Dynamic aggregation of set-partitioning constraints in column generation

Dynamic aggregation of set-partitioning constraints in column generation

0.00 Avg rating0 Votes
Article ID: iaor2008973
Country: United States
Volume: 53
Issue: 4
Start Page Number: 632
End Page Number: 645
Publication Date: Jul 2005
Journal: Operations Research
Authors: , , ,
Keywords: programming: integer, sets
Abstract:

Column generation is often used to solve problems involving set-partitioning constraints, such as vehicle-routing and crew-scheduling problems. When these constraints are in large numbers and the columns have on average more than 8–12 nonzero elements, column generation often becomes inefficient because solving the master problem requires very long solution times at each iteration due to high degeneracy. To overcome this difficulty, we introduce a dynamic constraint aggregation method that reduces the number of set-partitioning constraints in the master problem by aggregating some of them according to an equivalence relation. To guarantee optimality, this equivalence relation is updated dynamically throughout the solution process. Tests on the linear relaxation of the simultaneous vehicle and crew-scheduling problem in urban mass transit show that this method significantly reduces the size of the master problem, degeneracy, and solution times, especially for larger problems. In fact, for an instance involving 1,600 set-partitioning constraints, the master problem solution time is reduced by a factor of 8.

Reviews

Required fields are marked *. Your email address will not be published.