Models for algorithm selection for combinatorial optimisation problems

Notice, Danielle and Pavlidis, Nicos and Kheiri, Ahmed (2026) Models for algorithm selection for combinatorial optimisation problems. PhD thesis, Lancaster University.

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Abstract

Combinatorial optimisation (CO) problems are often solved using approximate methods, such as heuristics, in practice. These solvers exhibit varying strengths in terms of solution quality and resource usage, making CO problems well-suited to automated algorithm selection. Effectively solving the algorithm selection problem (ASP) enables users to predict the most suitable algorithm for a given problem instance, thereby improving performance. Appropriate models also provide insights into the relationship between problem characteristics and algorithm behaviour. In this thesis, we explore multiple models for and elements of the algorithm selection problem. First, we assess the benefits of including dimensionality reduction (DR) in the ASP framework. We evaluate multiple classifiers paired with both unsupervised and supervised DR methods, as well as classifiers that inherently perform DR, across several combinatorial optimisation problem domains. We also study the impact of using regularisation during dimensionality reduction to obtain sparse representations of the feature space and promote feature elimination. We then apply the ASP and recent extensions of the framework to novel problem domains. Metadata is first generated for Sudoku puzzles as an illustrative example, then for the capacitated vehicle routing problem. For both domains, we evaluate the effect of using different performance metrics on the results from instance space analysis. We then propose the use of mixture discriminant analysis within the ISA framework to obtain both a low-dimensional representation of the instance space and a classifier of algorithm performance.