comp16-3idx

decomposition aggregations precedence variable_bound set_partitioning set_packing cardinality invariant_knapsack mixed_binary general_linear

Submitter Variables Constraints Density Status Group Objective MPS File
Matias Sørensen 64193 71594 7.55632e-05 hard coursetimetabling 18.0 comp16-3idx.mps.gz

Instances comp01-21 of curriculum based course timetabling from the International Timetabling Competition 2007. These are the full models using three-index decision variables.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 64193 53097
Constraints 71594 56908
Binaries 56745 45753
Integers 14 1790
Continuous 7434 5554
Implicit Integers 0 1778
Fixed Variables 10879 0
Nonzero Density 7.55632e-05 9.26423e-05
Nonzeroes 347276 279932
Constraint Classification Properties
Original Presolved
Total 71594 56908
Empty 0 0
Free 3 0
Singleton 2190 0
Aggregations 1 208
Precedence 4854 2030
Variable Bound 54625 46042
Set Partitioning 0 3702
Set Packing 2050 1651
Set Covering 0 0
Cardinality 2916 215
Invariant Knapsack 25 20
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 4918 2526
General Linear 12 514
Indicator 0 0

Structure

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

value min median mean max
Components 3.468790
Constraint % 0.00176 0.0287133 0.0298733 4.09616
Variable % 0.00376 0.0322705 0.0338843 3.32066
Score 0.843062

Best Known Solution(s)

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

## Warning in lapply(df["exactobjval"], as.numeric): NAs introduced by coercion
ID Objective Exact Int. Viol Cons. Viol Obj. Viol Submitter Date Description
4 18 18 0 0 0 Ed Klotz 2022-05-26 Found with Gurobi 9.5
3 24 0 0 0 Edward Rothberg 2019-12-13 Obtained with Gurobi 9.0
2 43 0 0 0 Ed Klotz 2019-11-15 Found by the Optimization Direct Heuristic and CPLEX 12.9
1 50 50 0 0 0 - 2018-10-12 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to comp16-3idx 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
piperout-27 easy 11659 11514 121 24 18442 54662 Gleb Belov piperout 8123.999999999973 benchmark benchmark_suitable aggregations precedence variable_bound set_partitioning set_packing set_covering invariant_knapsack equation_knapsack integer_knapsack mixed_binary general_linear
neos-4391920-timok easy 93846 93786 0 60 184575 585839 Jeff Linderoth neos-pseudoapplication-106 0.00545540819999822 benchmark_suitable aggregations precedence variable_bound set_partitioning mixed_binary
ns1631475 open 22696 22470 211 15 24496 116733 NEOS Server Submission neos-pseudoapplication-75 11100* decomposition precedence variable_bound set_partitioning cardinality mixed_binary general_linear
piperout-08 easy 10399 10245 130 24 14589 44959 Gleb Belov piperout 125054.9999999999 benchmark benchmark_suitable aggregations precedence variable_bound set_partitioning set_packing set_covering invariant_knapsack equation_knapsack integer_knapsack mixed_binary general_linear
mkc1 easy 5325 3087 0 2238 3411 17038 MIPLIB submission pool -607.20703 decomposition benchmark_suitable precedence variable_bound invariant_knapsack mixed_binary

Reference

ITC2007 webpage: www.cs.qub.ac.uk/itc2007/

Model reference: @Article{Lach2012,
author="Lach, Gerald
and L{\"u}bbecke, Marco E.",
title="Curriculum based course timetabling: new solutions to Udine benchmark instances",
journal="Annals of Operations Research",
year="2012",
volume="194",
number="1",
pages="255--272",
abstract="We present an integer programming approach to the university course timetabling problem, in which weekly lectures have to be scheduled and assigned to rooms. Students' curricula impose restrictions as to which courses may not be scheduled in parallel. Besides some hard constraints (no two courses in the same room at the same time, etc.), there are several soft constraints in practice which give a convenient structure to timetables; these should be met as well as possible.",
issn="1572-9338",
doi="10.1007/s10479-010-0700-7",
url="http://dx.doi.org/10.1007/s10479-010-0700-7"
}

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