Nested Partitions Method to Solving Examination Timetabling Problem

In this thesis, the examination timetabling problem is studied. A hybrid optimization method based on the Nested Partitions Method (NPM) is proposed where NPM is an optimization framework combining with heuristic rule and linear programming. By an analysis of the real problem, a mathematical model is established and a heuristic rule is used to generate an initial solution on which partitioning of the feasible region is followed. According to the sampling results, the solution space is further partitioned into different subregions and then the optimal region is gradually reduced. It is also necessary to apply a backtracking strategy to withdraw from the current promising region when the promising index of its surrounding region is better than those of its subregions. The test results show that when the data size is large, NPM saves large amount of computing time with the same results from the pure linear programming and performs more efficiently.