z26

binary variable_bound set_packing

Submitter Variables Constraints Density Status Group Objective MPS File
Daniel Bienstock 17937 850513 1.12458e-04 open – -1195.0* z26.mps.gz

Set packing problem arising from the ongoing “Frequency Spectrum Auction” in the U.S. Work is collaboration with Ion Media Networks, Inc.

Location of instance in collection

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 17937 17936
Constraints 850513 850473
Binaries 17937 17936
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.000112458 0.000112467
Nonzeroes 1715610 1715590
Constraint Classification Properties
Original Presolved
Total 850513 850473
Empty 14 0
Free 0 0
Singleton 26 0
Aggregations 0 0
Precedence 0 0
Variable Bound 848857 848857
Set Partitioning 0 0
Set Packing 1616 1616
Set Covering 0 0
Cardinality 0 0
Invariant Knapsack 0 0
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 0 0
General Linear 0 0
Indicator 0 0

Structure

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

Nonzero entries of original problem

Nonzero entries of original problem

Matrix after trivial presolving

Nonzero entries after trivial presolving

Decomposed structure of original problem

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving

Decomposed structure after trivial presolving (dec-file)

value min median mean max
Components 1.973128
Constraint % 0.0002350 1.07323 0.0007050 88.1868
Variable % 0.0111501 1.06442 0.0167252 77.6830
Score 0.308955

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
7 -1195 -1195 0 0 0 Mars Davletshin 2023-11-23 It was obtained with Huawei OptVerse solver using neural heuristic and a neighborhood search.
6 -1194 -1194 0 0 0 Ed Rothberg 2023-05-19 Found with the NoRel heuristic.
5 -1192 -1192 0 0 0 Edward Rothberg 2020-09-14 Found with Gurobi
4 -1187 -1187 0 0 0 Edward Rothberg 2020-05-15 Obtained with Gurobi 9.0 using the solution improvement heuristic
3 -1186 0 0 0 Edward Rothberg 2019-12-13 Obtained with Gurobi 9.0
2 -1184 0 0 0 Robert Ashford and Alkis Vazacopoulus 2019-12-18 Found using ODH|CPlex
1 -1101 -1101 0 0 0 - 2018-10-12 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to z26 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
sorrell4 hard 2048 2048 0 0 504451 1008902 Toni Sorrell independentset -24 binary variable_bound
sorrell3 easy 1024 1024 0 0 169162 338324 Toni Sorrell independentset -16 benchmark binary benchmark_suitable variable_bound
sorrell7 open 2048 2048 0 0 78848 157696 Toni Sorrell independentset -198.0* binary variable_bound
sorrell8 easy 2046 2046 0 0 18944 37888 Toni Sorrell independentset -350 binary decomposition variable_bound
manna81 easy 3321 18 3303 0 6480 12960 MIPLIB submission pool – -13164 variable_bound

Reference

No bibliographic information available
Last Update 2024 by Julian Manns
generated with R Markdown
© by Zuse Institute Berlin (ZIB)
Imprint