GA-optimal partially balanced fractional 2m1+m2 factorial designs of resolution R({00,10,01,20} | Ω) with 2 ≤ m1, m2 ≤ 4

We consider a partially balanced fractional 2(m1+m2) factorial design derived from a simple partially balanced array such that the general mean, all the m(1) + m(2) main effects, all the ((m1)(2)) two-factor interactions and some linear combinations of the ((m2)(2)) two-factor ones, and all of the m(1)m(2) two-factor ones are estimable, where the three-factor and higher-order interactions are assumed to be negligible and 2 <= m(k) for k = 1, 2. In this article, we present optimal designs with respect to the generalized A-optimality criterion when the number of assemblies is less than the number of non negligible factorial effects, where 2 <= m(1), m(2) <= 4.