Benchmarking Derivative-Free Global Optimization Algorithms Under Limited Dimensions and Large Evaluation Budgets

journal article in Web of Science

en

This article addresses the challenge of selecting the most suitable optimization algorithm by presenting a comprehensive computational comparison between stochastic and deterministic methods. The complexity of algorithm selection arises from the absence of a universal algorithm and the abundance of available options. Manual selection without comprehensive studies can lead to suboptimal or incorrect results. In order to address this issue, we carefully selected 25 promising and representative state-of-the-art algorithms from both aforementioned classes. The evaluation with up to the 20 dimensions and large evaluation budgets $(10<^>{5}{\times }n)$ was carried out in a significantly expanded and improved version of the DIRECTGOLib v2.0 library, which included ten distinct collections of primarily continuous test functions. The evaluation covered various aspects, such as solution quality, time complexity, and function evaluation usage. The rankings were determined using statistical tests and performance profiles. When it comes to the problems and algorithms examined in this study, EA4eig, EBOwithCMAR, APGSK-IMODE, 1-DTC-GL, OQNLP, and DIRMIN stand out as superior to other derivative-free solvers in terms of solution quality. While deterministic algorithms can locate reasonable solutions with comparatively fewer function evaluations, most stochastic algorithms require more extensive evaluation budgets to deliver comparable results. However, the performance of stochastic algorithms tends to excel in more complex and higher-dimensional problems. These research findings offer valuable insights for practitioners and researchers, enabling them to tackle diverse optimization problems effectively.

This article addresses the challenge of selecting the most suitable optimization algorithm by presenting a comprehensive computational comparison between stochastic and deterministic methods. The complexity of algorithm selection arises from the absence of a universal algorithm and the abundance of available options. Manual selection without comprehensive studies can lead to suboptimal or incorrect results. In order to address this issue, we carefully selected 25 promising and representative state-of-the-art algorithms from both aforementioned classes. The evaluation with up to the 20 dimensions and large evaluation budgets $(10<^>{5}{\times }n)$ was carried out in a significantly expanded and improved version of the DIRECTGOLib v2.0 library, which included ten distinct collections of primarily continuous test functions. The evaluation covered various aspects, such as solution quality, time complexity, and function evaluation usage. The rankings were determined using statistical tests and performance profiles. When it comes to the problems and algorithms examined in this study, EA4eig, EBOwithCMAR, APGSK-IMODE, 1-DTC-GL, OQNLP, and DIRMIN stand out as superior to other derivative-free solvers in terms of solution quality. While deterministic algorithms can locate reasonable solutions with comparatively fewer function evaluations, most stochastic algorithms require more extensive evaluation budgets to deliver comparable results. However, the performance of stochastic algorithms tends to excel in more complex and higher-dimensional problems. These research findings offer valuable insights for practitioners and researchers, enabling them to tackle diverse optimization problems effectively.

Derivative-free global optimization; deterministic algorithms; evolutionary computation (EC) algorithms; nature-inspired meta-heuristics; numerical benchmarking

01.02.2025

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

PISCATAWAY

1089-778X

29

1

187–204

18