brazil3

benchmark decomposition benchmark_suitable aggregations precedence variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack mixed_binary general_linear

Submitter Variables Constraints Density Status Group Objective MPS File
George Fonseca 23968 14646 3.79403e-04 easy timetabling 24 brazil3.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] http://www.sciencedirect.com/science/article/pii/S0377221717302242 [2] https://link.springer.com/article/10.1007/s10479-011-1012-2

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 23968 17802
Constraints 14646 10345
Binaries 23874 17708
Integers 94 94
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.000379403 0.000497324
Nonzeroes 133184 91588
Constraint Classification Properties
Original Presolved
Total 14646 10345
Empty 82 0
Free 0 0
Singleton 114 0
Aggregations 360 192
Precedence 1080 576
Variable Bound 1274 677
Set Partitioning 1270 1211
Set Packing 1170 1101
Set Covering 275 269
Cardinality 693 272
Invariant Knapsack 1217 662
Equation Knapsack 6987 5312
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 16 16
General Linear 108 57
Indicator 0 0

Structure

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

value min median mean max
Components 1.230449
Constraint % 3.29338 5.34627 5.98753 6.35292
Variable % 3.08938 5.91821 6.66336 7.13696
Score 0.802666

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 24 24 0 0 0 - 2018-10-15 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to brazil3 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
woodlands09 hard 382147 382119 28 0 194599 2646000 George Fonseca timetabling 0 aggregations variable_bound set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack general_linear
kosova1 open 614253 609591 4662 0 304931 3414760 George Fonseca timetabling 526* 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 1562170 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
csched007 easy 1758 1457 0 301 351 6379 Tallys Yunes csched 351 benchmark benchmark_suitable aggregations variable_bound set_partitioning mixed_binary general_linear

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"
}

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