**2. Problem Statement**

A synthesis of HEN involving the optimization of steam supply and utilization is desired in this study, and the entire problem can be described as follows: a set of hot and cold process streams which must be cooled and heated are given with their heat capacity flowrates, supply temperatures, target temperatures and heat transfer coefficients. To compensate the heating gap, a utility system is optimized to produce appropriate steam, in terms of multiple paralleled mains/levels with different pressures and as well temperatures. These steam branches are usually classified as high pressure steam, medium pressure steam, and low pressure steam (HPS, MPS, LPS), etc. In this study, a set of steam alternatives with certain pressures and temperatures are given for selection. The utility system follows the basic process of a Rankine cycle, but the properties and quantity of generated steam must be optimized towards the best benefit of the whole system. Additionally, all the cost-related parameters are also given in order to assess cold utility cost, fuel cost, equipment investment (for heat exchangers, boilers and turbines) and the profit from selling power. The integration problem aims at achieving the most cost-efficient configuration of steam supply HEN, by making trade-offs amongst the contribution of the mentioned economic sectors in the total annualized cost. For this purpose, the interaction between the two sub-systems must be comprehensively explored and the network details, such as fuel consumption, steam generation and allocation, generated power, stream matches, heat loads, operating temperatures, and area of heat exchangers must be optimized. In order to alleviate the solving difficulties caused by a complicated mathematical presentation, it is assumed that: (1) the heat capacity and heat transfer coefficient are constant throughout the whole process; (2) the heat exchange task is completed in a countercurrent heat exchanger; (3) all operations are adiabatic, ignoring the heat loss and mass loss; (4) transportation problems are not taken into account; (5) only the primary units in the utility system are considered, ignoring the auxiliary devices.
