woodlands09

aggregations variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack general_linear

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
George Fonseca	382147	194599	3.55811e-05	hard	timetabling	0	woodlands09.mps.gz

Educational timetabling problems from several real schools/universities around the world. These instances were originally expressed in the xhstt file format [1] and formulated as Integer Programming models as described at [2].

[1] https://www.sciencedirect.com/science/article/pii/S0377221717302242 [2] https://link.springer.com/article/10.1007/s10479-011-1012-2 Reported to be solved after 243275 seconds with ParaSCIP using 72 cores.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	382147	365837
Constraints	194599	179345
Binaries	382119	365809
Integers	28	28
Continuous	0	0
Implicit Integers	0	4
Fixed Variables	0	0
Nonzero Density	3.55811e-05	3.69208e-05
Nonzeroes	2646000	2422410

Constraint Classification Properties
	Original	Presolved
Total	194599	179345
Empty	0	0
Free	0	0
Singleton	3877	0
Aggregations	58718	56236
Precedence	0	0
Variable Bound	6720	3840
Set Partitioning	9030	9119
Set Packing	8787	8787
Set Covering	2943	1289
Cardinality	3039	1480
Invariant Knapsack	6102	6088
Equation Knapsack	95376	92499
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	0	0
General Linear	7	7
Indicator	0	0

Structure

Available nonzero structure and decomposition information. Further information can be found here.

Nonzero entries of original problem

Nonzero entries after trivial presolving

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving (dec-file)

	value	min	median	mean	max
Components
Constraint %
Variable %
Score

Best Known Solution(s)

Find solutions below. Download the archive containing all solutions from the Download page.

ID	Objective	Exact	Int. Viol	Cons. Viol	Obj. Viol	Submitter	Date	Description
1	0	0	0	0	0	Yuji Shinano	2018-11-01	Found with ParaSCIP using 72 cores

Similar instances in collection

The following instances are most similar to woodlands09 in the collection. This similarity analysis is based on 100 scaled instance features describing properties of the variables, objective function, bounds, constraints, and right hand sides.

Instance	Status	Variables	Binaries	Integers	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
brazil3	easy	23968	23874	94	0	14646	133184	George Fonseca	timetabling	24	benchmark decomposition benchmark_suitable aggregations precedence variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack mixed_binary general_linear
kosova1	open	614253	609591	4662	0	304931	3414761	George Fonseca	timetabling	6.0*	aggregations precedence variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack binpacking general_linear
highschool1-aigio	hard	320404	319686	718	0	92568	1562168	George Fonseca	timetabling	0	benchmark benchmark_suitable aggregations variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack general_linear
neos-3045796-mogo	easy	11016	11016	0	0	2226	44442	Jeff Linderoth	neos-pseudoapplication-22	-175	binary decomposition set_partitioning set_packing set_covering invariant_knapsack equation_knapsack
uccase7	hard	33020	7224	0	25796	47132	335644	Daniel Espinoza	uccase	26834.28427331005	aggregations precedence variable_bound set_partitioning invariant_knapsack binpacking knapsack mixed_binary

Reference

@article{FONSECA201728,
title = "Integer programming techniques for educational timetabling",
journal = "European Journal of Operational Research",
volume = "262",
number = "1",
pages = "28 - 39",
year = "2017",
note = "",
issn = "0377-2217",
doi = "http://dx.doi.org/10.1016/j.ejor.2017.03.020",
url = "http://www.sciencedirect.com/science/article/pii/S0377221717302242",
author = "George H.G. Fonseca and Haroldo G. Santos and Eduardo G. Carrano and Thomas J.R. Stidsen",
keywords = "Timetabling",
keywords = "Integer Programming",
keywords = "Formulation"
}