Efficient Computational Algorithms for Searching for Good Designs According to the Generalized Minimum Aberration Criterion

SYNOPTIC ABSTRACT

Generalized minimum aberration was introduced by Deng and Tang (1999) as a criterion for comparing and assessing the “goodness” of nonregular fractional factorial designs. For small run sizes, generalized minimum aberration designs can be obtained by a complete search of Hadamard matrices; however, for larger run sizes a complete search is impractical. The main purpose of this paper is to study the use of efficient computational algorithms to construct generalized minimum aberration designs. Application to small run sizes shows that our algorithms perform almost as well as complete search, but with much less computing time. This strongly suggests that our algorithms should be successful in finding good designs for larger run sizes.

Key Words and Phrases:

• nonregular fractional factorial
• Hadamard matrix
• generalized minimum aberration