Lower bounds for the ITC-2007 curriculum-based course timetabling problem

This paper describes an approach for generating lower bounds for the curriculum-based course timetabling problem, which was presented at the International Timetabling Competition (ITC-2007, Track 3). So far, several methods based on integer linear programming have been proposed for computing lower b...

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Published in:	European journal of operational research Vol. 212; no. 3; pp. 464 - 472
Main Authors:	Hao, Jin-Kao, Benlic, Una
Format:	Journal Article
Language:	English
Published:	Amsterdam Elsevier B.V 01.08.2011 Elsevier Elsevier Sequoia S.A
Series:	European Journal of Operational Research
Subjects:	Applied sciences Benchmarking Bounds Bounds Partitioning Tabu search Timetabling Computation Computer Science Curricula Curriculum development Divide & conquer algorithms Estimates Exact sciences and technology Heuristic Integer programming Linear programming Lower bounds Mathematical programming Operational research Operational research and scientific management Operational research. Management science Optimization Optimization algorithms Partitioning Scheduling, sequencing Solvers Studies Tabu search Timetabling Upper bounds Timetabling Partitioning Tabu search Bounds Lower bound Partition Curriculum guides Minimization Iterative method Linear programming Integer programming Educational program Upper bound Heuristic method Timetabling problem Divide and conquer method
ISSN:	0377-2217, 1872-6860
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Abstract	This paper describes an approach for generating lower bounds for the curriculum-based course timetabling problem, which was presented at the International Timetabling Competition (ITC-2007, Track 3). So far, several methods based on integer linear programming have been proposed for computing lower bounds of this minimization problem. We present a new partition-based approach that is based on the “divide and conquer” principle. The proposed approach uses iterative tabu search to partition the initial problem into sub-problems which are solved with an ILP solver. Computational outcomes show that this approach is able to improve on the current best lower bounds for 12 out of the 21 benchmark instances, and to prove optimality for 6 of them. These new lower bounds are useful to estimate the quality of the upper bounds obtained with various heuristic approaches.
AbstractList	This paper describes an approach for generating lower bounds for the curriculum-based course timetabling problem, which was presented at the International Timetabling Competition (ITC-2007, Track 3). So far, several methods based on integer linear programming have been proposed for computing lower bounds of this minimization problem. We present a new partition-based approach that is based on the “divide and conquer” principle. The proposed approach uses iterative tabu search to partition the initial problem into sub-problems which are solved with an ILP solver. Computational outcomes show that this approach is able to improve on the current best lower bounds for 12 out of the 21 benchmark instances, and to prove optimality for 6 of them. These new lower bounds are useful to estimate the quality of the upper bounds obtained with various heuristic approaches. This paper describes an approach for generating lower bounds for the curriculum-based course timetabling problem, which was presented at the International Timetabling Competition (ITC-2007, Track 3). So far, several methods based on integer linear programming have been proposed for computing lower bounds of this minimization problem. We present a new partition-based approach that is based on the "divide and conquer" principle. The proposed approach uses iterative tabu search to partition the initial problem into sub-problems which are solved with an ILP solver. Computational outcomes show that this approach is able to improve on the current best lower bounds for 12 out of the 21 benchmark instances, and to prove optimality for 6 of them. These new lower bounds are useful to estimate the quality of the upper bounds obtained with various heuristic approaches. [PUBLICATION ABSTRACT]
Author	Benlic, Una Hao, Jin-Kao
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SubjectTerms	Applied sciences Benchmarking Bounds Bounds Partitioning Tabu search Timetabling Computation Computer Science Curricula Curriculum development Divide & conquer algorithms Estimates Exact sciences and technology Heuristic Integer programming Linear programming Lower bounds Mathematical programming Operational research Operational research and scientific management Operational research. Management science Optimization Optimization algorithms Partitioning Scheduling, sequencing Solvers Studies Tabu search Timetabling Upper bounds
Title	Lower bounds for the ITC-2007 curriculum-based course timetabling problem
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