Mixed integer linear models for the optimization of dynamical transport networks

We introduce a mixed integer linear modeling approach for the optimization of dynamic transport networks based on the piecewise linearization of nonlinear constraints and we show how to apply this method by two examples, transient gas and water supply network optimization. We state the mixed integer linear programs for both cases and provide numerical evidence for their suitability.

[1]  Rolf Rannacher,et al.  Modeling, Simulation and Optimization of Complex Processes: Proceedings of the International Conference on High Performance Scientific Computing, March 10-14, 2003, Hanoi, Vietnam , 2005 .

[2]  Manfred W. Padberg,et al.  Approximating Separable Nonlinear Functions Via Mixed Zero-One Programs , 1998, Oper. Res. Lett..

[3]  J. Tomlin A Suggested Extension of Special Ordered Sets to Non-Separable Non-Convex Programming Problems* , 1981 .

[4]  Jens Lang,et al.  An implicit box scheme for subsonic compressible flow with dissipative source term , 2010, Numerical Algorithms.

[5]  Jon Lee,et al.  Polyhedral methods for piecewise-linear functions I: the lambda method , 2001, Discret. Appl. Math..

[6]  S. Moritz A Mixed Integer Approach for the Transient Case of Gas Network Optimization , 2007 .

[7]  Björn Geißler,et al.  Using Piecewise Linear Functions for Solving MINLP s , 2012 .

[8]  A. S. Manne,et al.  On the Solution of Discrete Programming Problems , 1956 .

[9]  R. LeVeque Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[10]  Burton Wendroff,et al.  On Centered Difference Equations for Hyperbolic Systems , 1960 .

[11]  Laurence A. Wolsey,et al.  Integer and Combinatorial Optimization , 1988, Wiley interscience series in discrete mathematics and optimization.

[12]  Joaquín Izquierdo,et al.  FLOW MODELING IN PRESSURIZED SYSTEMS REVISITED , 1999 .

[13]  Markus Möller,et al.  Mixed Integer Models for the Optimisation of Gas Networks in the Stationary Case , 2004 .

[14]  Alexander Martin,et al.  Combination of Nonlinear and Linear Optimization of Transient Gas Networks , 2011, INFORMS J. Comput..

[15]  Ted K. Ralphs,et al.  Integer and Combinatorial Optimization , 2013 .

[16]  François Margot,et al.  Min-up/min-down polytopes , 2004, Discret. Optim..

[17]  Marc C. Steinbach,et al.  Nonlinear Optimization in Gas Networks , 2003, HPSC.