This paper details results of a comparative study of the formulation of equality constraints used in the method of Simultaneous ANalysis and Design (SAND). A Generalized Reduced Gradient (GRG) optimizer is used to evaluate the efficacy of three different forms of equality constraints referred to as compatibility constraints in the SAND based optimization procedure. Three Multidisciplinary Design Optimization (MDO) test problems are used in evaluating the efficacy of the compatibility constraint formulations. Results highlight that the form of the compatibility constraints can have a significant impact on the performance of the SAND based procedure.