TY - JOUR

T1 - Decomposing and solving timetabling constraint networks

AU - Meisels, Amnon

AU - Ell-Sana, Jihad

AU - Gudes, Ehud

PY - 1997/1/1

Y1 - 1997/1/1

N2 - The binary version of the school timetabling (STT) problem is a real-world example of a constraint network that includes only constraints of inequality. A new and useful representation for this real-world problem, the STT-Grid, leads to a generic decomposition technique. The paper presents proofs of necessary and sufficient conditions for the existence of a solution to decomposed STT_Grids. The decomposition procedure is of low enough complexity to be practical for large problems, such as a real-world high school. To test the decomposition approach, a typical high school was analyzed and used as a model for generating STT_Grids of various sizes. Experiments were conducted to test the difficulty of large STT networks and their solution by decomposition. The experimental results show that the decomposition procedure enables the solution of large STT_Grids (620 variables for a real school) in reasonable time. The constraint network of a typical STT_Grid is sparse and belongs to the class of easy problems. Still, due to the sizes of STTs, good constraint satisfaction problem search techniques (i.e., BackJumping and ForwardChecking) do not terminate in reasonable times for STT_Grids that are larger than 300 variables.

AB - The binary version of the school timetabling (STT) problem is a real-world example of a constraint network that includes only constraints of inequality. A new and useful representation for this real-world problem, the STT-Grid, leads to a generic decomposition technique. The paper presents proofs of necessary and sufficient conditions for the existence of a solution to decomposed STT_Grids. The decomposition procedure is of low enough complexity to be practical for large problems, such as a real-world high school. To test the decomposition approach, a typical high school was analyzed and used as a model for generating STT_Grids of various sizes. Experiments were conducted to test the difficulty of large STT networks and their solution by decomposition. The experimental results show that the decomposition procedure enables the solution of large STT_Grids (620 variables for a real school) in reasonable time. The constraint network of a typical STT_Grid is sparse and belongs to the class of easy problems. Still, due to the sizes of STTs, good constraint satisfaction problem search techniques (i.e., BackJumping and ForwardChecking) do not terminate in reasonable times for STT_Grids that are larger than 300 variables.

KW - Constraint satisfaction problems

KW - Heuristic search

KW - Timetabling

UR - http://www.scopus.com/inward/record.url?scp=0031269073&partnerID=8YFLogxK

U2 - 10.1111/0824-7935.00049

DO - 10.1111/0824-7935.00049

M3 - Article

AN - SCOPUS:0031269073

VL - 13

SP - 486

EP - 505

JO - Computational Intelligence

JF - Computational Intelligence

SN - 0824-7935

IS - 4

ER -