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Coupling Stochastic and Deterministic Local Search in Examination Timetabling

Dipartimento di Ingegneria dell’Impresa, University of Rome "Tor Vergata," Via del Politecnico, 1, 00133, Rome, Italy
Dipartimento di Statistica, Probabilità e Statistiche Applicate, University of Rome "La Sapienza," Piazzale Aldo Moro, 5, 00185 Rome, Italy
caramia{at}disp.uniroma2.it
paolo.dellolmo{at}uniroma1.it

In this paper, we propose a novel optimization algorithm for examination timetabling. It works by alternating two phases; one based on a stochastic local search and the other on a deterministic local search. The stochastic phase is fundamentally based on biased random sampling that iteratively constructs schedules according to a matrix whose entries are the probability with which exams can be assigned to time slots. The deterministic phase, instead, consists of assigning (according to a given ordering) each exam sequentially to the time slot that causes the lowest increase in the schedule penalty. After a schedule is constructed, swap operations are executed to improve performance. These two phases are coupled and made closely interactive by tunnelling information on what has happened during one phase to the successive ones. Moreover, the length of a phase and the parameter framework to be used in a new phase are automatically determined by a record of the process. We tested the proposed technique on known benchmarks, and a comparison with 17 algorithms drawn from the state of the art appears to show that our algorithm is able to improve best-known results. In particular, in reference to uncapacitated problems, i.e., the ones without room constraints, our algorithm bested the state of the art in 70% to 90% of the tested instances, while in capacitated problems with overnight conflicts (second-order conflicts), it was superior to all the other algorithms.

Subject classifications: scheduling; heuristic; deterministic algorithm; stochastic algorithm; biased random sampling; examination timetabling; local search.
History: Received November 2004; revision received March 2006; accepted March 2006.