A novel criterion and searching algorithm for constructing Latin hypercube designs

The optimal Latin hypercube designs have been applied in many computer experiments as a basic method of experiment design. In this paper, we propose a novel criterion for constructing optimal Latin hypercube designs. The corresponding foundation of the novel criterion ideas is that the each point of the uniform design should have approximately equal distance with adjacent points. It means if we count the average and variance of distance between each point of design with its adjacent points, then the minimum variance of those distance will be a new criterion for optimal Latin hypercube designs. Only limit adjacent distances has been chosen to count above variance for convenience. The criterion come from limit variance will have an effect on the uniformity of a design. So another criterion was proposed that is maximum average adjacent distance. The final criterions are synthesized by minimum variance and maximum average of the adjacent distance which are connected by a coefficient. A novel searching algorithms was also proposed that take advantage of the columnwise-pairwise algorithm and the simulated annealing algorithm. The novel searching algorithm only could be used to the criteria above mentioned because it use some special information connected with the adjacent distance deviation. A software has been programmed that can generate Latin hypercube designs with the proposed criteria and searching algorithm. The properties of different criterion and searching algorithm were compared by generating large quantity designs and count the statistical properties of criterion. The result from some case of designs can account that the proposed novel criterion and searching algorithm is better than other distance criterion and searching algorithm.