Enhanced branching Latin hypercube design and its application in automatic algorithm configuration

Designing experiments that involve branching and nested factors is challenging due to the complex relationships between these factors. Identification of optimal settings requires designs with good stratification properties for both nested and shared factors. To meet this requirement, we defined a type of enhanced branching Latin hypercube designs and developed several novel construction methods by integrating orthogonal arrays and sliced Latin hypercube designs. These designs exhibit attractive low‐dimensional stratification properties and perform well in terms of column correlation. Additionally, the size of each design can be flexibly chosen based on the trade‐off between the experimental budget and estimation accuracy. The simulation results demonstrate that the proposed design method exhibits significant superiority in terms of design metrics and estimation accuracy. Furthermore, we showcase the application of these designs in initializing automatic algorithm configuration. The proofs and additional design tables are provided in the Appendix.