An algorithmic-evolutionary approach to the systematic synthesis of minimum cost networks of exchangers, heaters, and coolers is proposed. The new approach is easy to apply by hand calculations, requiring no special mathematical background and computational skill from the user. In addition to generating many cheaper networks for sample problems ranging in size from 4 to 10 streams as compared to previous studies, the proposed method provides an explicit theoretical guidance on the optimal exchange among hot and cold streams and on the optimal locations of heating and cooling utilities in the network. It also has a provision for the use of stream splitting and for generating a cyclic network. The new method is particularly effective in the synthesis of minimum cost networks for industrial crude unit preheat recovery.