Towards Simulation Based Mixed-Integer Optimization with Differential Equations

Gugat M, Leugering G, Martin A, Schmidt M, Sirvent M, Wintergerst D (2018)


Publication Language: English

Publication Status: Submitted

Publication Type: Journal article

Future Publication Type: Journal article

Publication year: 2018

Journal

Book Volume: 72

Pages Range: 60-83

Journal Issue: 1

URI: https://onlinelibrary.wiley.com/doi/abs/10.1002/net.21812

DOI: 10.1002/net.21812

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.

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APA:

Gugat, M., Leugering, G., Martin, A., Schmidt, M., Sirvent, M., & Wintergerst, D. (2018). Towards Simulation Based Mixed-Integer Optimization with Differential Equations. Networks, 72(1), 60-83. https://dx.doi.org/10.1002/net.21812

MLA:

Gugat, Martin, et al. "Towards Simulation Based Mixed-Integer Optimization with Differential Equations." Networks 72.1 (2018): 60-83.

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