Constructions Of Mixed-level Uniform Design With Weighted Discrete Discrepancy

Experimental design plays an an important role in industry,agriculture and scientific innovation.As a common type of experimental design,uniform design can handle high-level and multi-factor complex test systems with fewer test times.Uniform design aims to "evenly distributo" test points in the experimental area,and uniform criterion is the index to measure whether the test points are "evenly"dispersed.Many uniform criterion have been propose,among which weighted discrete discrepancy has a unique advantage in dealing with the test area of mixed-level discrete state.Therefore,this paper chooses weighted discrete discrepancy as criterio n to construct uniform design.Many existing literatures have studied the construction methods of uniform design,including good lattice point method,Latin method and stochastic optimization algorithm.Although these methods are intuitive and simple,they cannot ensure that the constructed design can reach the theoretical lower bound of the corresponding discrepancy.Based on the in-depth analysis of the combinatorial properties of weighted discrete discrepancy.a series of combinatorial methods for constructing uniform design are given in this paper.These construction are supported by combinatorial theory,which can make the design obtained by the construction reach the theoretical lower bound under the weighted discrete discrepancy.At the same time.the obtained uniform design has two different levels,which can be applied to move test systems.The main work of this paper can be divided into two parts:The first is the construction part.Combining with RGDD.Hadamard matrix.SSRBIBD and composite decomposition.we give a series of general methods to construct uniform design under weighted discrete deviation.The next is the part of existence research,we discuss the necessary conditions for the existence of related designs in various situations,and give a series of infinite classes about the existence of uniform designs under weighted discrete deviations by combining the existence theorems of related combinatorial constructions.For each construction method,we also give specific examples.