Adaptive large neighborhood search for the curriculum-based course timetabling problem

In curriculum-based course timetabling, lectures have to be assigned to periods and rooms, while avoiding overlaps between courses of the same curriculum. Taking into account the inherent complexity of the problem, a metaheuristic solution approach is proposed, more precisely an adaptive large neighborhood search, which is based on repetitively destroying and subsequently repairing relatively large parts of the solution. Several problem-specific operators are introduced. The proposed algorithm proves to be very effective for the curriculum-based course timetabling problem. In particular, it outperforms the best algorithms of the international timetabling competition in 2007 and finds five new best known solutions for benchmark instances of the competition.

[1]  Sara Ceschia,et al.  Design, engineering, and experimental analysis of a simulated annealing approach to the post-enrolment course timetabling problem , 2011, Comput. Oper. Res..

[2]  Tomás Müller,et al.  ITC2007 solver description: a hybrid approach , 2009, Ann. Oper. Res..

[3]  Gilbert Laporte,et al.  A Tabu Search Heuristic for the Vehicle Routing Problem , 1991 .

[4]  Edmund K. Burke,et al.  A branch-and-cut procedure for the Udine Course Timetabling problem , 2012, Ann. Oper. Res..

[5]  Matias Stidsen Sørensen,et al.  High School Timetabling: Modeling and solving a large number of cases in Denmark , 2013 .

[6]  Barry McCollum,et al.  The Second International Timetabling Competition (ITC-2007): Curriculum-based Course Timetabling (Track 3) — preliminary presentation — , 2007 .

[7]  G. Dueck,et al.  Record Breaking Optimization Results Using the Ruin and Recreate Principle , 2000 .

[8]  Shu-Cherng Fang,et al.  An Electromagnetism-like Mechanism for Global Optimization , 2003, J. Glob. Optim..

[9]  Marco E. Lübbecke,et al.  Curriculum based course timetabling: new solutions to Udine benchmark instances , 2012, Ann. Oper. Res..

[10]  Andrea Schaerf,et al.  Local search techniques for large high school timetabling problems , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[11]  Jin-Kao Hao,et al.  Adaptive Tabu Search for course timetabling , 2010, Eur. J. Oper. Res..

[12]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[13]  Thomas R. Stidsen,et al.  The consultation timetabling problem at Danish high schools , 2013, J. Heuristics.

[14]  Luca Di Gaspero,et al.  Benchmarking curriculum-based course timetabling: formulations, data formats, instances, validation, visualization, and results , 2012, Ann. Oper. Res..

[15]  Paul Shaw,et al.  Using Constraint Programming and Local Search Methods to Solve Vehicle Routing Problems , 1998, CP.

[16]  Daniel Brélaz,et al.  New methods to color the vertices of a graph , 1979, CACM.

[17]  Salwani Abdullah,et al.  A hybrid metaheuristic approach to the university course timetabling problem , 2010, Journal of Heuristics.

[18]  Gilbert Laporte,et al.  Examination Timetabling: Algorithmic Strategies and Applications , 1994 .

[19]  Simon Kristiansen,et al.  International Timetabling Competition 2011: An Adaptive Large Neighborhood Search algorithm , 2012 .

[20]  D. de Werra,et al.  An introduction to timetabling , 1985 .

[21]  Martin Henz,et al.  QuikFix A Repair-based Timetable Solver , 2008 .

[22]  Edmund K. Burke,et al.  The Second International Timetabling Competition : Examination Timetabling Track , 2007 .

[23]  Moshe Dror,et al.  A tabu-based large neighbourhood search methodology for the capacitated examination timetabling problem , 2007, J. Oper. Res. Soc..

[24]  Edmund K. Burke,et al.  Decomposition, reformulation, and diving in university course timetabling , 2009, Comput. Oper. Res..

[25]  Ben Paechter,et al.  Setting the Research Agenda in Automated Timetabling: The Second International Timetabling Competition , 2010, INFORMS J. Comput..

[26]  Luca Di Gaspero,et al.  Multi-neighbourhood Local Search with Application to Course Timetabling , 2002, PATAT.

[27]  Andrea Schaerf,et al.  A Survey of Automated Timetabling , 1999, Artificial Intelligence Review.

[28]  David Pisinger,et al.  A hybrid adaptive large neighborhood search heuristic for lot-sizing with setup times , 2012, Eur. J. Oper. Res..

[29]  Abraham P. Punnen,et al.  A survey of very large-scale neighborhood search techniques , 2002, Discret. Appl. Math..

[30]  Moshe Dror,et al.  Investigating Ahuja–Orlin’s large neighbourhood search approach for examination timetabling , 2007, OR Spectr..

[31]  Barry McCollum,et al.  Post enrolment based course timetabling: a description ofthe problem model used for track two of the secondInternational Timetabling Competition , 2007 .

[32]  Francisco Herrera,et al.  A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms , 2011, Swarm Evol. Comput..

[33]  D. Landa-Silva,et al.  Great deluge with non-linear decay rate for solving course timetabling problems , 2008, 2008 4th International IEEE Conference Intelligent Systems.

[34]  Rhyd Lewis,et al.  A survey of metaheuristic-based techniques for University Timetabling problems , 2007, OR Spectr..

[35]  Luca Di Gaspero,et al.  Design and statistical analysis of a hybrid local search algorithm for course timetabling , 2012, J. Sched..

[36]  David Pisinger,et al.  An Adaptive Large Neighborhood Search Heuristic for the Pickup and Delivery Problem with Time Windows , 2006, Transp. Sci..

[37]  Pierre Hansen,et al.  Variable neighborhood search , 1997, Eur. J. Oper. Res..

[38]  Paolo Toth,et al.  An overview of curriculum-based course timetabling , 2015 .

[39]  Salwani Abdullah,et al.  On the use of multi neighbourhood structures within a Tabu-based memetic approach to university timetabling problems , 2012, Inf. Sci..

[40]  Edmund K. Burke,et al.  A survey of search methodologies and automated system development for examination timetabling , 2009, J. Sched..

[41]  Laurent Flindt Muller,et al.  An Adaptive Large Neighborhood Search Algorithm for the Resource-constrained Project Scheduling Problem , 2009 .

[42]  Sanja Petrovic,et al.  A time-predefined approach to course timetabling , 2003 .

[43]  G. Dueck.  New optimization heuristics , 1993 .

[44]  Jonathan M. Thompson,et al.  Analysing the effects of solution space connectivity with an effective metaheuristic for the course timetabling problem , 2015, Eur. J. Oper. Res..

[45]  David Pisinger,et al.  A general heuristic for vehicle routing problems , 2007, Comput. Oper. Res..

[46]  David C. Wood.  A system for computing university examination timetables , 1968, Comput. J..

[47]  Alon Itai,et al.  On the Complexity of Timetable and Multicommodity Flow Problems , 1976, SIAM J. Comput..

[48]  Helena Ramalhinho Dias Lourenço,et al.  Iterated Local Search , 2001, Handbook of Metaheuristics.

[49]  Sara Ceschia,et al.  Feature-based tuning of simulated annealing applied to the curriculum-based course timetabling problem , 2014, Comput. Oper. Res..

[50]  D. J. A. Welsh,et al.  An upper bound for the chromatic number of a graph and its application to timetabling problems , 1967, Comput. J..

[51]  Jeffrey H. Kingston,et al.  The Complexity of Timetable Construction Problems , 1995, PATAT.

[52]  Fred W. Glover,et al.  Tabu Search , 1997, Handbook of Heuristics.

[53]  David Connolly,et al.  General Purpose Simulated Annealing , 1992 .

[54]  Sol Broder,et al.  Final examination scheduling , 1964, Commun. ACM.