Performance Analyses of Graph Heuristics and Selected Trajectory Metaheuristics on Examination Timetable Problem

Abstract

Examination timetabling problem is hard to solve due to its NP-hard nature, with a large number of constraints having to be accommodated. To deal with the problem effectually, frequently heuristics are used for constructing a feasible examination timetable, while meta-heuristics are applied for improving the solution quality. In this paper, we present the combination of graph heuristics and major trajectory metaheuristics for addressing both capacitated and un-capacitated examination timetabling problem. For constructing the feasible solution, six graph heuristics are used. They are largest degree (LD), largest weighted degree (LWD), largest enrolment degree (LE), and three hybrid heuristics with saturation degree (SD) such as SD-LD, SD-LE, and SD-LWD. Five trajectory algorithms comprising of tabu search (TS), simulated annealing (SA), late acceptance hill-climbing (LAHC), great deluge algorithm (GDA), and variable neighborhood search (VNS) are employed for improving the solution quality. Experiments have been tested on several instances of un-capacitated and capacitated benchmark datasets, which are Toronto and ITC2007 datasets, respectively. Experimental results indicate that hybrid graph heuristics produce the best initial solutions across both these benchmark problems. The study also reveals that, during improvement, GDA, SA, and LAHC can produce better quality solutions compared to TS and VNS for solving both benchmark datasets. Moreover, the performance of our method is comparable with other approaches in the scientific literature.

An introduction of preference based stepping ahead firefly algorithm for the uncapacitated examination timetabling

“…In order to confine the exploration to the feasible solution space, Leite et al (2018) developed a population-based algorithm that uses the threshold acceptance local search metaheuristic. Mandal & Kahar (2020) carried out a hybridization of two techniques, graph heuristics and major trajectory metaheuristics. This resulted in multiple algorithms exploited to gave best performance in capacitated and un-capacitated examination timetabling problems.…”

“…While, the only soft constraint is to spread examinations out as evenly as possible, where penalty is applied on the distribution. In the literature, exams ordering include random order (RO), largest degree (LD), largest weighted degree (LWD), largest penalty (LP), and saturation degree (SD) ( Burke, Qu & Soghier, 2014 ; Rahman et al, 2014 ; Mandal & Kahar, 2020 ). These are referred to as graph heuristics ordering strategies ( Carter, Laporte & Lee, 1996 ).…”