Search Design Under β-wordlength Pattern With Stochastic Optimization Algorithm

This passage provides a method to constructing “good” designs under β-wordlengthpatter using stochastic optimization algorithm. Based on Cheng and Ye (2004), β-wordlength pattern can describe the statistical properties of designs with quantitativefactors under polynomial model. However, it will take high algorithmic complexity ifdoing corresponding calculations directly through the definition of β-wordlength pat-tern. By introducing the concept of row similarity expression E(D) for a design D, wefirst build the relationship between E(D) and β-wordlength pattern. On this basis, wediscuss the theoretical lower bound of E(D). Then we propose an indirect method tosearch for designs with less β-wordlength pattern combining with stochastic optimiza-tion algorithm. The numerical examples illustrate that the algorithm here is highlyefective as well as feasible. For three-or four-level designs, the β-wordlength patternsof the examples we find are almost close or approaching the corresponding theoreticallower bounds.