## Penalising Patterns in Timetables: Novel Integer Programming Formulations

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Citations: | 2 - 2 self |

### BibTeX

@MISC{Burke_penalisingpatterns,

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

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

year = {}

}

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### Abstract

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

### Citations

104 | Recent Research Directions in Automated Timetabling
- Burke, Petrovic
- 2002
(Show Context)
Citation Context ...ryk University Faculty of Informatics Botanická 68a, Brno 602 00, The Czech Republic 1 Introduction Many complex timetabling problems, such as employee rostering [1] and university course timetabling =-=[2, 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 ... |

57 | R.F.: Examination timetabling in British universities - A survey
- Burke, Elliman, et al.
- 1996
(Show Context)
Citation Context ...c,p〉∈F r∈R (1) 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 =-=[12]-=-, but most notably penalise patterns in timetables [13]. Their integer programming formulations, although often crucial for the performance of the model, are still largely unexplored. Although instanc... |

44 |
2004a) “An Annotated Bibliography of Personnel Scheduling and Rostering
- Ernst, Jiang, et al.
(Show Context)
Citation Context ...on Road, Nottingham 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 employee rostering =-=[1]-=- and university course timetabling [2, 3], have an underpinning bounded graph colouring component, a pattern penalisation component and a number of side constraints. The bounded graph colouring compon... |

28 | K.: University course timetabling with soft constraints
- Rudova, Murray
- 2003
(Show Context)
Citation Context ...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 [12], but most notably penalise patterns in timetables =-=[13]-=-. 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 ...metabling Throughout the paper, the Udine Course Timetabling Problem is used as an illustrative example of timetabling with soft constraints. The problem has been formulated by Schaerf and Di Gaspero =-=[6, 7]-=- at the University of Udine. Its input can be outlined as follows: • C, T , R, D, P are sets representing courses, teachers, rooms, days, and periods, respectively • U is a set representing distinct e... |

21 | University timetabling: Bridging the gap between research and practice
- McCollum
- 2006
(Show Context)
Citation Context ...colouring, it is often easy to generate feasible solutions for instances with hundreds of events and hundreds of distinct enrolments. See [4] for more details. However, real-world timetabling systems =-=[5]-=- have to cope with much more challenging requirements, such as “students should not have gaps in their individual daily timetables”, which often make the problem over-constrained. The key to tackling ... |

17 |
All-different polytopes
- Lee
- 2002
(Show Context)
Citation Context ...ted to the Graph Colouring Problem [4]. In integer programming, most researchers [8, for example] study a natural assignment-type formulation, although some focus also on a binary encoded formulation =-=[9]-=-, a scheduling formulation [10], and four other distinct formulations. A brief survey can be seen in [11]. For timetabling applications, a cliquebased formulation has recently been proposed [11]: assu... |

16 |
Representations of the all_different predicate constraint satisfaction in integer programming
- Williams, Yan
- 1999
(Show Context)
Citation Context ...blem [4]. In integer programming, most researchers [8, for example] study a natural assignment-type formulation, although some focus also on a binary encoded formulation [9], a scheduling formulation =-=[10]-=-, and four other distinct formulations. A brief survey can be seen in [11]. For timetabling applications, a cliquebased formulation has recently been proposed [11]: assuming there are courses with mul... |

15 | Rapid mathematical programming
- Koch
- 2004
(Show Context)
Citation Context ...se right-hand side is replaced with � s∈Check M[u, d, s]. 5 Empirical Results The five formulations, together with Formulation C of the decision version of graph colouring, have been encoded in Zimpl =-=[15]-=- and tested on four real-life instances from the University of Udine School of Engineering [6] and 18 semi-randomly generated instances, available from the authors’ website 3 . The results in Table 1 ... |

12 |
A cutting plane algorithm for graph coloring
- Méndez-Díaz, Zabala
- 2008
(Show Context)
Citation Context ...ommended days of instruction. This enables addition of the following constraints: ∀c∈C � ∀d∈D ∀p∈HasP[d] r∈R � � ∀c∈C ∀d∈D r∈R p∈HasP[d] � ∀c∈C d∈D T [p, r, c] ≤ CTT[c, d] (7) T [p, r, c] ≥ CTT[c, d] =-=(8)-=- CTT[c, d] ≥ HasMinD[c] − Miss[c] (9) The term 5 � c∈C Miss[c] can then be added to the objective function. 3 Pattern Penalisation by Feature The natural formulation of penalisation of patterns of cla... |

11 | A computational study of a cutting plane algorithm for university course timetabling
- Avella, Vasil’ev
- 2005
(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 =-=[14]-=-, 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 ...a natural assignment-type formulation, although some focus also on a binary encoded formulation [9], a scheduling formulation [10], and four other distinct formulations. A brief survey can be seen in =-=[11]-=-. For timetabling applications, a cliquebased formulation has recently been proposed [11]: assuming there are courses with multiple events per week, it is possible to use array T of binary decision va... |

8 |
Multi neighborhood local search with application to the course timetabling problem
- Gaspero, Schaerf
(Show Context)
Citation Context ...metabling Throughout the paper, the Udine Course Timetabling Problem is used as an illustrative example of timetabling with soft constraints. The problem has been formulated by Schaerf and Di Gaspero =-=[6, 7]-=- at the University of Udine. Its input can be outlined as follows: • C, T , R, D, P are sets representing courses, teachers, rooms, days, and periods, respectively • U is a set representing distinct e... |

7 |
Applications to Timetabling, Handbook of Graph Theory
- Burke, Kingston, et al.
- 2003
(Show Context)
Citation Context ...intractability and hardness of approximation of bounded graph colouring, it is often easy to generate feasible solutions for instances with hundreds of events and hundreds of distinct enrolments. See =-=[4]-=- for more details. However, real-world timetabling systems [5] have to cope with much more challenging requirements, such as “students should not have gaps in their individual daily timetables”, which... |

5 |
University timetabling. Handbook of Scheduling: Algorithms, Models and Performance Analysis, Chapter 45, (Editor
- Petrovic, Burke
- 2004
(Show Context)
Citation Context ...ryk University Faculty of Informatics Botanická 68a, Brno 602 00, The Czech Republic 1 Introduction Many complex timetabling problems, such as employee rostering [1] and university course timetabling =-=[2, 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 ... |

2 |
Constraint (I)nteger (P)rogramming”, Phd Thesis, Technische Universität
- Achterberg
- 2010
(Show Context)
Citation Context ...ated instances, available from the authors’ website 3 . The results in Table 1 have been obtained with SCIP 0.82 using SoPlex, the present-best freely-available integer programming solver from Berlin =-=[16]-=-, running on Linux-based Sun V20z with dual Opteron 248 and 2 GB of memory. Notice that all constraints were given explicitly in these experiments, although extended formulations seem to promise consi... |