Inspired by natural examples of microvascular systems in a wide variety of living organisms, we perform the computational design of a new class of polymer-based composite materials with the unique ability to heal and/or cool in a completely autonomic fashion, i.e., without any external intervention. The design process combines graph theory to represent and evaluate the microvascular network and Genetic Algorithms (GA) to optimize the diameter of its microchannels. In this work, a multi-objective GA scheme has been adopted to optimize the network topology against conflicting objectives, which include (i) optimizing the flow properties of the network (i.e., reducing the flow resistance of the network to a prescribed mass flow rate) and (ii) minimizing the impact of the network on the stiffness and strength of the resulting composite in terms of the void volume fraction associated with the presence of the microvascular network. The flow analysis of the network is performed based on the assumption of fully established Poiseuille flow in all segments of the network, leading to the classical proportionality relation between the pressure drop along a segment and the mass flow rate. The optimized structures resulting from the optimization can then be manufactured using an automated process ("robotic deposition") that involves the extrusion of a fugitive wax to define the network. Once manufactured, the computer-aided design can then be validated through a comparison with the results obtained from flow tests. This presentation focuses on the results of the optimization of an epoxy-based composite material containing a two-dimensional microvascular network.