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A Primal Heuristic for MINLP based on Dual Information

Please always quote using this URN: urn:nbn:de:0297-zib-43110
  • We present a novel heuristic algorithm to identify feasible solutions of a mixed-integer nonlinear programming problem arising in natural gas transportation: the selection of new pipelines to enhance the network's capacity to a desired level in a cost-efficient way. We solve this problem in a linear programming based branch-and-cut approach, where we deal with the nonlinearities by linear outer approximation and spatial branching. At certain nodes of the branching tree, we compute a KKT point for a nonlinear relaxation. Based on the information from the KKT point we alter some of the integer variables in a locally promising way. We describe this heuristic for general MINLPs and then show how to tailor the heuristic to exploit our problem-specific structure. On a test set of real-world instances, we are able to increase the chance of identifying feasible solutions by some order of magnitude compared to standard MINLP heuristics that are already built in the general-purpose MINLP solver SCIP.

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Author:Jesco Humpola, Armin Fügenschuh, Thomas Lehmann
Document Type:ZIB-Report
Tag:Duality; Heuristics; Mixed-Integer Nonlinear Programming; Nonlinear Network Design Applications; Relaxations
Date of first Publication:2013/11/21
Series (Serial Number):ZIB-Report (13-49)
Published in:Appeared under the title "A primal heuristic for optimizing the topology of gas networks based on dual information" in: EURO Journal on Computational Optimization 2014
Licence (German):License LogoCreative Commons - Namensnennung-Nicht kommerziell-Keine Bearbeitung
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