This work presents a methodology for optimizing heat-integrated crude oil distillation systems. Part I of this three-part series presents a modeling strategy where artificial neural networks are used to represent the distillation process. Part II presents a new methodology to retrofit heat exchanger networks (HENs) and Part III presents the application of this distillation model to perform operational optimization of the crude oil distillation unit while proposing retrofit modifications to the associated HEN. Independent variables of the distillation model include flow rates of products, stripping steam, pump-around specifications, and furnace exit temperature. Dependent variables include those related to product quality, and temperatures, duties, and heat capacities of process streams involved in heat integration. The resulting neural network model is able to overcome convergence problems presented by rigorous or simplified models. Simulation time is significantly improved using neural networks, compared to rigorous models, with practically no detriment to model accuracy.