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

Ashis Kumar Mandal,M.N.M. Kahar

doi:10.52549/ijeei.v8i1.1660

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 feasible examination timetable while meta-heuristics are applied for improving the solution quality. This paper presents the performances of graph heuristics and major trajectory metaheuristics or S-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 heuristic 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 dataset respectively. Experimental results indicate that, in terms of construction of solution of datasets, hybridizing of SD produces the best initial solutions. 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 examination timetabling datasets.

Highlights

In the last few decades, the examination timetabling problem has been studied vastly in the artificial intelligence (AI) and operational research (OR) communities due to its complexity and practical significance in educational institutions [1]
To subsequent tables, the best results obtained from all the approaches for each problem instance are highlighted in the table with bold font, while ‘–‘ indicates no solution obtained
As it is observed from the table, saturation degree (SD)-largest degree (LD) achieved the best results on 5 instances, whereas SD-largest weighted degree (LWD) outperformed others on 4 instances

Summary

Introduction

In the last few decades, the examination timetabling problem has been studied vastly in the artificial intelligence (AI) and operational research (OR) communities due to its complexity and practical significance in educational institutions [1]. Academic institutions frequently face a considerable amount of challenges in the effective scheduling of their examinations with limited resources in a reasonable time. An examination timetabling is a system of allocating a set of examinations into a limited number of time slots and rooms in order to satisfy all hard constraints and to minimize the soft constraint violations as much as possible. Examination timetable problems can be categorized as capacitated and un-capacitated problems [4]. In an un-capacitated branch, room capacity is not considered. Room capacity is considered as a hard constraint. An example of an un-capacitated problem is Toronto datasets, whereas ITC2007 datasets are a capacitated problem [5]

Methods

Results

Conclusion