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

arXiv: https://arxiv.org/abs/2608.08898 · HTML: https://mlsanity.com/paper/2608.08898/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 26 references that are in the map.
- First posted on arXiv 9 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [Automated Algorithm Selection on Continuous Black-Box Problems By Combining Exploratory Landscape Analysis and Machine Learning](https://mlsanity.com/paper/1711.08921/) (2017)
- [Comprehensive Feature-Based Landscape Analysis of Continuous and Constrained Optimization Problems Using the R-Package flacco](https://mlsanity.com/paper/1708.05258/) (2017)
- [Exploratory Landscape Analysis is Strongly Sensitive to the Sampling Strategy](https://mlsanity.com/paper/2006.11135/) (2020)
- [MA-BBOB: Many-Affine Combinations of BBOB Functions for Evaluating AutoML Approaches in Noiseless Numerical Black-Box Optimization Contexts](https://mlsanity.com/paper/2306.10627/) (2023)
- [Improving Nevergrad's Algorithm Selection Wizard NGOpt through Automated Algorithm Configuration](https://mlsanity.com/paper/2209.04412/) (2022)
- [A Continuous Optimisation Benchmark Suite from Neural Network Regression](https://mlsanity.com/paper/2109.05606/) (2021)

## Abstract (arXiv)

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.