Decomposition and Parallelization of Multi-resource Timetabling Problems
This paper presents a model of generalized timetabling problem and a decomposition algorithm which can decompose large problems into independent smaller subproblems—the search for a feasible solution can then be easily parallelized. The timetabling problem consists in fixing a sequence of meetings between teachers and students in a prefixed period of time (typically a week), satisfying a set of constraints of various types . Course timetabling is a multi-dimensional NP-complete problem . In this paper we present the multi-resource timetabling problem (MRTP), our model for the generalized high-school timetabling problem. The MRTP is a search problem—a feasible solution is searched. The main contribution of this paper is the Decomposition Algorithm for MRTP to parallelize the search, so the whole MRTP can be easily distributed and parallelized. Our approach was applied to real-life instances of high-school timetabling problems. Results are discussed at the end of this paper and parallelized search is compared with the centralized one.
KeywordsDecomposition Algorithm Timetabling Problem Color Marking Independent Subproblem School Timetabling Problem
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