This is the practice of assembling a diverse set of potential algorithms, or a portfolio, from which one can be selected to solve a particular problem. Portfolios can be static, with their constitution determined a priori, or dynamic, where they may be modified through the addition of new algorithms or configurations.
2. Selection Strategy: A selection strategy involves determining how and when algorithms should be selected from the portfolio. This could involve choosing a single algorithm for the entire problem-solving process or switching between multiple algorithms based on a scheduling mechanism or problem characteristics.
3. Performance Modeling: Modeling performance is integral to the selection process, with potential use of machine learning techniques to predict the efficacy of individual algorithms or entire portfolios on specific problem instances.
4. Feature Extraction: Effective algorithm selection often hinges on identifying relevant features of problems, which can be gathered before problem solving (statically) or during the solving process (dynamically). This information feeds into performance models to facilitate accurate algorithm recommendations.

Implications for Research and Practice

The integration of algorithm selection techniques offers both theoretical and practical implications. Theoretically, it challenges the previous paradigm of seeking universally optimal algorithms for broad classes of problems, instead emphasizing adaptability and problem-specific optimization. Practically, these techniques can profoundly enhance computational efficiency, offering substantial performance gains by selecting algorithms that are tailored to particular problem characteristics.

Numerical Results and Contributions

Kotthoff's paper emphasizes the impressive empirical results achieved through algorithm selection. By dynamically choosing the most suitable algorithms, researchers have recorded significant reductions in computational time and improvements in solution quality. Such results underscore the potential of algorithm selection systems to revolutionize performance outcomes in combinatorial search problems.

Future Directions

Future research is likely to explore:

• Refinements in Machine Learning Approaches: As techniques for algorithm selection mature, more sophisticated models and learning strategies are likely to be developed to improve accuracy and generalizability.
• Parallel and Distributed Computing: Parallel algorithm portfolios have begun to show promise, suggesting that further exploration into concurrent algorithm execution could unlock new levels of efficiency.
• Cross-Domain Applications: The principles of algorithm selection could have transformative impacts in domains beyond combinatorial search, including areas such as automated machine learning, data science, and complex system optimization.

Conclusion

Algorithm selection remains a dynamic and evolving field with significant implications for solving combinatorial search problems. Kotthoff's survey not only synthesizes a wide array of research findings but also provides a blueprint for implementing and expanding algorithm selection systems. As this domain advances, it promises to enhance our ability to efficiently tackle increasingly complex problems across a range of disciplines.