A mathematical formulation is presented for the minimum hot/cold/electric utility cost problem for heat exchange networks. The formulation allows optimal integration of heat exchangers, heat engines and heat pumps in heat exchange networks. Both heat exchangers and heat pumps/engines may consume hot/cold utilities, while heat engine pumps generate/consume electric utility. Calculation of the optimum does not require any prior commitment to network structure. Application of the technique to an existing industrial facility indicates potential cost savings of 50-330% (depending on the method) compared with the pinch optimum.