On PDE Solution in Transient Optimization of Gas Networks

Operative planning in gas distribution networks leads to large-scale mixedinteger optimization problems involving a hyperbolic P D E defined on a graph. We consider the N L P obtained under prescribed combinatorial decisions—or as relaxation in a branch and bound framework, addressing in particular the K K T systems arising in primal-dual interior methods. We propose a custom solution algorithm using sparse local projections, based on the K K T systems’ structural properties 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 control space method and with the multifrontal solver MA27 are provided.