A reliable benchmark library is essential for advancing research in global optimization by enabling fair comparisons and rigorous testing of optimization algorithms across diverse problem landscapes. In this article, we focus on instance selection methods, which aim to choose representative problems for evaluating algorithm performance. We present a comprehensive review of existing instance selection methods, highlighting their strengths and limitations, particularly in balancing the consideration of algorithm performance and the analysis of problem characteristics using exploratory landscape analysis. Building on these insights, we introduce two novel instance selection methods that leverage both algorithm performance data and landscape analysis information to construct diverse and informative benchmark sets. For evaluation, we benchmark our approaches against four existing instance selection methods on the recently expanded DIRECTGOLib v2.0 library. Our results demonstrate that the proposed methods effectively identify representative instances that capture a wide range of problem characteristics, enabling a more comprehensive evaluation of algorithm performance. These findings have significant implications for the development and assessment of new optimization algorithms, ultimately contributing to more reliable and robust solutions for real-world optimization problems.

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.

In this work, we introduce DIRECTGO , a new MATLAB toolbox for derivative-free global optimization. DIRECTGO collects various deterministic derivative-free DIRECT -type algorithms for box-constrained, generally constrained, and problems with hidden constraints. Each sequential algorithm is implemented in two ways: using static and dynamic data structures for more efficient information storage and organization. Furthermore, parallel schemes are applied to some promising algorithms within DIRECTGO . The toolbox is equipped with a graphical user interface (GUI), ensuring the user-friendly use of all functionalities available in DIRECTGO . Available features are demonstrated in detailed computational studies using a comprehensive DIRECTGOLib v1.0 library of global optimization test problems. Additionally, 11 classical engineering design problems illustrate the potential of DIRECTGO to solve challenging real-world problems. Finally, the appendix gives examples of accompanying MATLAB programs and provides a synopsis of its use on the test problems with box and general constraints.