A primal heuristic for optimizing the topology of gas networks based on dual information

We present a novel heuristic 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 programmi...

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Bibliographic Details
Published in:	EURO journal on computational optimization 2015-02, Vol.3 (1), p.53-78
Main Authors:	Humpola, Jesco, Fügenschuh, Armin, Lehmann, Thomas
Format:	Article
Language:	eng
Subjects:	90-xx Mathematical Programming Approximation Business and Management Duality Heuristic Heuristics Integer programming Linear programming Management Science Mathematical programming Mixed-integer nonlinear programming Natural gas distribution Nonlinear network design applications Operations Management Operations Research Operations Research/Decision Theory Optimization Original Paper Pipelines Relaxations Studies Variables
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Summary:	We present a novel heuristic 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 of a nonlinear relaxation. Based on the information from the KKT point we alter some of the binary variables in a locally promising way exploiting 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.
ISSN:	2192-4406 2192-4414