On PDE solution in transient optimization of gas networks

Operative planning in gas distribution networks leads to large-scale mixed-integer optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions—or as relaxation in a branch-and-bound framework, addressing in particular the KKT systems arising in primal–dual interior methods. We propose a custom solution algorithm using sparse projections locally in time, based on the KKT systems’ structural properties in space as induced by the discretized gas flow equations in combination with the underlying network topology. The numerical efficiency and accuracy of the algorithm are investigated, and detailed computational comparisons with a previously developed control space method and with the multifrontal solver MA27 are provided.