An efficient methodology for constructing optimal foldover designs in terms of mixture discrepancy

摘要: Abstract Mixture discrepancy criterion (Zhou et al., 2013) is more reasonable than other discrepancies criteria for measuring the uniformity of experimental designs. In this paper, we take mixture as optimality measure to assess optimal foldover plans, which serve benchmarks constructing and combined designs (see Definition 2). New analytical expressions well new lower bounds both symmetric two-level three-level under general plans are obtained. We also describe necessary conditions existence meeting these bounds. An algorithm searching developed. Illustrative examples provided, where numerical studies lend further support our theoretical results. These results may help provide some powerful efficient algorithms