chromaticindex128-5

binary benchmark_suitable set_partitioning set_packing

Submitter Variables Constraints Density Status Group Objective MPS File
Pierre Le Bodic 9216 8447 4.33925e-04 easy chromaticindex 4 chromaticindex128-5.mps.gz

Simple edge-coloring model on chains of Petersen-like subgraphs, designed to fool MIP solvers into producing very large Branch-and-Bound trees.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 9216 9216
Constraints 8447 8447
Binaries 9216 9216
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.000433925 0.000433925
Nonzeroes 33780 33780
Constraint Classification Properties
Original Presolved
Total 8447 8447
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 0 0
Set Partitioning 2303 2303
Set Packing 6144 6144
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.

value min median mean max
Components 0.698970
Constraint % 18.184 18.184 18.184 18.184
Variable % 25.000 25.000 25.000 25.000
Score 0.545519

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 4 4 0 0 0 - 2018-10-13 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to chromaticindex128-5 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
chromaticindex256-8 easy 18432 18432 0 0 16895 67572 Pierre Le Bodic chromaticindex 4 binary benchmark_suitable set_partitioning set_packing
chromaticindex32-8 easy 2304 2304 0 0 2111 8436 Pierre Le Bodic chromaticindex 4 binary benchmark_suitable set_partitioning set_packing
chromaticindex512-7 easy 36864 36864 0 0 33791 135156 Pierre Le Bodic chromaticindex 4 benchmark binary benchmark_suitable set_partitioning set_packing
chromaticindex1024-7 easy 73728 73728 0 0 67583 270324 Pierre Le Bodic chromaticindex 4 benchmark binary benchmark_suitable set_partitioning set_packing
neos-691058 easy 3006 1755 0 1251 2667 30837 NEOS Server Submission neos-pseudoapplication-110 296.999999999986 benchmark_suitable set_partitioning cardinality mixed_binary

Reference

@article{lebodicnemhauser2015,
title = "How important are branching decisions: Fooling \{MIP\} solvers ",
journal = "Operations Research Letters ",
volume = "43",
number = "3",
pages = "273 - 278",
year = "2015",
note = "",
issn = "0167-6377",
doi = "http://dx.doi.org/10.1016/j.orl.2015.03.003",
url = "//www.sciencedirect.com/science/article/pii/S0167637715000413",
author = "Pierre Le Bodic and George L. Nemhauser",
keywords = "Mixed integer programming solvers",
keywords = "Branch and bound",
keywords = "Tree size",
keywords = "Edge coloring",
keywords = "Chromatic index "
}

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