Optimal Sparse Projection Design for Systems with Treatment Cardinality Constraint

Music City Center 

Modern experimental designs often face the so-called treatment cardinality constraint, which is the constraint on the number of included factors in each treatment. Experiments with such constraints are commonly encountered in engineering simulation, AI system tuning, and large-scale system verification. This calls for the development of adequate designs to enable statistical efficiency for modeling and analysis within feasible constraints. In this work, we propose an optimal sparse projection (OSP) design for systems with treatment cardinality constraints. We introduce a tailored optimal projection (TOP) criterion that ensures a good space-filling properties in subspaces and promotes orthogonality or near-orthogonality among factors. To construct the proposed OSP design, we develop an efficient construction algorithm based on orthogonal arrays and employ parallel-level permutation and expansion techniques to efficiently explore the design space with treatment cardinality constraints. Numerical examples demonstrate the merits of the proposed method.

Experimental designs

Space-filling design

Orthogonal arrays

Constraint space

Treatment constraint 

Quality and Productivity Section