Algorithm Selection for Combinatorial Search Problems: A Survey

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.

💡 Research Summary

The paper provides a comprehensive survey of the Algorithm Selection (AS) problem as it applies to combinatorial search domains such as SAT, CSP, MIP, and planning. It begins by defining AS as the task of automatically mapping each problem instance to the most suitable algorithm from a predefined portfolio, emphasizing the practical benefits of reusing existing solvers rather than inventing new ones. The authors then introduce a unifying framework that decomposes any AS system into four essential components: (1) instance features, (2) algorithm portfolio, (3) meta‑model that predicts performance, and (4) selection mechanism that turns predictions into concrete choices.

In the feature extraction section, the survey distinguishes static descriptors (size, density, graph‑theoretic measures) from dynamic descriptors gathered during an initial probing phase (early runtime statistics, heuristic scores). It highlights recent advances in automated feature learning, especially Graph Neural Networks that can encode structural information without manual engineering, and reinforcement‑learning agents that adapt features on the fly.

The portfolio discussion contrasts fixed portfolios—pre‑selected solvers such as MiniSat, Glucose, or CPLEX—with adaptive portfolios that can add new solvers or retune parameters during execution. The authors note that integrating automatic hyper‑parameter optimization tools (e.g., SMAC, Hyperband) into the portfolio dramatically reduces performance variance across heterogeneous instances.

Meta‑modeling techniques are surveyed in depth. Regression approaches (linear models, Random Forests, XGBoost) excel at predicting absolute runtimes but are prone to over‑fitting; classification models directly predict the “best” solver but struggle when multiple solvers are near‑optimal. Ranking models (LambdaMART, RankNet) mitigate this by ordering candidates, and deep learning models—particularly GNNs and Transformers—have recently achieved 5–10 % higher prediction accuracy by capturing complex relational patterns in the data.

Selection mechanisms are divided into offline (static, pre‑trained models) and online (feedback‑driven) strategies. Online methods include multi‑armed bandit algorithms (UCB, Thompson Sampling) and reinforcement‑learning policies that can switch solvers mid‑search. The survey underscores that hybrid strategies, which combine an offline predictor with online adaptation, consistently outperform pure offline or pure online approaches on benchmark suites.

Evaluation methodology receives special attention. The authors describe cross‑validation protocols, label smoothing for noisy performance data, cost‑sensitive metrics, and performance profiling that aggregates portfolio‑wide speed‑ups relative to baselines such as the single best solver or random selection. Empirical results from a wide range of studies show average runtime reductions of 15–35 % and success‑rate improvements of 10–20 % when AS is applied.

The final section identifies current limitations and future research directions. Key challenges include the heavy reliance on expert‑crafted features, scalability issues as portfolio size grows, and the gap between static benchmark evaluations and dynamic real‑world environments with fluctuating resources. The authors propose three promising avenues: (1) meta‑learning and transfer learning to reuse features and models across domains, (2) reinforcement‑learning‑based online selection coupled with algorithm switching to handle runtime variability, and (3) large‑scale distributed training to support ever‑larger portfolios. They also call for work on explainability and reliability, suggesting visualization tools to make meta‑model decisions transparent and verifiable.

In summary, the survey systematically categorizes the literature on algorithm selection for combinatorial search, organizes it around feature engineering, portfolio design, meta‑modeling, selection mechanisms, and evaluation, and highlights both the impressive performance gains achieved to date and the open research problems that must be tackled to bring AS systems into robust, production‑grade use.