Optimal coverage design for experiments with multiple types of factors

Many experiments involve various types of input factors, including continuously numerical, discretely numerical, ordinary and categorical variables. Designs with strong space-filling properties are essential for reducing costs and improving efficiency in such experiments. While some existing methods address multiple factor types, they are often limited by sample size constraints or fail to ensure orthogonality in discrete sub-designs. In this article, we propose a novel coverage-based space-filling criterion and introduce a simulated annealing algorithm to generate optimal coverage designs. The proposed criterion accounts for both the space-filling properties of continuous factors and the orthogonality of discrete factors, offering flexibility in run size. Numerical results confirm that the proposed design exhibits the desired properties.