Submitter Variables Constraints Density Status Group Objective MPS File
Shunji Umetani 100000 2000 5e-03 open scp 327 scpk4.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 1e+05 1e+05
Constraints 2000 2000
Binaries 1e+05 1e+05
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.005 0.005
Nonzeroes 1e+06 1e+06
Constraint Classification Properties
Original Presolved
Total 2000 2000
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 2000 2000
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
1 327 327 0 0 0 - 2018-10-12 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to scpk4 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 Variables Binaries Integers Continuous Constraints Nonz. Submitter Group Status Objective
scpj4scip 99947 99947 0 0 1000 999893 Shunji Umetani scp open 133*
scpl4 200000 200000 0 0 2000 2000000 Shunji Umetani scp open 274*
scpm1 500000 500000 0 0 5000 6250000 Shunji Umetani scp open 592*
scpn2 1000000 1000000 0 0 5000 12500000 Shunji Umetani scp open 540*
ex1010-pi 25200 25200 0 0 1468 102114 M. Winkler open 239*

Reference

No bibliographic information available

Last Update Nov 09, 2018 by Gregor Hendel
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