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## Nova scientia

*versión On-line* ISSN 2007-0705

#### Resumen

SANCHEZ-PARTIDA, Diana; BAQUELA, Enrique Gabriel; MORA-VARGAS, Jaime y SMITH, Neale R.. Case study: Simulated annealing for improving the educational timetable.* Nova scientia* [online]. 2016, vol.8, n.17, pp.340-360.
ISSN 2007-0705.

Introduction:

On occasions, Combinatorial Optimization Problems (COP), like the University Course Timetabling Problem (CTTP), can be solved using Operational Research (OR) techniques; however, when the problem increases in size, finding a solution becomes more complex. This type of problem is NP-hard, requiring procedures like metaheuristic methods in order to solve the problem. This paper confronts a real world situation in Mexico concerning the Curriculum-Based Timetabling Problem (CB-CTT). Each institution have their own operationals rules due to the modeling of the problema is unique because preserve their own characteristics. First, as part of the contribution to the solution of the problem, it was implemented a Mediation Software (MS) in order to organize the raw data and eliminate a hard constraint related to curricula. Subsequently, the problem handle here was split into five instances in accordance to the courses that share the same physical space, which was solved using a typical Simulated Annealing (SA) metaheuristic. In addition, The problem was satisfactorily solved, assigning 9620 lectures in 174.5 hours approximatly, providing a solution without partitioning the problem into two subproblems, impacting positivly reducing the labor time, and providing a feasible and without errors educational timetable to the whole university.

Method:

The Simulated Annealing (SA) algorithm is a meta-heuristic search for global optimization problems; the overall objective of such algorithms is to find a good approximation to the optimal value of a function in a large search space. This value is called "global or local optimum".The name and inspiration comes from the process of annealing the steel and ceramics, a technique that involves heating and then slowly cooling the material to vary its physical properties. The heat causes the atoms increase their energy and can thus move from their initial (a local minimum energy) positions; slow cooling gives them more likely to recrystallize in configurations with lower energy than the initial (minimum overall) .The method was independently described by Scott Kirkpatrick, C. Daniel Gelatt and Mario P. Vecchi at 1983.

Results:

Concluding this work, is shown that is confronted a large real CB-CTT problem with 2507 courses conform by 1, 2, 3, 4, 5, 6, 7, or 8 lectures or hours, totalizing 9620 lectures; being able to assign into 316 rooms with different capacities, and also satisfying all the requested of 2178 professors and 1668 groups.

Discussion or Conclusion:

In this research were developed various instances, where 3 of 5 are considered by the research community like large instances, and solved with SA Algorithm, regarding all feasible solutions. Thereby the metaheuristic methods are relatively good depending on the instance, and for this institution can offer a good solution.

**Palabras llave
:
**Timetabling problem; combinatorial optimization simulated annealing metaheuristic; mediation software.