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Solving Highly Detailed Gas Transport MINLPs: Block Separability and Penalty Alternating Direction Methods

Bj÷rn Gei▀ler (bjoern.geissler***at***math.uni-erlangen.de)
Antonio Morsi (antonio.morsi***at***math.uni-erlangen.de)
Lars Schewe (lars.schewe***at***math.uni-erlangen.de)
Martin Schmidt (mar.schmidt***at***fau.de)

Abstract: Detailed modeling of gas transport problems leads to nonlinear and nonconvex mixed-integer optimization or feasibility models (MINLPs) because both the incorporation of discrete controls of the network as well as accurate physical and technical modeling is required in order to achieve practical solutions. Hence, ignoring certain parts of the physics model is not valid for practice. In the present contribution we extend an approach based on linear relaxations of the underlying nonlinearities by tailored model reformulation techniques yielding block-separable MINLPs. This combination of techniques allows us to apply a penalty alternating direction method and thus to solve highly detailed MINLPs for large-scale real-world instances. The practical strength of the proposed method is demonstrated by a computational study in which we apply the method to instances from steady-state gas transport including both pooling effects with respect to the mixing of gases of different composition and a highly detailed compressor station model.

Keywords: Nonconvex Mixed-Integer Nonlinear Optimization, Penalty Methods, Alternating Direction Methods, Block Separability, Gas Transport

Category 1: Applications -- Science and Engineering

Category 2: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 3: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 06/30/2016
Entry Accepted: 06/30/2016
Entry Last Modified: 03/02/2017

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