An extensive numerical benchmark study of deterministic vs. stochastic derivative-free global optimization algorithms

TL;DR

This extensive benchmark compares 64 deterministic and stochastic derivative-free global optimization algorithms across diverse problems, revealing their strengths and limitations in different scenarios.

Contribution

The paper provides a comprehensive, up-to-date empirical comparison of deterministic and stochastic global optimizers on a large, diverse set of benchmark problems.

Findings

Deterministic algorithms excel on low-dimensional and GKLS-type problems.

Stochastic algorithms are more efficient in high-dimensional settings.

Over 239,400 solver runs were performed, totaling more than 531 days of CPU time.

Abstract

Research in derivative-free global optimization is under active development, and many solution techniques are available today. Therefore, the experimental comparison of previous and emerging algorithms must be kept up to date. This paper considers the solution to the bound-constrained, possibly black-box global optimization problem. It compares 64 derivative-free deterministic algorithms against classic and state-of-the-art stochastic solvers. Among deterministic ones, a particular emphasis is on DIRECT-type, where, in recent years, significant progress has been made. A set of 800 test problems generated by the well-known GKLS generator and 397 traditional test problems from DIRECTGOLib v1.2 collection are utilized in a computational study. More than 239400 solver runs were carried out, requiring more than 531 days of single CPU time to complete them. It has been found that deterministic algorithms perform excellently on GKLS-type and low-dimensional problems, while stochastic algorithms have shown to be more efficient in higher dimensions.