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<p>Computer experiments are indispensable when a physical experiment is time-consuming, unaffordable, or impossible. Its main objective is to provide a meta-model or simulated model, simplifying and making the complex models less expensive. This necessitates finding space-filling designs, which provide maximum information by choosing fewer design points from different sub-spaces of the design space. Latin Hypercube Designs (LHD) as space-filling designs are in huge demand for model-based engineering and scientific applications. In this paper, we propose hybrid algorithmic construction methods inspired by geometrical shapes and the genetic algorithm to obtain high-dimensional LHDs, with the provision of assigning weights to different criteria. A comparative study with the existing classes of standard designs has revealed that the proposed designs possess good space-filling, orthogonality, and predictive modeling properties, making them highly desirable for computer experimentation. An R- package ‘CompExpDes’ is developed to easily implement these methods and calculate the required measures to study the properties of generated designs.</p>

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Algo-Geometric Construction of Weighted Criteria-Based Latin Hypercube Designs

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Ashutosh Dalal,
  • Cini Varghese,
  • Rajender Parsad,
  • Mohd Harun

摘要

Computer experiments are indispensable when a physical experiment is time-consuming, unaffordable, or impossible. Its main objective is to provide a meta-model or simulated model, simplifying and making the complex models less expensive. This necessitates finding space-filling designs, which provide maximum information by choosing fewer design points from different sub-spaces of the design space. Latin Hypercube Designs (LHD) as space-filling designs are in huge demand for model-based engineering and scientific applications. In this paper, we propose hybrid algorithmic construction methods inspired by geometrical shapes and the genetic algorithm to obtain high-dimensional LHDs, with the provision of assigning weights to different criteria. A comparative study with the existing classes of standard designs has revealed that the proposed designs possess good space-filling, orthogonality, and predictive modeling properties, making them highly desirable for computer experimentation. An R- package ‘CompExpDes’ is developed to easily implement these methods and calculate the required measures to study the properties of generated designs.