Orthogonal Latin hypercube designs (LHDs) and maximum projection (MaxPro) LHDs are widely used in computer experiments. They are efficient for estimating the trend and Gaussian process (GP) parts of the universal Kriging (i.e. GP) model, respectively, especially when only some of the factors are active. However, the orthogonality is found, and the MaxPro criteria often do not agree with each other. Thus, a new class of optimal designs, orthogonal-MaxPro LHDs, is proposed, optimizing a well-defined multi-objective criterion combining the correlation and the MaxPro metrics. An efficient paralleled algorithm is developed via level permutations and expansions, whose efficiency is guaranteed by theories. Numerical results are presented to show that the construction is fast and the obtained designs are attractive, especially for large computer experiments.

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