Optimization Online


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


Download: [PDF]

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

Modify/Update this entry

  Visitors Authors More about us Links
  Subscribe, Unsubscribe
Digest Archive
Search, Browse the Repository


Coordinator's Board
Classification Scheme
Give us feedback
Optimization Journals, Sites, Societies
Mathematical Optimization Society