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In this paper, a mixed integer nonlinear programming (MINLP) model is presented which can generate networks where utility cost, exchanger areas and selection of matches are optimized simultaneously. The proposed model does not rely on the assumption of fixed temperature approaches (HRAT or EMAT), nor on the prediction of the pinch point for the partitioning into subnetworks. The model is based on the stage-wise representation introduced in Part I of this series of papers, where within each stage, potential exchanges between each hot and cold stream can occur. The simplifying assumption on isothermal mixing to calculate heat transfer area for stream splits allows the feasible space to be defined by a set of linear constraints. As a result, the model is robust and can be solved with relative ease. Constraints on the network design that simplify its structure, e.g. no stream splits, forbidden matches, required and …