Please use this identifier to cite or link to this item: http://hdl.handle.net/1893/15778
Appears in Collections:Computing Science and Mathematics Journal Articles
Peer Review Status: Refereed
Title: Decomposition, reformulation, and diving in university course timetabling
Authors: Burke, Edmund
Maracek, Jakub
Parkes, Andrew J
Rudova, Hana
Contact Email: e.k.burke@stir.ac.uk
Keywords: Integer programming
Decomposition
Reformulation
Diving
Heuristic
Metaheuristic
University course timetabling
Soft constraints
Issue Date: Mar-2010
Publisher: Elsevier
Citation: Burke E, Maracek J, Parkes AJ & Rudova H (2010) Decomposition, reformulation, and diving in university course timetabling, Computers and Operations Research, 37 (3), pp. 582-597.
Abstract: In many real-life optimisation problems, there are multiple interacting components in a solution. For example, different components might specify assignments to different kinds of resource. Often, each component is associated with different sets of soft constraints, and so with different measures of soft constraint violation. The goal is then to minimise a linear combination of such measures. This paper studies an approach to such problems, which can be thought of as multiphase exploitation of multiple objective-/value-restricted submodels. In this approach, only one computationally difficult component of a problem and the associated subset of objectives is considered at first. This produces partial solutions, which define interesting neighbourhoods in the search space of the complete problem. Often, it is possible to pick the initial component so that variable aggregation can be performed at the first stage, and the neighbourhoods to be explored next are guaranteed to contain feasible solutions. Using integer programming, it is then easy to implement heuristics producing solutions with bounds on their quality. Our study is performed on a university course timetabling problem used in the 2007 International Timetabling Competition (ITC), also known as the Udine Course Timetabling problem. The goal is to find an assignment of events to periods and rooms, so that the assignment of events to periods is a feasible bounded colouring of an associated conflict graph and the linear combination of the numbers of violations of four soft constraints is minimised. In the proposed heuristic, an objective-restricted neighbourhood generator produces assignments of periods to events, with decreasing numbers of violations of two period-related soft constraints. Those are relaxed into assignments of events to days, which define neighbourhoods that are easier to search with respect to all four soft constraints. Integer programming formulations for all subproblems are given and evaluated using ILOG CPLEX 11. The wider applicability of this approach is analysed and discussed.
Type: Journal Article
URI: http://hdl.handle.net/1893/15778
DOI Link: http://dx.doi.org/10.1016/j.cor.2009.02.023
Rights: The publisher does not allow this work to be made publicly available in this Repository. Please use the Request a Copy feature at the foot of the Repository record to request a copy directly from the author. You can only request a copy if you wish to use this work for your own research or private study.
Affiliation: Deputy Principal's Office
University of Nottingham
University of Nottingham
Masaryk University

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