A systematic procedure is proposed in this paper to incorporate the options of merging and/or splitting streams from multiple origins in process synthesis. In particular, design problems associated with the heat exchanger networks (HENs) are discussed in detail. First, an input-output system structure is described to facilitate the derivation of the modified LP and MILP models for calculating the design targets corresponding to the operating and capital costs. Next, construction procedure of a generalized stream structure is presented and the modified NLP model for generating the optimal networks is formulated accordingly. To accelerate the convergence rate of the corresponding iterative solution process, an evolutionary short-cut method is provided to produce feasible networks for use as the initial guesses. Two examples are also presented to demonstrate the effectiveness of the proposed approach. The results show that, without increasing the operating costs, the capital costs of HENs can be reduced significantly by considering the proposed stream structure in design.