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Conclusions

We have successfully applied simulated annealing to the difficult problem of academic scheduling for a large university. Feasible schedules were obtained for real data sets, including student preferences, without requiring enormous computational effort.

We found that simulated annealing was more effective than mean-field annealing for this problem, and that using a preprocessor to provide a good initial solution greatly improved the quality of the results. We used a fairly complex rule-based expert system for the preprocessor, however the type of preprocessor may not be crucial. Other fast heuristics could possibly be used, for example a graph coloring approach [23], or it may be possible to just utilize the schedule from the same semester for the previous year.

As expected, for the simulated annealing, adaptive cooling performed better than geometric cooling, and using reheating improved the results even further. The best results were obtained using simulated annealing with adaptive cooling and reheating as a function of cost, and with a rule-based preprocessor to provide a good initial solution. Using this method, and with careful selection of parameters and update steps, we were able to generate solutions to the class scheduling problem using real data for a large university. None of the other methods were able to provide a complete solution.

Mean-field annealing works well for small scheduling problems, but does not appear to scale well to large problems with many complex constraints. It is more difficult to tune the parameters, and use a preprocessor to take advantage of a good initial solution, than is simulated annealing. Because of the complexity and size of the Potts neural encoding in MFA, there seems to be no clear way of preserving the state of an initial configuration provided by a preprocessor when carrying out the Potts encoding.

Our main conclusion from this work is that simulated annealing, with a good cooling schedule, optimized parameters, carefully selected update moves, and a good initial solution provided by a preprocessor, can be used to solve the academic scheduling problem at a large university, including student preferences. Similar approaches should prove fruitful for other difficult scheduling problems.


next up previous
Next: Acknowledgments Up: No Title Previous: Experimental Results

Saleh Elmohamed
Tue Apr 29 19:08:49 EDT 1997