Approximate Scheduling of Final Exams at Memorial University

We describe one type of scheduling problem, that of scheduling final exams at Memorial University (MUN), a comprehensive Canadian university. It is well-known that the general scheduling problem is NP-complete [1]. Over the years, this problem has attracted a lot of attention and many different approaches have been tried in finding approximate solutions [2]. Here we propose an approximate solution to the problem at MUN.We use an evolutionary programming approach [4] implemented on a commercial grid computing environment; for our experiments we used a system including 1 master and 10 slaves. The grid algorithm, not accounting for the communication complexity, achieves optimal parallelization, i.e., reduces the time complexity of its serial implementation t(n), where n is the number of evolution steps, to t(n)/NumOfSlaves. The communication complexity on a network implementing a grid computing system may be the most important factor in the complexity of the algorithm. We alleviate the communication complexity using a feature of the software that allows for global virtual variables. These are variables that can be accessed by any of the computers on the grid and maintained by the master. On each slave we run 2 processes, since the slaves are based on dual core processors. We generate schedules better than those obtained by the current system in use. While the system is intended to be used at MUN, many universities impose very similar constrains on the scheduling of their exams. We expect the same approach to yield similar results to ours. keywords: grid computing, combinatorial optimization, evolutionary programming, NP-completeness, approximation algorithms, scheduling.