A multiobjective framework for heavily constrained examination timetabling problems

University examination timetabling is a challenging set partitioning problem that comes in many variations, and real world applications usually carry multiple constraints and require the simultaneous optimization of several (often conflicting) objectives. This paper presents a multiobjective framework capable of solving heavily constrained timetabling problems. In this prototype study, we focus on the two objectives: minimizing timetable length while simultaneously optimizing the spread of examinations for individual students. Candidate solutions are presented to a multiobjective memetic algorithm as orderings of examinations, and a greedy algorithm is used to construct violation free timetables from permutation sequences of exams. The role of the multiobjective algorithm is to iteratively improve a population of orderings, with respect to the given objectives, using various mutation and reordering heuristics.

[1]  Krzysztof R. Apt,et al.  Principles of constraint programming , 2003 .

[2]  Edmund K. Burke,et al.  A Memetic Algorithm for University Exam Timetabling , 1995, PATAT.

[3]  Edmund K. Burke,et al.  Examination Timetabling in British Universities: A Survey , 1995, PATAT.

[4]  David W. Matula,et al.  GRAPH COLORING ALGORITHMS , 1972 .

[5]  Sanja Petrovic,et al.  A Novel Similarity Measure for Heuristic Selection in Examination Timetabling , 2004, PATAT.

[6]  Edmund K. Burke,et al.  Selected papers from the First International Conference on Practice and Theory of Automated Timetabling , 1995 .

[7]  Kathryn A. Dowsland,et al.  A robust simulated annealing based examination timetabling system , 1998, Comput. Oper. Res..

[8]  Kay Chen Tan,et al.  Solving the Exam Timetabling Problem via a Multi-Objective Evolutionary Algorithm - A More General Approach , 2007, 2007 IEEE Symposium on Computational Intelligence in Scheduling.

[9]  Gilbert Laporte,et al.  Recent Developments in Practical Examination Timetabling , 1995, PATAT.

[10]  Feng Luo,et al.  Exploring the k-colorable landscape with Iterated Greedy , 1993, Cliques, Coloring, and Satisfiability.

[11]  Sanja Petrovic,et al.  Hybrid variable neighbourhood approaches to university exam timetabling , 2010, Eur. J. Oper. Res..

[12]  Robert Sabourin,et al.  A hybrid MOEA for the capacitated exam proximity problem , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

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

[14]  Jonathan M. Thompson,et al.  GRASPing the Examination Scheduling Problem , 2002, PATAT.

[15]  Sanja Petrovic,et al.  Recent research directions in automated timetabling , 2002, Eur. J. Oper. Res..

[16]  Christine L. Mumford.  Simple Population Replacement Strategies for a Steady-State Multi-objective Evolutionary Algorithm , 2004, GECCO.

[17]  Giuseppe F. Italiano,et al.  New Algorithms for Examination Timetabling , 2000, WAE.

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

[19]  Sanja Petrovic,et al.  A Multicriteria Approach to Examination Timetabling , 2000, PATAT.

[20]  Edward P. K. Tsang,et al.  Foundations of constraint satisfaction , 1993, Computation in cognitive science.

[21]  Edmund K. Burke,et al.  Parallel Problem Solving from Nature - PPSN IX: 9th International Conference, Reykjavik, Iceland, September 9-13, 2006, Proceedings , 2006, PPSN.

[22]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[23]  Gilbert Laporte,et al.  Examination timetabling by computer , 1982, Comput. Oper. Res..

[24]  Michael W. Carter,et al.  OR Practice - A Survey of Practical Applications of Examination Timetabling Algorithms , 1986, Oper. Res..

[25]  Hishammuddin Asmuni,et al.  Fuzzy Multiple Ordering Criteria for Examination Timetabling , 2004 .

[26]  Sanja Petrovic,et al.  A graph-based hyper-heuristic for educational timetabling problems , 2007, Eur. J. Oper. Res..

[27]  Ronald C. Read,et al.  Graph theory and computing , 1972 .

[28]  Edmund K. Burke,et al.  Solving Examination Timetabling Problems through Adaption of Heuristic Orderings , 2004, Ann. Oper. Res..

[29]  Edmund K. Burke,et al.  A multistage evolutionary algorithm for the timetable problem , 1999, IEEE Trans. Evol. Comput..

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

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

[32]  Christine L. Mumford.  New Order-Based Crossovers for the Graph Coloring Problem , 2006, PPSN.

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

[34]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[35]  Christine L. Mumford.  An Order Based Evolutionary Approach to Dual Objective Examination Timetabling , 2007, 2007 IEEE Symposium on Computational Intelligence in Scheduling.

[36]  Peter J. Stuckey,et al.  A Hybrid Algorithm for the Examination Timetabling Problem , 2002, PATAT.

[37]  Robert Sabourin,et al.  A Hybrid Multi-objective Evolutionary Algorithm for the Uncapacitated Exam Proximity Problem , 2004, PATAT.

[38]  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..

[39]  C. L. Valenzuela.  A simple evolutionary algorithm for multi-objective optimization (SEAMO) , 2002, Proceedings of the 2002 Congress on Evolutionary Computation. CEC'02 (Cat. No.02TH8600).

[40]  Edmund K. Burke,et al.  Practice and Theory of Automated Timetabling IV , 2002, Lecture Notes in Computer Science.