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Towards Simulation Based Mixed-Integer Optimization with Differential Equations

Martin Gugat (martin.gugat***at***fau.de)
GŁnter Leugering (guenter.leugering***at***fau.de)
Alexander Martin (alexander.martin***at***fau.de)
Martin Schmidt (mar.schmidt***at***fau.de)
Mathias Sirvent (mathias.sirvent***at***fau.de)
David Wintergerst (david.wintergerst***at***fau.de)

Abstract: We propose a decomposition based method for solving mixed-integer nonlinear optimization problems with "black-box" nonlinearities, where the latter, e.g., may arise due to differential equations or expensive simulation runs. The method alternatingly solves a mixed-integer linear master problem and a separation problem for iteratively refining the mixed-integer linear relaxation of the nonlinearity. We prove that our algorithm finitely terminates with an approximate feasible global optimal solution of the mixed-integer nonlinear problem. Additionally, we show the applicability of our approach by three case studies from mixed-integer optimal control, from the field of pressurized flows in pipes with elastic walls, and from steady-state gas transport. For the latter we also present promising numerical results of our method applied to real-world instances.

Keywords: Mixed-Integer Optimization, Simulation Based Optimization, Optimization with Differential Equations, Decomposition Method, Gas Transport Networks

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

Category 2: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 3: Applications -- Science and Engineering

Citation:

Download: [PDF]

Entry Submitted: 07/14/2016
Entry Accepted: 07/14/2016
Entry Last Modified: 09/25/2017

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