A Mathematical Programming Model and Enhanced Simulated Annealing Algorithm for the School Timetabling Problem

Despite significant research efforts for School Timetabling Problem (STP) and other timetabling problems, an effective solution approach (model and algorithm) which provides boundless use and high quality solution has not been developed. Hence, this paper presents a novel solution approach for solving school timetabling problem which characterizes the problem-setting in the timetabling problem of the high school system in Nigeria. We developed a mixed integer linear programming model and meta-heuristic method - Enhanced Simulated Annealing (ESA) algorithm. Our method incorporates specific features of Simulated Annealing (SA) and Genetic Algorithms (GA) in order to solve the school timetabling problem. Both our solution approach and SA approach were implemented using Matrix Laboratory 8.6 software. In order to validate and demonstrate the performance of the developed solution approach, it was tested with the highly constrained school timetabling datasets provided by a Nigerian high school using constraints violation, simulation time and solution cost as evaluation metrics. Our developed solution approach is able to find optimal solution as it satisfied all the specified hard and soft constraints with average simulation time of 37.91 and 42.16 seconds and solution cost of 17.03 and 18.99, respectively, for JSS and SSS to the problem instance. A comparison with results obtained with SA approach shows that the developed solution approach produced optimal solution in smaller simulation time and solution cost, and has a great potential to solve school timetabling problems with satisfactory results. The developed ESA algorithm can be used for solving other related optimization problems.