Approach to the Timetabling Problems for Junior High Schools

Abstract

In this paper, the problem of automatically making timetables for junior high schools is approached. This is one of the combinatorial optimization problems, and is called the "school timetabling problem". In the case of a large school, solving the problem is very difficult because there are many constraints and much space to search for solutions. In a junior high school that has 24 classes, it takes about one week for four or five persons to make a school timetable. Three algorithms using tabu search are applied to the problem. In the first algorithm, the initial solution is created by allocating all subjects, and the solution progresses to a feasible solution using tabu search. In the second algorithm, all subjects are divided into three groups by the strength of the constraints. The first group is strong constraint, second group is intermediate and third group is weak. In the first stage, subjects in the first group are allocated to class using tabu search. The process is repeated to the third stage to make a feasible solution. In the third algorithm, subjects in the third group are divided into three grades and the same process as the second algorithm repeats itself to the fifth stage. The effectiveness of the second algorithm is presented using a numerical experiment for an existing school. Two parameters (number of class to search neighborhood solutions and weight to some estimation value of constraint) have a great influence on the search, and this is explained. In addition, the distribution of feasible solutions is described.