A comparison of optimisation algorithms for high-dimensional particle and astrophysics applications

TL;DR

This paper compares various global optimisation algorithms for high-dimensional problems in particle and astrophysics, benchmarking their performance on test functions and a real-world supersymmetry fit.

Contribution

It provides a comprehensive comparison of multiple optimisation algorithms, including some less commonly used in astrophysics, highlighting their relative strengths and weaknesses.

Findings

Differential Evolution and Particle Swarm Optimisation perform well on high-dimensional problems.

Bayesian Optimisation is effective for expensive-to-evaluate functions.

Algorithm performance varies depending on the specific problem characteristics.

Abstract

Optimisation problems are ubiquitous in particle and astrophysics, and involve locating the optimum of a complicated function of many parameters that may be computationally expensive to evaluate. We describe a number of global optimisation algorithms that are not yet widely used in particle astrophysics, benchmark them against random sampling and existing techniques, and perform a detailed comparison of their performance on a range of test functions. These include four analytic test functions of varying dimensionality, and a realistic example derived from a recent global fit of weak-scale supersymmetry. Although the best algorithm to use depends on the function being investigated, we are able to present general conclusions about the relative merits of random sampling, Differential Evolution, Particle Swarm Optimisation, the Covariance Matrix Adaptation Evolution Strategy, Bayesian Optimisation, Grey Wolf Optimisation, and the PyGMO Artificial Bee Colony, Gaussian Particle Filter and Adaptive Memory Programming for Global Optimisation algorithms.