NP-hardness of the discretized gas-network optimization problem

Establish whether the combinatorial integer program obtained by discretizing the natural-gas transmission-network throughput maximization problem under the Panhandle-B hydraulic equation is NP-hard.

Background

The paper formulates maximum-throughput operation of a natural-gas transmission network as an optimization over discretized squared nodal pressures. The formulation incorporates the nonlinear Panhandle-B pipe-flow relation, flow conservation at intermediate junctions, directed-flow consistency, and minimum customer-pressure constraints.

The authors state that the continuous problem is nonlinear and non-convex and that discretization produces a combinatorial integer program whose state space grows exponentially with the number of decision nodes and pressure-resolution bits. The computational complexity classification of this resulting integer program is not established in the paper; its NP-hardness is presented only as a conjecture supported by cited complexity literature.