A New Approach to Characterising Optimisation Problems Using Programmatic Representation and Complexity Measures

2026-08-09

AI Summary

This work proposes a novel approach to characterizing optimization problems by leveraging the program implementation of their objective functions, introducing code complexity metrics—such as Halstead volume and entropy—into algorithm selection for the first time. The method is sampling-free, transformation-invariant, and computationally efficient, automatically extracting meta-features using existing code analysis tools. Experimental results on the BBOB benchmark suite and neural network training tasks demonstrate that the proposed complexity measures exhibit a significant negative correlation with optimization algorithm performance, highlighting their effectiveness and potential as predictive meta-features for algorithm selection.

Abstract

Characterising optimisation problem instances is a fundamental part of understanding the behaviour and performance of different algorithms as well as providing information for algorithm selection and configuration. In this paper we propose a novel approach to problem characterisation based on the representation of instances when implemented as a program. The intuition is that the complexity of the code required to express an objective function should relate to the complexity of the search landscape. We identify the Halstead volume as a measure of code complexity, which can be seen as a simplified version of the entropy of the program. Given a code implementation of the objective function, the Halstead volume and entropy can be quickly calculated using existing libraries. We apply the proposed complexity measures to the well-known BBOB optimisation problem suite and the simple feed-forward neural network training task. We also show that the measures are negatively correlated with algorithm performance and therefore show potential as predictive meta-features for algorithm selection and other problem analysis. We envisage the proposed measures as complementary to other problem characterisation approaches, but with the advantages of not requiring any sampling of the search space, being invariant to transformations, and being very quick to calculate automatically.

Problem

• optimisation problem characterisation
• algorithm selection
• code complexity
• search landscape
• meta-features

Innovation

• programmatic representation
• Halstead volume
• code complexity
• algorithm selection
• meta-features