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

This paper 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 twenty-five promising and representative state-of-the-art algorithms from both aforementioned classes. The evaluation with up to the twenty dimensions and large evaluation budgets (105×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.