Introduced in 1993, the DIRECT global optimization algorithm provided a fresh approach to minimizing a black-box function subject to lower and upper bounds on the variables. In contrast to the plethora of nature-inspired heuristics, DIRECT was deterministic and had only one hyperparameter (the desired accuracy). Moreover, the algorithm was simple, easy to implement, and usually performed well on low-dimensional problems (up to six variables). Most importantly, DIRECT balanced local and global search (exploitation vs. exploration) in a unique way: in each iteration, several points were sampled, some for global and some for local search. This approach eliminated the need for “tuning parameters” that set the balance between local and global search. However, the very same features that made DIRECT simple and conceptually attractive also created weaknesses. For example, it was commonly observed that, while DIRECT is often fast to find the basin of the global optimum, it can be slow to fine-tune the solution to high accuracy. In this paper, we identify several such weaknesses and survey the work of various researchers to extend DIRECT so that it performs better. All of the extensions show substantial improvement over DIRECT on various test functions. An outstanding challenge is to improve performance robustly across problems of different degrees of difficulty, ranging from simple (unimodal, few variables) to very hard (multimodal, sharply peaked, many variables). Opportunities for further improvement may lie in combining the best features of the different extensions.

DIRECT全局优化算法于1993年推出，它提供了一种新颖的方法来最小化受变量上下限限制的黑盒函数。与大量自然启发式启发法相反，DIRECT是确定性的并且只有一个超参数（所需的精度）。此外，该算法简单，易于实现，并且通常在低维问题（最多六个变量）上表现良好。最重要的是，DIRECT以独特的方式平衡了本地和全局搜索（开发与探索）：在每次迭代中，采样了多个点，其中一些用于全局搜索，而某些则用于局部搜索。这种方法消除了在局部和全局搜索之间建立平衡的“调整参数”的需要。但是，使DIRECT简单且在概念上具有吸引力的相同功能也造成了弱点。例如，通常可以观察到，尽管DIRECT通常可以很快找到全局最优值的盆地，但是将解决方案微调到高精度可能会很慢。在本文中，我们找出了几个这样的弱点，并调查了许多研究人员的工作以扩展DIRECT，使其表现更好。所有扩展在各种测试功能上都比DIRECT有了实质性的改进。一个突出的挑战是提高性能稳健跨越不同程度的困难，从简单的（单峰，几个变量）非常努力的问题（多模式，大幅见顶，许多变量）。进一步改进的机会可能在于结合不同扩展的最佳功能。