scpj4scip

binary set_covering

Submitter Variables Constraints Density Status Group Objective MPS File
Shunji Umetani 99947 1000 1.00042e-02 open scp 129.0* scpj4scip.mps.gz

This is a random test instance generator for SCP using the scheme of the following paper, namely the column cost c[j] are integer randomly generated from [1,100]; every column covers at least one row; and every row is covered by at least two columns. see reference: E. Balas and A. Ho, Set covering algorithms using cutting planes, heuristics, and subgradient optimization: A computational study, Mathematical Programming, 12 (1980), 37-60. We have newly generated Classes I-N with the following parameter values, where each class has five instances. We have also generated reduced instances by a standard pricing method in the following paper: S. Umetani and M. Yagiura, Relaxation heuristics for the set covering problem, Journal of the Operations Research Society of Japan, 50 (2007), 350-375. You can obtain the instance generator program from the following web site. https://sites.google.com/site/shunjiumetani/benchmark

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 99947 99947
Constraints 1000 1000
Binaries 99947 99947
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.0100042 0.0100042
Nonzeroes 999893 999893
Constraint Classification Properties
Original Presolved
Total 1000 1000
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 0 0
Set Partitioning 0 0
Set Packing 0 0
Set Covering 1000 1000
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.

value min median mean max
Components 0.30103
Constraint % 100 100 100 100
Variable % 100 100 100 100
Score 0.00000

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 3 129 129 0 0 0 Shunsuke Kamiya 2020-05-17 Computed with weighting local search with exploiting variable associations (WLS) ([1]) [1] Umetani, Shunji. “Exploiting variable associations to configure efficient local search algorithms in large-scale binary integer programs.” European Journal of Operational Research 263.1 (2017): 72-81.
3 2 132 0 0 0 Edward Rothberg 2019-12-13 Obtained with Gurobi 9.0
2 1 133 133 0 0 0 - 2018-10-12 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to scpj4scip 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
scpl4 open 200000 200000 0 0 2000 2000000 Shunji Umetani scp 263.0* binary set_covering
scpk4 open 100000 100000 0 0 2000 1000000 Shunji Umetani scp 321.0* binary set_covering
scpm1 open 500000 500000 0 0 5000 6250000 Shunji Umetani scp 561.0* binary set_covering
scpn2 open 1000000 1000000 0 0 5000 12500000 Shunji Umetani scp 528.0* binary set_covering
ex1010-pi open 25200 25200 0 0 1468 102114 M. Winkler 235* binary set_covering

Reference

No bibliographic information available

Last Update Aug 13, 2020 by Gabriel Kressin
generated with R Markdown
© 2020 by Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)
Imprint