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Revista de Matemática Teoría y Aplicaciones
Print version ISSN 1409-2433
Rev. Mat vol.22 n.1 San José Jan./Jun. 2015
Cognitive rhythms and evolutionary algorithms in university timetables scheduling
Ritmos cognitivos y algoritmos evolutivos en la programación de horarios universitarios
Ritmos cognitivos y algoritmos evolutivos en la programación de horarios universitarios
Abstract
The main purpose of this research is to design a methodology based on evolutionary algorithms to university timetable scheduling. This methodology will consider the students' cognitive rhythms, which establish that teaching certain subjects in specific time intervals is much better than other techniques. This project takes place in three phases. First of all, there is a description of the different tech¬niques used to solve this problem. Then, a new methodology based on cognitive rhythms and evolutionary algorithms is proposed, and finally, different methodologies are compared to determine the best. It is concluded that evolutionary algorithms are more efficient than other techniques in the university timetable scheduling. Future lines of research will determine the impact of these techniques within the students' learning process.
Keywords: scheduling, university timetables, genetic algorithms, fitness.
Resumen
El propósito de esta investigación es diseñar una metodología basada en algoritmos evolutivos para la programacion de horarios universitarios. Esta metodología considerara los ritmos cognitivos de los estudiantes, los cuales establecen que enseñar algunas materias en intervalos de tiempo específicos es mejor que otras técnicas. Este proyecto es desarrollado en tres fases. Primero se realiza una descripción de las diferentes tíecnicas empleadas para solucionar este problema. Posteriormente una nueva metodología basada en ritmos cognitivos y algoritmos evolutivos es propuesta. Finalmente diferentes metodologías son comparadas para determinar la mejor. Se concluye que los algoritmos evolutivos son más eficientes que otras tecnicas en la programaciíon de horarios universitarios. Futuras líneas de investigación determinarían el impacto de estas tíecnicas en los procesos de aprendizaje de los estudiantes.
Palabras clave: programación; horarios universitarios; algoritmos genéticos; función objetivo.
Mathematics Subject Classification: 97P30.
Ver contenido en pdf.
References
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[2] Burke, E.K.; Petrovic, S. (2002) "Recent research directions in automated timetabling", European Journal of Operational Research 140(2): 266-280. [ Links ]
[3] Burke, E.K.; Marecek, J.; Parkes, A.J.; Rudova H. (2010) "Decomposition, reformulation, and diving in university course timetabling", Computers & Operations Research 37(3): 582-597. [ Links ]
[4] Burke, E.K.; Kendall, G.; Misir, M.; Ozcan, E. (2012) "MonteCarlo hyper-heuristics for examination timetabling", Annals of Operations Research 196(1): 73-90. [ Links ]
[5] Cacchiani, V.; Caprara, A.; Roberti, R.; Toth, P. (2013) "A new lower bound for curriculum-based course timetabling", Computers & Operations Research 40(10): 2466-2477. [ Links ]
[6] Castiñeiras, I.; Saenz-Perez, F. (2013) "Applying CP(F D), CLP(F D) and CFLP(F D) to a Real-life Employee Timetabling Problem", Procedia Computer Science 18: 531-540. [ Links ]
[7] Castrillón, O.D. (2013) "Planning University Schedules Using Evolutionary Algorithms and Cognitive Rhythms", EIIC-2013 2nd Electronic International Interdisciplinary Conference 2013, Budapest virtual conference: 448-450. [ Links ]
[8] Castrillón, O.D. (2014) "Combinación entre un Algoritmo Genético y Aleatorio para Programación de Horarios Universitarios Basado en Ritmos Cognitivos", Información Tecnológica 25(4): 51-62. [ Links ]
[9] Daskalaki, S.; Birbas, T.; Housos, E. (2004) "An integer programming formulation for a case study in university timetabling", European Journal of Operational Research 153(1): 117-135. [ Links ]
[10] De Causmaecker, P.; Demeester, P.; Vanden Berghe, G. (2009) "A decomposed metaheuristic approach for a real-world university timetabling problem", European Journal of Operational Research 195(1): 307-318. [ Links ]
[11] Dimopoulou, M.; Miliotis, P. (2001) "Implementation of a university course and examination timetabling system", European Journal of Operational Research 130(1): 202-213. [ Links ]
[12] Dimopoulou, M.; Miliotis, P. (2004) "An automated university course timetabling system developed in a distributed environment: A case study", European Journal of Operational Research 153(1): 136-147. [ Links ]
[13] Fahrion, R.; Dollansky, G. (1992) "Construction of university faculty timetables using logic programming techniques", Discrete Applied Mathematics 35(3): 221-236. [ Links ]
[14] Ferland, J.A.; Lavoie, A. (1992) "Exchanges procedures for timetabling problems", Discrete Applied Mathematics 35(3): 237-253. [ Links ]
[15] Foulds, L.R.; Johnson, D.G. (2000) "SlotManager: a microcomputer-based decision support system for university timetabling", Decision Support Systems 27(4): 367-381. [ Links ]
[16] Goerigk, M.; Obel, A. (2013) "Improving the modulo simplex algorithm for large-scale periodic timetabling", Computers & Operations Research 40(5): 1363-1370. [ Links ]
[17] Head, C.; Shaban, S. (2007) "A heuristic approach to simultaneous course/student timetabling", Computers & Operations Research 34(4): 919-933. [ Links ]
18 Hernández, R.; Miranda, J.; Rey, P.A. (2008) "Programación de Horarios de Clases y Asignación de Salas para la Facultad de Ingeniería de la Universidad Diego Portales Mediante un Enfoque de programación Entera", Revista Ingeniería de Sistemas 22: 121-141. [ Links ]
[19] Hertz, A. (1992). "Finding a feasible course schedule using Tabu search", Discrete Applied Mathematics 35(3): 255-270. [ Links ]
[20] Kahar, M.; Kendall, G. (2010) "The examination timetabling problem at University Malaysia Pahang: Comparison of a constructive heuristic with an existing software solution", European Journal of Operational Research 207(2): 557-565. [ Links ]
[21] Lu, Z.; Hao, J.-K. (2010) "Adaptive Tabu Search for course timetabling", European Journal of Operational Research 200(1) 235-244. [ Links ]
[22] Martínez, H.; Camargo, C.; Reyes, M. (2004) Ritmos Cognitivos en la Escuela. Universidad Pedagógica Nacional, Bogotá [ Links ].
[23] McCollum, B.; McMullan, P.; Burke, E.K.; Parkes, A.J.; Qu, R. (2008) "A New Model for Automated Examination Timetabling", School of Computer Science, University of Nottingham: 1-24. [ Links ]
[24] Mejía, J.; Paternina, C. (2010) "Asignación de horarios de clases Universitarias Mediante Algoritmos Evolutivos", Educación e Ingeniería 5(9): 140-149. [ Links ]
[25] Mejía, J.C. (2008) Asignación de Horarios de Clases Universitarias Mediante Algoritmos Evolutivos. Universidad del Norte, Barranquilla. [ Links ]
[26] MirHassani, S.A. (2006) "A computational approach to enhancing course timetabling with integer programming". Applied Mathematics and Computation 175(1): 814-822. [ Links ]
[27] Ozcan, E.; Parkes, A.J.; Alkan, A. (2012) "The Interleaved Constructive Memetic Algorithm and its application to timetabling", Computers & Operations Research 39(10): 2310-2322. [ Links ]
[28] Pillay, N.; Banzhaf, W. (2009) "A study of heuristic combinations for hyper-heuristic systems for the uncapacitated examina-tion timetabling problem", European Journal of Operational Research 197(2): 482-491. [ Links ]
[29] Pillay, N.; Banzhaf, W. (2010) "An informed genetic algorithm for the examination timetabling problem", Applied Soft Computing 10(2): 457-467. [ Links ]
[30] Rahman, S.; Bargiela, A.; Burke, E.; Ouzcan. E.; McCollum, B.; Mc-Mullan, P. (2014) "Adaptive linear combination of heuristic orderings in constructing examination timetables", European Journal of Operational Research 232(2): 287-297. [ Links ]
[31] Soza, C.; Landa, R.; Riff, M.C.; Coello, C.A. (2011) "Solving timetabling problems using a cultural algorithm", Applied Soft Computing 11(1): 337-344. [ Links ]
32 Suarez, V.; Castrillón, O. (2011) "Diseño de una metodología basada en técnicas inteligentes para la distribución de procesos académicos en ambientes de trabajo Job Shop", XV Congreso de Ingeniería de la Organización, Universidad Politécnica de Cartagena, España: 285-289. [ Links ]
[33] Suarez, V. (2012) Asignación de horarios de clase en instituciones de educación básica y media de acuerdo a ritmos de eficiencia cognitiva. Tesis de Maestría, Universidad Nacional de Colombia. [ Links ]
34 Suarez, V.; Castrillón, O.; Guerrero, A. (2013) "Asignación de horarios de clase basado en los ritmos de aprendizaje de los estudiantes usando un algoritmo genético", Ingeniería y Ciencia 9(17): 77-95. [ Links ]
35 Suarez, V.; Guerrero. A.; Castrillón, O. (2013) "Programacióon de Horarios Escolares basados en Ritmos Cognitivos usando un Algoritmo Genético de Clasificación No-dominada, NSGA-II", Informacion Tecnológica 24(1): 103-113. [ Links ]
[36] Tassopoulos, I.X.; Beligiannis, G.N. (2012a) "A hybrid particle swarm optimization based algorithm for high school timetabling problems", Applied Soft Computing 12(11), 3472-3489. [ Links ]
[37] Tassopoulos, I.X.; Beligiannis, G.N. (2012b). "Solving effectively the school timetabling problem using particle swarm optimization", Expert Systems with Applications 39(5): 6029-6040. [ Links ]
[38] Valentinuzzi, V.; Fontenele, J. (2008) "Los ritmos biológicos y el aprendizaje", Ingenierías XI(40): 41-46. [ Links ]
[39] Valouxis, C.; Housos, E. (2003) "Constraint programming approach for school timetabling", Computers & Operations Research 30(10): 1555-1572. [ Links ]
[40] Van den Broek, J.; Hurkens, C.; Woeginger, G. (2006) "Timetabling problems at the TU Eindhoven", Electronic Notes in Discrete Mathematics 25: 27-28. [ Links ]
[2] Burke, E.K.; Petrovic, S. (2002) "Recent research directions in automated timetabling", European Journal of Operational Research 140(2): 266-280. [ Links ]
[3] Burke, E.K.; Marecek, J.; Parkes, A.J.; Rudova H. (2010) "Decomposition, reformulation, and diving in university course timetabling", Computers & Operations Research 37(3): 582-597. [ Links ]
[4] Burke, E.K.; Kendall, G.; Misir, M.; Ozcan, E. (2012) "MonteCarlo hyper-heuristics for examination timetabling", Annals of Operations Research 196(1): 73-90. [ Links ]
[5] Cacchiani, V.; Caprara, A.; Roberti, R.; Toth, P. (2013) "A new lower bound for curriculum-based course timetabling", Computers & Operations Research 40(10): 2466-2477. [ Links ]
[6] Castiñeiras, I.; Saenz-Perez, F. (2013) "Applying CP(F D), CLP(F D) and CFLP(F D) to a Real-life Employee Timetabling Problem", Procedia Computer Science 18: 531-540. [ Links ]
[7] Castrillón, O.D. (2013) "Planning University Schedules Using Evolutionary Algorithms and Cognitive Rhythms", EIIC-2013 2nd Electronic International Interdisciplinary Conference 2013, Budapest virtual conference: 448-450. [ Links ]
[8] Castrillón, O.D. (2014) "Combinación entre un Algoritmo Genético y Aleatorio para Programación de Horarios Universitarios Basado en Ritmos Cognitivos", Información Tecnológica 25(4): 51-62. [ Links ]
[9] Daskalaki, S.; Birbas, T.; Housos, E. (2004) "An integer programming formulation for a case study in university timetabling", European Journal of Operational Research 153(1): 117-135. [ Links ]
[10] De Causmaecker, P.; Demeester, P.; Vanden Berghe, G. (2009) "A decomposed metaheuristic approach for a real-world university timetabling problem", European Journal of Operational Research 195(1): 307-318. [ Links ]
[11] Dimopoulou, M.; Miliotis, P. (2001) "Implementation of a university course and examination timetabling system", European Journal of Operational Research 130(1): 202-213. [ Links ]
[12] Dimopoulou, M.; Miliotis, P. (2004) "An automated university course timetabling system developed in a distributed environment: A case study", European Journal of Operational Research 153(1): 136-147. [ Links ]
[13] Fahrion, R.; Dollansky, G. (1992) "Construction of university faculty timetables using logic programming techniques", Discrete Applied Mathematics 35(3): 221-236. [ Links ]
[14] Ferland, J.A.; Lavoie, A. (1992) "Exchanges procedures for timetabling problems", Discrete Applied Mathematics 35(3): 237-253. [ Links ]
[15] Foulds, L.R.; Johnson, D.G. (2000) "SlotManager: a microcomputer-based decision support system for university timetabling", Decision Support Systems 27(4): 367-381. [ Links ]
[16] Goerigk, M.; Obel, A. (2013) "Improving the modulo simplex algorithm for large-scale periodic timetabling", Computers & Operations Research 40(5): 1363-1370. [ Links ]
[17] Head, C.; Shaban, S. (2007) "A heuristic approach to simultaneous course/student timetabling", Computers & Operations Research 34(4): 919-933. [ Links ]
18 Hernández, R.; Miranda, J.; Rey, P.A. (2008) "Programación de Horarios de Clases y Asignación de Salas para la Facultad de Ingeniería de la Universidad Diego Portales Mediante un Enfoque de programación Entera", Revista Ingeniería de Sistemas 22: 121-141. [ Links ]
[19] Hertz, A. (1992). "Finding a feasible course schedule using Tabu search", Discrete Applied Mathematics 35(3): 255-270. [ Links ]
[20] Kahar, M.; Kendall, G. (2010) "The examination timetabling problem at University Malaysia Pahang: Comparison of a constructive heuristic with an existing software solution", European Journal of Operational Research 207(2): 557-565. [ Links ]
[21] Lu, Z.; Hao, J.-K. (2010) "Adaptive Tabu Search for course timetabling", European Journal of Operational Research 200(1) 235-244. [ Links ]
[22] Martínez, H.; Camargo, C.; Reyes, M. (2004) Ritmos Cognitivos en la Escuela. Universidad Pedagógica Nacional, Bogotá [ Links ].
[23] McCollum, B.; McMullan, P.; Burke, E.K.; Parkes, A.J.; Qu, R. (2008) "A New Model for Automated Examination Timetabling", School of Computer Science, University of Nottingham: 1-24. [ Links ]
[24] Mejía, J.; Paternina, C. (2010) "Asignación de horarios de clases Universitarias Mediante Algoritmos Evolutivos", Educación e Ingeniería 5(9): 140-149. [ Links ]
[25] Mejía, J.C. (2008) Asignación de Horarios de Clases Universitarias Mediante Algoritmos Evolutivos. Universidad del Norte, Barranquilla. [ Links ]
[26] MirHassani, S.A. (2006) "A computational approach to enhancing course timetabling with integer programming". Applied Mathematics and Computation 175(1): 814-822. [ Links ]
[27] Ozcan, E.; Parkes, A.J.; Alkan, A. (2012) "The Interleaved Constructive Memetic Algorithm and its application to timetabling", Computers & Operations Research 39(10): 2310-2322. [ Links ]
[28] Pillay, N.; Banzhaf, W. (2009) "A study of heuristic combinations for hyper-heuristic systems for the uncapacitated examina-tion timetabling problem", European Journal of Operational Research 197(2): 482-491. [ Links ]
[29] Pillay, N.; Banzhaf, W. (2010) "An informed genetic algorithm for the examination timetabling problem", Applied Soft Computing 10(2): 457-467. [ Links ]
[30] Rahman, S.; Bargiela, A.; Burke, E.; Ouzcan. E.; McCollum, B.; Mc-Mullan, P. (2014) "Adaptive linear combination of heuristic orderings in constructing examination timetables", European Journal of Operational Research 232(2): 287-297. [ Links ]
[31] Soza, C.; Landa, R.; Riff, M.C.; Coello, C.A. (2011) "Solving timetabling problems using a cultural algorithm", Applied Soft Computing 11(1): 337-344. [ Links ]
32 Suarez, V.; Castrillón, O. (2011) "Diseño de una metodología basada en técnicas inteligentes para la distribución de procesos académicos en ambientes de trabajo Job Shop", XV Congreso de Ingeniería de la Organización, Universidad Politécnica de Cartagena, España: 285-289. [ Links ]
[33] Suarez, V. (2012) Asignación de horarios de clase en instituciones de educación básica y media de acuerdo a ritmos de eficiencia cognitiva. Tesis de Maestría, Universidad Nacional de Colombia. [ Links ]
34 Suarez, V.; Castrillón, O.; Guerrero, A. (2013) "Asignación de horarios de clase basado en los ritmos de aprendizaje de los estudiantes usando un algoritmo genético", Ingeniería y Ciencia 9(17): 77-95. [ Links ]
35 Suarez, V.; Guerrero. A.; Castrillón, O. (2013) "Programacióon de Horarios Escolares basados en Ritmos Cognitivos usando un Algoritmo Genético de Clasificación No-dominada, NSGA-II", Informacion Tecnológica 24(1): 103-113. [ Links ]
[36] Tassopoulos, I.X.; Beligiannis, G.N. (2012a) "A hybrid particle swarm optimization based algorithm for high school timetabling problems", Applied Soft Computing 12(11), 3472-3489. [ Links ]
[37] Tassopoulos, I.X.; Beligiannis, G.N. (2012b). "Solving effectively the school timetabling problem using particle swarm optimization", Expert Systems with Applications 39(5): 6029-6040. [ Links ]
[38] Valentinuzzi, V.; Fontenele, J. (2008) "Los ritmos biológicos y el aprendizaje", Ingenierías XI(40): 41-46. [ Links ]
[39] Valouxis, C.; Housos, E. (2003) "Constraint programming approach for school timetabling", Computers & Operations Research 30(10): 1555-1572. [ Links ]
[40] Van den Broek, J.; Hurkens, C.; Woeginger, G. (2006) "Timetabling problems at the TU Eindhoven", Electronic Notes in Discrete Mathematics 25: 27-28. [ Links ]
*Universidad Nacional de Colombia—Sede Manizales— Facultad de Ingeniería y Arquitectura—Departamento de Ingeniería Industrial—GTA en Innovación y Desarrollo Tecnológico, Campus la Nubia—Manizales—Codigo Postal 170001, Colombia. E-mail: odcastrillong@unal.edu.co
Received: 25/Feb/2014; Revised: 6/Aug/2014; Accepted: 28/Aug/2014