# Metaheuristic with Cooperative Processes for the University Course Timetabling Problem
## 1 Introduction
They model the constraints with specification and validation tools, typical of the Unified Modeling Language (UML). They establish their solution strategy through two stages with a version of the tabu search, and a software to test their solution proposal is implemented. In [35], the authors solve a particular case of UCTP, focused on the assignment of teacher-course timetabling for an academic department considering the traditional restrictions of full-time and part-time teachers, academic profiles, availability of the courses and time. They present a linear integer programming model to solve the case of study and obtain the optimal solution with low computational effort through a classic branch and bound algorithm. In [36], a parallel genetic algorithm to solve UCTP is presented. The authors introduce some parallelization techniques using MPI libraries. They assume the master-slave management structure and, based on the number of processing nodes and the size of the population, the scalability of the system and the quality of the solution is estimated. In [37], the authors present a novel real application to maximize the use of resources. They developed a genetic algorithm which uses a simple weighted sum formula to manage conflicts and contemplate teacher preferences. Moreover, a composite aptitude function that considers the use of space is applied. For the tests, they used a large set of real data from the Faculty of Commerce of the University of Alexandria, in Egypt. In [38], a mixed integer linear programming model is present. A hybrid genetic algorithm (HGA) that includes a tabu search strategy is implemented to solve the model. For the analysis, the authors indicate how to map UCTP to the 3D container packaging problem. The tabu search algorithm is used to compare results with the hybrid genetic algorithm. They show that HGA obtains a better solution than the tabu search algorithm in a reasonable time. In [39], a hybrid algorithm based on parallel genetic algorithm and local search to solve UCTP is presented. They combine direct representation of timetabling with crossover operators to ensure that hard constraints are not violated to always obtain feasible solutions. The authors apply instances of [PERSON]'s competences and reproduce some of the known results in the state of the art. In [40], they propose to solve UCTP with a hybrid method based on genetic algorithms and tabu search. They propose a mixed linear programming model, which serves as a reference when defining the problem and the constraints to be considered. For the validation, they use real data for the scheduling of the academic periods, semester 1 of 2018 and semester 2 of 2018, for the academic program of Industrial Engineering, at the Industrial Santander University. The results are compared with the data of the timetabling courses manually obtained by the coordinator. The authors say it can take from hours to days to obtain the data manually, depending on the designer's ability, while their algorithm can obtain the results in a limited time. As a consequence of the boom that UCTP has had as a model for the assignment and obtaining of timetabling of university courses and the interest of obtaining feasible solutions, in 1995, the International Conference on the Practice and Theory of Automated Timetabling (PATAT) was born. It has been regularly held every 2 years, and its 13 th version will be carried out in the year 2022. PATAT also works as a forum for an international community of researchers and practitioners. It has also been supporting a range of competitions and challenges. PATAT is considered as the main conference for the EURO Working Group on Automated Timetabling (EWG-PATAT). Until the fourth conference, held in 2002, UCTP was the main theme and, from 2004, they extended to other topics on timetabling. In this work, a metaheuristic that addresses the university course timetabling problem (UCTP), which applies processes cooperation with collective communication and point-to-point communication, is presented.