关于灵活尺寸最优拉丁超立方体设计构造的思考
Musings on Constructions of Optimal Latin Hypercube Designs with Flexible Sizes
AI总结：
综述了代数构造和搜索算法在灵活尺寸最优拉丁超立方体设计中的优劣，为不同目标选择设计策略提供指导。
摘要：
拉丁超立方体设计（LHD）在计算机实验中扮演重要角色，在多种最优性准则（包括最大最小距离、最大投影和正交性）下提供灵活且高效的空间填充特性。由于理论结果（即具有可证明最优性保证的代数构造）的有限可用性以及搜索算法遇到的快速扩展的搜索空间，构造具有灵活尺寸的最优LHD具有挑战性。对于已知代数构造范围之外的设计尺寸，基于搜索的算法被广泛使用，但它们通常涉及大量计算工作且缺乏全局最优性的保证。本文对当前流行的最优LHD代数构造和广泛采用的生成高质量LHD的搜索算法进行了全面回顾和比较。通过回顾它们的理论性质以及在各种准则下的实证表现，我们提供了关于它们相对优势和局限性的统一视角。本文提出的比较旨在帮助实践者针对不同目标和约束选择合适的设计策略。本工作的见解也突出了开放的挑战，并可能作为未来最优LHD构造发展的基准。
英文摘要：
Latin hypercube designs (LHDs) play an important role in computer experiments, offering flexible and efficient space-filling properties under a variety of optimality criteria, including maximin distance, maximum projection, and orthogonality. Constructing optimal LHDs with flexible sizes is challenging due to the limited availability of theoretical results, namely, algebraic constructions with provable optimality guarantees, and the rapidly expanding search space encountered by search algorithms. For design sizes outside the scope of known algebraic constructions, search-based algorithms are widely used, but they often involve substantial computational effort and lack assurances of global optimality. This paper provides a comprehensive review and comparison of current popular algebraic constructions for optimal LHDs and widely adopted search algorithms for generating high-quality LHDs. By reviewing their theoretical properties and empirical performance across a range of criteria, we offer a unified perspective on their relative strengths and limitations. The comparisons presented herein aim to assist practitioners in selecting appropriate design strategies for different objectives and constraints. The insights from this work also highlight open challenges and may serve as a benchmark for future development in optimal LHD construction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
