Sequential good lattice point sets for computer experiments

Abstract

Sequential Latin hypercube designs (SLHDs) have recently received great attention for computer experiments, with much of the research restricted to invariant spaces. The related systematic construction methods are inflexible, and algorithmic methods are ineffective for large designs. For designs in contracting spaces, systematic construction methods have not been investigated yet. This paper proposes a new method for constructing SLHDs via good lattice point sets in various experimental spaces. These designs are called sequential good lattice point (SGLP) sets. Moreover, we provide efficient approaches for identifying the (nearly) optimal SGLP sets under a given criterion. Combining the linear level permutation technique, we obtain a class of asymptotically optimal SLHDs in invariant spaces, where the L1-distance in each stage is either optimal or asymptotically optimal. Numerical results demonstrate that the SGLP set has a better space-filling property than the existing SLHDs in invariant spaces. It is also shown that SGLP sets have less computational complexity and more adaptability.