A procedure was developed for on-line optimization and control systems of heat-exchanger networks, which features a two-level control structure, one for a constant configuration control system and the other for a supervisor on-line optimizer. The coordination between is achieved by adjusting the formulation of the the optimization problem to meet requirements of the adopted control system. The general goal is always to work without losing stream temperature targets while keeping the highest energy integration. The operations constraints used for heat-exchanger and utility units emphasize the computation of heat-exchanger duties rather than intermediate stream temperatures. This simplifies the modeling task and provides clear links with the limits of the manipulated variables. The optimal conditions is determined using LP or NLP, depending on the final problem formulation. Degrees of freedom for optimization and equation constraints for considering simple and multiple bypasses are rigorously discussed. An example used shows how the optimization problem can be adjusted to a specific network design, its expected operating space, and the control configuration. Dynamic simulations also show benefits and limitations of this procedure.