Under the assumption that the three-factor and higher-order interactions are negligible, we consider two kinds of partially balanced fractional 2 m 1+ m 2 factorial designs derived from simple partially balanced arrays, where 2 ≤ m k for k = 1, 2. One is a design such that the general mean, the m 1 + m 2 main effects, the ( m 12) two-factor interactions, the ( m 22) two-factor ones and some linear combinations of the m 1 m 2 two-factor ones are estimable, and the other is a design such that the general mean, the m 1 + m 2 main effects, the ( m 12) two-factor interactions, the m 1 m 2 two-factor ones and some linear combinations of the ( m 22) two-factor ones are estimable. In each kind of designs, 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 ≤ m 1, m 2 ≤ 4.