Accelerating column generation schemes: applications to routing problems
2005 (English)Doctoral thesis, comprehensive summary (Other academic)
Many integer optimization problems of great practical importance are today attacked with column generation. Merits of column generation is that it enables the use of compact and flexible formulations of many complex optimization problems, and that it often gives rise to good (strong) formulations. A potential drawback with column generation is the well-known tailing-off phenomenon, that is, that the objective value is improved rapidly in early iterations but very slowly in the late iterations.
We study various techniques for accelerating column generation methods for (integer) linear programs. We evaluate the use of stabilized column generation on a Traveling Salesman Subtour Problem, TSSP, a problem which is closely related to the Prize Collecting Traveling Salesman Problem. We further study how subgradient optimization can be used with the purpose of predicting optimal columns (and, optionally, non-binding restrictions). This technique is tested on the TSSP and the multicommodity network flow problem.
Another idea evaluated in this thesis is the use of over-generation of columns in a column generation scheme for an integer programming problem, in this case a vehicle routing problem with a heterogeneous fleet of vehicles.
The thesis also includes a note on a class of relatives to the Held and Karp 1–tree problem. It is shown that two subclasses have polynomial time-complexity. Further, we note a mistake in an earlier work and provide a counter-example to the erroneous result.
Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2005. , 34 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 978
IdentifiersURN: urn:nbn:se:liu:diva-30273Local ID: 15790ISBN: 91-85457-50-7OAI: oai:DiVA.org:liu-30273DiVA: diva2:251095
2005-11-28, Glashuset, Hus B, Campus Valla, Linköping, 10:15 (Swedish)
Madsen, Oli, Professor
List of papers