Benchmark of mixed-integer linear programming formulations for district heating network design

Optimal routing and investment decisions are key design criteria to reduce the high investment costs of district heating systems. However, these optimization problems have prohibitively high computational costs for large districts. Four different mixed-integer linear optimization frameworks are benchmarked in this study in order to compare their computational scaling. The frameworks exhibit significant differences in solving times for synthetic benchmarks and real-world urban districts of up to 9587 potential edges. The new open-source framework topotherm, developed for this work, exhibits the best computational performance when only one time step is optimized. The comparison between the models Résimont, DHmin, DHNx, and topotherm shows two main trends. First, fewer integer variables do not necessarily translate to lower solving times, and second, using redundant binary variables, which introduce symmetries into the constraints, leads to higher solving times. None of the considered optimization frameworks is able to solve the largest benchmark problems for five time steps within the allowed time limit and tolerance. These findings highlight the challenges of and pressing need to develop efficient models for simultaneous optimization of district heating network topology, pipe sizing, and operation.