Roulette Wheel Graph Colouring for Solving Examination Timetabling Problems

This work presents a simple graph based heuristic that employs a roulette wheel selection mechanism for solving examination timetabling problems. We arrange exams in non-increasing order of the number of conflicts (degree) that they have with other exams. The difficulty of each exam to be scheduled is estimated based on the degree of exams in conflict. The degree determines the size of a segment in a roulette wheel, with a larger degree giving a larger segment. The roulette wheel selection mechanism selects an exam if the generated random number falls within the exam’s segment. This overcomes the problem of repeatedly choosing and scheduling the same sequence of exams. We utilise the proposed Roulette Wheel Graph Colouring heuristic on the uncapacitated Carter’s benchmark datasets. Results showed that this simple heuristic is capable of producing feasible solutions for all 13 instances.