论文标题
Lipschitz为灵感的半晶算法，用于无衍生的全局优化
Lipschitz-inspired HALRECT Algorithm for Derivative-free Global Optimization
论文作者
论文摘要
本文考虑了lipschitz连续函数的盒子受限的全局优化问题，该函数具有未知的Lipschitz常数。由著名的直接（分隔矩形）的动机，引入了一种新的半矩形（减半矩形）算法。一种新的确定性方法将减半（分配）与新的多点采样方案相结合，与最现有的直接型算法中使用的三角形和中点采样相反。新的分区和抽样方案利用有关目标函数的更全面的信息。引入了选择潜在的最佳超矩形的四种不同策略，以有效利用有关目标函数的信息。测试了原始的半晶算法和其他引入的半部变化（总共十二个），并与最近的十二个最近引入了直接型算法的$ 96 $ box限制的基准函数，该基准受到了DirectGolib v1.1的限制，并与96个构成了他们的版本。广泛的实验结果表明，与最先进的直接型全球优化相比，性能非常有前途。新的半程方法在不同程度的复杂性问题上提供了高鲁棒性，从简单的 - 单模式和低维度到复杂的 - 多模式和更高的维度。
This article considers a box-constrained global optimization problem for Lipschitz-continuous functions with an unknown Lipschitz constant. Motivated by the famous DIRECT (DIviding RECTangles), a new HALRECT (HALving RECTangles) algorithm is introduced. A new deterministic approach combines halving (bisection) with a new multi-point sampling scheme in contrast to trisection and midpoint sampling used in the most existing DIRECT-type algorithms. A new partitioning and sampling scheme utilizes more comprehensive information about the objective function. Four different strategies of selecting potentially optimal hyper-rectangles are introduced to exploit the information about the objective function effectively. The original HALRECT algorithm and other introduced HALRECT variations (twelve in total) are tested and compared with the other twelve recently introduced DIRECT-type algorithms on $96$ box-constrained benchmark functions from DIRECTGOLib v1.1, and 96 perturbed their versions. The extensive experimental results show a very promising performance compared to state-of-the-art DIRECT-type global optimization. New HALRECT approaches offers high robustness across problems of different degrees of complexity, varying from simple - uni-modal and low dimensional to complex - multi-modal and higher dimensionality.
