A multi-objective genetic algorithm is used to design 2D and 3D microvascular networks embedded in bio-mimetic self-healing/self-cooling polymeric materials. Various objective functions and constraints are considered, ranging from flow efficiency and homogeneity to network redundancy and void volume fraction. The design variables include the network topology defined over a template and the microchannel diameters chosen among a finite set of values. The effect of network redundancy, template geometry and microchannel diameters on the Pareto-optimal fronts generated by the genetic algorithm is investigated.