Traditional evolutionary methods for the synthesis of heat exchanger networks normally produce an initial network containing excess units when compared to the minimum units target. Subsequently, this network is simplified by energy relaxation. However, current methods fail to guarantee that the evolution follows a pathway ensuring that the minimum energy penalty is incurred. A new method to guide this evolution is presented. It is based on the application of Kirchhoff's Law to the network. This enables easy prediction of the actual energy penalties incurred by instituting different loop-breaking strategies. The minimum energy penalty may be discovered and the units to be removed to constitute an optimal solution readily identified. The precedence order for loop breaking in networks containing multiple loops can also be determined according to their respective energy penalties. The proposed algorithm enables the designer to undertake the loop-breaking phase of network design with confidence. The minimum energy path may be followed until a final network is discovered.