Generating an optimal timetabling for multi-departments common lecturers using hybrid fuzzy and clustering algorithms

University course timetabling is a NP-hard problem that be performed for each semester frequently. In this paper, we use a two-step algorithm for timetabling of common lecturers among departments. In the first step, we use a fuzzy multi-criteria decision-making comparison and local search algorithms with seven neighborhood structures and random iteration. It means that we use a fuzzy multi-criteria comparison algorithm to eliminate the ambiguities and soft constraints of common lecturers among departments. In addition, we apply the local search algorithm with seven neighboring structures to avoid trapping into local optima and improve the fuzzy multi-criteria comparison over the preferences and soft constraints of lecturers. In the second step, the common lecturers’ timetable generated in the first step by the clustering approach (k-means, fuzzy c-means and funnel shape) is clustered based on the preferences and soft constraints of common lecturers among departments. Now, our common lecturers prepared by the clustering algorithms are mapped to the traversed free resources according to the paper’s aims: (1) descending satisfaction of preferences and soft constraints of common lecturers among departments and (2) minimizing the loss of extra resources of each faculty, so that an optimal instance of our common lecturers timetabling is generated among departments. The applied datasets are in terms of satisfying the scheduling requirements in the real world for multi-departments of Islamic Azad University of Ahar branch.