graph40-80-1rand

binary precedence set_partitioning invariant_knapsack

Submitter Variables Constraints Density Status Group Objective MPS File
Michael Bastubbe 283648 1050112 1.23263e-05 open graphs -7* graph40-80-1rand.mps.gz

Packing Cuts in Undirected Graphs. Instances are described in 4.1.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 283648 283136
Constraints 1050112 1025024
Binaries 283648 283136
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 1.23263e-05 1.23104e-05
Nonzeroes 3671550 3572740
Constraint Classification Properties
Original Presolved
Total 1050112 1025024
Empty 0 0
Free 0 0
Singleton 512 0
Aggregations 0 0
Precedence 0 24576
Variable Bound 0 0
Set Partitioning 512 512
Set Packing 0 0
Set Covering 524288 0
Cardinality 0 0
Invariant Knapsack 524800 999936
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
Constraint %
Variable %
Score

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
2 2 -7 -7 0 0 0 Frederic Didier 2020-01-22 Obtained by fixing part of the current solution and trying to solve them with a sub CP-SAT solver
1 1 -6 0 0 0 Robert Ashford and Alkis Vazacopoulus 2019-12-18 Found using ODH|CPlex

Similar instances in collection

The following instances are most similar to graph40-80-1rand 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
graph40-40-1rand open 102600 102600 0 0 360900 1260900 Michael Bastubbe graphs -9* binary precedence set_partitioning invariant_knapsack
graph40-20-1rand open 31243 31243 0 0 99067 345557 Michael Bastubbe graphs -15* binary decomposition precedence set_partitioning invariant_knapsack
graph20-80-1rand hard 16263 16263 0 0 55107 191997 Michael Bastubbe graphs -6 binary decomposition precedence set_partitioning invariant_knapsack
neos-3555904-turama easy 37461 37461 0 0 146493 793605 Hans Mittelmann neos-pseudoapplication-81 -34.7 benchmark binary benchmark_suitable aggregations precedence variable_bound set_partitioning set_packing cardinality invariant_knapsack
graph20-20-1rand easy 2183 2183 0 0 5587 19277 Michael Bastubbe graphs -9 benchmark binary decomposition benchmark_suitable precedence set_partitioning invariant_knapsack

Reference

@article{or:BergnerLuebbeckeWitt:16,
   Author   = {
M. Bergner and M.E. L\"{u}bbecke and J.T. Witt},
   Title    = {A Branch-Price-and-Cut Algorithm for Packing Cuts in Undirected Graphs},
   Journal  = {Journal of Experimental Algorithmics (JEA)},
   Year     = {2016},
   Volume   = {21 },
   Number   = {2016--},
   Pages    = {Article No. 1.2},
   Month   = {Jan},
   Publisher    = {ACM New York, NY, USA},
   DOI      = {10.1145/2851492}
}

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