The paper proposes a new design approach for the optimal synthesis of heat exchanger networks. The approach combines thermodynamics, engineering knowledge, and mathematical programming and leads to Conceptual programming methodology with a clear potential to address industrial applications from a systematic and rigorous perspective. The methodology employs a Conceptual Programming model, the Area Target Model, to screen and scope the solution space for primal, promising options. The model embeds targeting terms from the pinch analysis and supports the development of Hypertargets, a graphical targeting tool with functions similar but much more general and rigorous than Supertargets. Following the targeting stage, a network optimisation stage is facilitated with an extended mathematical formulation that handles complexity issues, and accounts for the development of functional layouts without the need for evolution.