Combination of Nonlinear and Linear Optimization of Transient Gas Networks

In this paper, we study the problem of technical transient gas network optimization, which can be considered as a minimum cost flow problem with a nonlinear objective function and additional nonlinear constraints on the network arcs. Applying an implicit box scheme to the isothermal Euler equation, we derive a mixed integer nonlinear program. This is solved by means of a combination of (i) a novel mixed integer linear programming approach based on piecewise linearization and (ii) a classical sequential quadratic program extended with a continuous treatment of combinatorial constraints. Numerical experiments for example problems as well as for a real-life application show that best optimal control solutions can be achieved by a combination of both approaches.