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Integral column generation for the set partitioning problem

Integral column generation for the set partitioning problem The integral simplex using decomposition (ISUD) algorithm was recently developed to solve efficiently set partitioning problems containing a number of variables that can all be enumerated a priori. This primal algorithm generates a sequence of integer solutions with decreasing costs, leading to an optimal or near-optimal solution depending on the stopping criterion used. In this paper, we develop an integral column generation (ICG) heuristic that combines ISUD and column generation to solve set partitioning problems with a very large number of variables. Computational experiments on instances of the public transit vehicle and crew scheduling problem and of the airline crew pairing problem involving up to 2000 constraints show that ICG clearly outperforms two popular column generation heuristics (the restricted master heuristic and the diving heuristic). ICG can yield optimal or near-optimal solutions in less than 1 hour of computational time, generating up to 300 integer solutions during the solution process. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png EURO Journal on Transportation and Logistics Springer Journals

Integral column generation for the set partitioning problem

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References (27)

Publisher
Springer Journals
Copyright
Copyright © 2019 by The Association of European Operational Research Societies and Springer-Verlag GmbH Berlin Heidelberg
Subject
Business and Management; Operations Research/Decision Theory; Logistics; Operations Research, Management Science; Optimization
ISSN
2192-4376
eISSN
2192-4384
DOI
10.1007/s13676-019-00145-6
Publisher site
See Article on Publisher Site

Abstract

The integral simplex using decomposition (ISUD) algorithm was recently developed to solve efficiently set partitioning problems containing a number of variables that can all be enumerated a priori. This primal algorithm generates a sequence of integer solutions with decreasing costs, leading to an optimal or near-optimal solution depending on the stopping criterion used. In this paper, we develop an integral column generation (ICG) heuristic that combines ISUD and column generation to solve set partitioning problems with a very large number of variables. Computational experiments on instances of the public transit vehicle and crew scheduling problem and of the airline crew pairing problem involving up to 2000 constraints show that ICG clearly outperforms two popular column generation heuristics (the restricted master heuristic and the diving heuristic). ICG can yield optimal or near-optimal solutions in less than 1 hour of computational time, generating up to 300 integer solutions during the solution process.

Journal

EURO Journal on Transportation and Logistics – Springer Journals

Published: Jun 26, 2019

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