Currently, there is a lack of reliable computational methods to automatically synthesize separation networks within specific product targets. Computational methods exploring the combinatorial wealth of different separation configurations, while simultaneously selecting feasible or detecting globally optimal operating conditions, are not available for problems of practical size. In this paper, we extend the minimum bubble point distance algorithm embedded in the temperature collocation methodology to rigorously design complex networks to separate nonideal multicomponent mixtures into products of desired purity using heat-integrated prefractionating columns. Our employed inverse design procedure enables the systematic design of physically realizable separations for mixtures with a large number of species. The computer procedure robustly converges to the desired purity targets, unless the desired purity target is thermodynamically impossible to realize. The algorithm also rapidly identifies infeasible specifications without fail. Finally, synthesized networks were validated with Aspen Plus matching exactly the inverse design results with the target purity. The rigorous flowsheet design combined with validation of the networks with commercial flowsheet simulators enables the systematic design of energy-efficient separation networks. The methodology is ready to address currently unresolved design problems such as the computer-aided design of energy-efficient separations, the design of biorefineries, or new process designs for carbon sequestration.