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Mixed-Integer PDE-Constrained Optimal Control of Gas Networks

Mirko Hahn (hahnm***at***anl.gov)
Sven Leyffer (leyffer***at***anl.gov)
Victor Zavala (victor.zavala***at***wisc.edu)

Abstract: We develop a mixed-integer optimal control model with partial differential equation (PDE) constraints for gas transport networks, designed for controlling extreme state transitions, such as flow reversals. Our model shows how to combine binary compressor controls with PDE flow models. We model the flow of gas using a variant of the Euler equations, which we dis- cretize using a finite volume scheme, which obeys conservation of mass and average impulse independent of the direction of flow. The resulting large-scale mixed-integer nonlinear opti- mization problem is difficult to solve by using standard branch-and-bound solvers, and we propose a new tree-search strategy that allow us to solve realistic instances. We compare the performance of several solution schemes on twelve test instances, showing that our custom tree-search strategy greatly outperforms a generic strategy in most instances.

Keywords: Gas networks, flow reversal, PDE constraints, mixed-integer nonlinear optimization

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Applications -- Science and Engineering (Optimization of Systems modeled by PDEs )

Category 3: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Citation: Hahn, Mirko, Leyffer, Sven and Zavala, Victor. "Mixed-Integer PDE-Constrained Optimal Control of Gas Networks", Argonne National Laboratory, Preprint ANL/MCS-P7095-0817

Download: [PDF]

Entry Submitted: 12/18/2017
Entry Accepted: 12/18/2017
Entry Last Modified: 12/18/2017

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