Automated Solution of a Highly Constrained School Timetabling Problem - Preliminary Results

Abstract

This work introduces a highly constrained school timetabling problem which was modeled from the requirements of a German high school. The concept for solving the problem uses a hybrid approach. On the one hand an evolutionary algorithm searches the space of all permutations of the events from which a timetable builder generates the school timetables. Those timetables are further optimized by local search using specific mutation operators. Thus, only valid (partial) timetables are generated which fulfill all hard constraints.

A Hidden Markov Model Approach to the Problem of Heuristic Selection in Hyper-Heuristics with a Case Study in High School Timetabling Problems

“…An initial population of feasible timetables are produced in an initial procedure and the GA is used to improve the quality of the generated population. A highly constrained school timetabling problem extracted from the requirements of a German high school was investigated by Bufé et al (2001) using a hybrid approach. An evolutionary algorithm combined with local search that uses specific mutation operators to optimise the given timetables was used to find feasible solutions.…”

A Standard Framework for Timetabling Problems

“…reference(Project) [1] firstChoice; reference(Project) [1] secondChoice; reference(Participant) [1] friends; } class Project extends Event { string signature; } firstChoice and secondChoice are containers holding the preferred and alternative projects of the participant. friends are the friends that should be assigned to courses taking place at the same time as the courses the participant has been assigned to.…”

“…class Staff extends Resource { string firstName; double workLoad; // target working hours // list of shifts the employee cannot be assigned to reference(Shift) [1] absent; } // end of class Staff Additional standard member variables, such as an array containing references to the assigned events, are automatically provided by the timetabling framework as described in Section 4.…”

“…For example, the German high school timetabling problem [1,15] has several entities such as classes or single students, teachers, subjects, lessons and rooms. All these entities have properties.…”

“…Furthermore, there exist many problem solving methods, which usually use the concepts of standard optimisation algorithms such as Backtracking [14] Evolutionary Algorithms [1,4,6,8] or Constraint Logic Programming [10,13].…”