This work investigates the solution of Mixed-Integer Optimal Control Problems (MIOCPs) for an existing residential heating network. The network consists of several buildings that are interconnected through a district heating network and a biomethane combined heat and power (CHP) plant. All buildings have access to decentralized heat generation, in the form of solar thermal collectors on the rooftops of the buildings. Buildings with surplus heat are intended to transfer heat to buildings with heating demands in order to prevent the activation of the CHP plant. Additional storage provide further flexibility for storage and utilization of heat. Binary variables represent the exchange relations between buildings and the CHP plant. For this system, we solve an MIOCP in two different ways. On the one hand, we keep the system related nonlinearities and apply the Combinatorial Integral Approximation (CIA) method to the arising Mixed-Integer Nonlinear Program (MINLP). On the other hand, we apply a linear reformulation yielding a Mixed-Integer Linear Program (MILP), which we solve using a standard MILP solver. We show that the MINLP approach has a computational advantage over the MILP approach, while yielding only slightly worse results in the single-digit percentage range for selected key figures.