A Multiobjective Optimisation Technique for Exam Timetabling Based on Trajectories

University examination timetabling problems comprise arranging exams in the given number of timeslots through the examination sessions. The primary objective of this process is avoiding of students ' clashes (i.e. no one student should take two exams simultaneously). This requirement is generally considered as a hard constraint and should be obligatory satisfied in a feasible timetable. However, the number of other restrictions and regulations, which depend on a particular institution, should be also taken into account while solving examination timetabling problems. Some of them are also considered as hard constraints, while other constraints are soft, i.e. they cannot be completely satisfied, and therefore their violations should be minimised. The soft constraints usually have different importance for the timetable officer (decision maker). They are generally incompatible and often conflicting with each other. Timetabling problems with various soft constraints typically have no single supreme solution. Formally, a number of solutions can be considered as optimal. The decision maker’s goal is to obtain a desirable one in accordance to his/her preferences. This can be done by grouping the soft constraints into several objectives, where objectives measure the number of violations of the soft constraints, and applying an appropriate multiobjective optimisation technique. Those technique