## Penalising Patterns in Timetables: Strengthened Integer Programming Formulations

Citations: | 1 - 0 self |

### BibTeX

@MISC{Burke_penalisingpatterns,

author = {Edmund K. Burke and Jakub Mareček and Andrew J. Parkes and Hana Rudová},

title = {Penalising Patterns in Timetables: Strengthened Integer Programming Formulations},

year = {}

}

### OpenURL

### Abstract

Many complex timetabling problems, such as university course timetabling [1, 2] and employee rostering [3], have an underpinning bounded graph colouring component, a pattern penalisation component and a number of side constraints. The bounded graph colouring component corresponds to hard constraints

### Citations

105 | Recent research directions in automated timetabling
- Burke, Petrovic
- 2002
(Show Context)
Citation Context ...ttingham NG8 1BB, UK 2 Masaryk University Faculty of Informatics Botanická 68a, Brno 602 00, The Czech Republic 1 Introduction Many complex timetabling problems, such as university course timetabling =-=[1, 2]-=- and employee rostering [3], have an underpinning bounded graph colouring component, a pattern penalisation component and a number of side constraints. The bounded graph colouring component correspond... |

71 |
Constraint Integer Programming
- Achterberg
- 2007
(Show Context)
Citation Context ...rated instances, available from the authors’ website 3 . The results in Table 1 have been obtained with SCIP 0.82 using SoPlex, the presentbest freely-available integer programming solver from Berlin =-=[13]-=-, running on Linux-based Sun V20z with dual Opteron 248 and 2 GB of memory. Notice that in this evaluation all constraints were given explicitly, although extended formulations seem to promise conside... |

50 |
Erben (eds): Practice and Theory of Automated Timetabling
- Burke, W
- 2001
(Show Context)
Citation Context ...(T [p2, r, c] − T [p1, r, c] − T [p3, r, c]) ≤ M[u, d, 3] (12) � (T [p3, r, c] − T [p2, r, c] − T [p4, r, c]) ≤ M[u, d, 4] . (13) The third term in the objective function is then 2 � � � M[u, d, s] . =-=(14)-=- u∈U d∈D s∈Check This formulation, referred to as T for “traditional” below, leaves plenty of room for improvement in terms of performance.s6 Pattern Penalisation by Enumeration Penalising Patterns in... |

45 |
An annotated bibliography of personnel scheduling and rostering
- Ernst, Jiang, et al.
- 2004
(Show Context)
Citation Context ... University Faculty of Informatics Botanická 68a, Brno 602 00, The Czech Republic 1 Introduction Many complex timetabling problems, such as university course timetabling [1, 2] and employee rostering =-=[3]-=-, have an underpinning bounded graph colouring component, a pattern penalisation component and a number of side constraints. The bounded graph colouring component corresponds to hard constraints such ... |

28 | K.: University course timetabling with soft constraints
- Rudova, Murray
- 2003
(Show Context)
Citation Context ... (3) T [p, r, c] ≤ 1 (4) T [p, r, c] ≤ 1 (5) T [p, r, c] = 0 (6) Soft constraints in timetabling problems vary widely from institution to institution, but most notably penalise patterns in timetables =-=[10]-=-. Their integer programming formulations, although often crucial for the performance of the model, are still largely unexplored. Although instances of up to two hundred events with dozens of distinct ... |

23 |
Neighborhood portfolio approach for local search applied to timetabling problems
- Gaspero, Schaerf
(Show Context)
Citation Context ...imetabling Throughout this paper, Udine Course Timetabling is used as an illustrative example of a timetabling problem with soft constraints. The problem has been formulated by Schaerf and Di Gaspero =-=[4, 5]-=- at the University of Udine. Its input can be outlined as follows: † Corresponding author: Jakub Mareček, e-mail: jakub@marecek.cz.s2 Jakub Mareček et al. • C, T , R, D, P are sets representing course... |

17 |
All-different polytopes
- Lee
- 2002
(Show Context)
Citation Context ...osely related to the Graph Colouring Problem. In integer programming, most researchers [6, e. g.] study a natural assignment-type formulation, although some focus also on a binary encoded formulation =-=[7]-=-, a scheduling formulation [8], and four other distinct formulations. See another paper by the authors [9] for a brief survey. For timetabling applications, a clique-based formulation has recently bee... |

16 |
Representations of the all_different predicate constraint satisfaction in integer programming
- Williams, Yan
- 1999
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Citation Context ...ouring Problem. In integer programming, most researchers [6, e. g.] study a natural assignment-type formulation, although some focus also on a binary encoded formulation [7], a scheduling formulation =-=[8]-=-, and four other distinct formulations. See another paper by the authors [9] for a brief survey. For timetabling applications, a clique-based formulation has recently been proposed [9]: assuming there... |

15 | Rapid mathematical programming
- Koch
- 2004
(Show Context)
Citation Context ... replaced with s∈Check M[u, d, s].s6 Jakub Mareček et al. 7 Empirical Results The five formulations, together with Formulation C of the decision version of graph colouring, have been encoded in Zimpl =-=[12]-=- and tested on four real-life instances from the University of Udine School of Engineering [4] and 18 semirandomly generated instances, available from the authors’ website 3 . The results in Table 1 h... |

12 | University timetabling
- Petrovic, Burke
- 2004
(Show Context)
Citation Context ...ttingham NG8 1BB, UK 2 Masaryk University Faculty of Informatics Botanická 68a, Brno 602 00, The Czech Republic 1 Introduction Many complex timetabling problems, such as university course timetabling =-=[1, 2]-=- and employee rostering [3], have an underpinning bounded graph colouring component, a pattern penalisation component and a number of side constraints. The bounded graph colouring component correspond... |

12 |
A cutting plane algorithm for graph coloring
- Méndez-Díaz, Zabala
- 2008
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Citation Context ...∈P ∀c∈C r∈R ∀p∈P ∀t∈T � � r∈R c∈Teaches[t] � � ∀p∈P ∀u∈U r∈R c∈Inc[u] ∀〈c,p〉∈F � r∈R 4 Soft Constraints T [p, r, c] ≤ 1 (2) T [p, r, c] ≤ 1 (3) T [p, r, c] ≤ 1 (4) T [p, r, c] ≤ 1 (5) T [p, r, c] = 0 =-=(6)-=- Soft constraints in timetabling problems vary widely from institution to institution, but most notably penalise patterns in timetables [10]. Their integer programming formulations, although often cru... |

12 | A computational study of a cutting plane algorithm for university course timetabling
- Avella, Vasil’ev
(Show Context)
Citation Context ...cial for the performance of the model, are still largely unexplored. Although instances of up to two hundred events with dozens of distinct enrolments are now being solved to optimum almost routinely =-=[11]-=-, larger instances are still approached only via heuristics. Out of the three soft constraints in the Udine Course Timetabling problem, the minimisation of the number of students left without a seat c... |

9 | On a clique-based integer programming formulation of vertex colouring with applications in course timetabling
- Burke, Mareček, et al.
- 2007
(Show Context)
Citation Context ...natural assignment-type formulation, although some focus also on a binary encoded formulation [7], a scheduling formulation [8], and four other distinct formulations. See another paper by the authors =-=[9]-=- for a brief survey. For timetabling applications, a clique-based formulation has recently been proposed [9]: assuming there are courses with multiple events per week, it is possible to use array T of... |

8 |
Multi neighborhood local search with application to the course timetabling problem
- Gaspero, Schaerf
(Show Context)
Citation Context ...imetabling Throughout this paper, Udine Course Timetabling is used as an illustrative example of a timetabling problem with soft constraints. The problem has been formulated by Schaerf and Di Gaspero =-=[4, 5]-=- at the University of Udine. Its input can be outlined as follows: † Corresponding author: Jakub Mareček, e-mail: jakub@marecek.cz.s2 Jakub Mareček et al. • C, T , R, D, P are sets representing course... |