**3. Method Overview**

To solve the mentioned synthesis problem, an optimization-based method is developed and presented in this study. Since a synthesis solution is characterized by two aspects: the network structure (referring mainly to where to exchange heat and whether generate the steam) and the network parameters (which should be quantified, such as flowrate, temperature, heat exchange areas), a superstructure embedding all potential network configurations is introduced as the first step of the method, to offer decision options for the network structure, then a mathematical model is formulated to perform the optimization, making an automatic determination for both network structure and network parameters. Although this method is developed from the general concepts of HEN and utility systems, the major contribution of this work is still worth mentioning, that is, the utilization of steam in the HEN is extended by considering various locations along streams, being in series or/and parallel with stream-stream heat exchange, and meanwhile not only with the given utility steam but having the generation and allocation of steam integrated, such that the interaction between HEN and utility system can be explored with more space. It is believed that better design solutions will be obtained by using this method. For clarity, the superstructure is described in Section 4, followed by the mathematical model presentation in Section 5.
