In this paper, we revisit a general class of multi-criteria multi-constrained network design problems and attempt to solve, in a novel way, with Evolutionary Algorithms (EAs). A major challenge to solving such problems is to capture possibly all the (representative) equivalent and diverse solutions. In this work, we formulate, without loss of generality, a bi-criteria bi- constrained communication network topological design problem. Two of the primary objectives to be optimized are network delay and cost subject to satisfaction of reliability and flowconstraints. This is a NP-hard problem so we use a hybrid approach (for initialization of the population) along with EA. Furthermore, the twoobjective optimal solution front is not known a priori. Therefore, we use a multiobjective EA which produces diverse solution space and monitors convergence; the EA has been demonstrated to work effectively across complex problems of unknown nature. We tested this approach for designing networks of ...