Algorithm Selection and Optimization Techniques in Combinatorial Problems
Summary
Combinatorial problems abound in domains such as scheduling, routing, resource allocation and logical inference. Owing to their typically NP-hard nature, no single algorithm uniformly outperforms all others across diverse instance sets. Algorithm selection addresses this challenge by predicting which solver or heuristic will deliver the best performance on a given instance, based on measurable instance features. Closely related is algorithm configuration, whereby parameter settings of a chosen solver are automatically tuned to maximise efficiency. Portfolio approaches combine multiple algorithms—either in parallel or in sequence—to exploit complementary strengths, while hyper-heuristics operate at a higher abstraction level, dynamically choosing or generating heuristics during the search. Recent advances have harnessed machine learning and meta-learning to extract structural and statistical features from instances, enabling rapid, data-driven decisions about algorithm choice and parameterisation. These techniques have yielded substantial gains in fields ranging from mixed-integer programming and satisfiability solving to vehicle routing and network design, underpinning practical systems that adapt to ever-evolving problem landscapes.
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Algorithm Selection and Optimization Techniques in Combinatorial Problems publication trend
The graph below shows the total number of articles in algorithm selection and optimization techniques in combinatorial problems across all publications each year (not limited to Nature Index journals).
Technical terms
Algorithm selection: The process of choosing, for a given problem instance, the most promising solver or heuristic from a predefined set, based on predictive models.
Algorithm configuration: Automated tuning of an algorithm’s internal parameters to optimise its performance on a target distribution of problem instances.
Algorithm portfolio: A curated collection of diverse algorithms run in parallel or sequence to exploit their complementary strengths and mitigate individual weaknesses.
Meta-learning: A higher-level learning paradigm that leverages past experience across instances or tasks to guide selection, configuration or control of algorithms.
Instance features: Quantitative or structural descriptors extracted from problem instances that inform predictive models for selection and configuration.
References
- Learn to optimize—a brief overview. National Science Review (2024).
- Instance-specific algorithm configuration via unsupervised deep graph clustering. Engineering Applications of Artificial Intelligence (2023).
- AutoFolio: An Automatically Configured Algorithm Selector. Journal of Artificial Intelligence Research (2015).
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