Submitter Variables Constraints Density Status Group Objective MPS File
Pierre Le Bodic 18432 16895 2.16988e-04 easy chromaticindex 4 chromaticindex256-8.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 18432 18432
Constraints 16895 16895
Binaries 18432 18432
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.000216988 0.000216988
Nonzeroes 67572 67572
Constraint Classification Properties
Original Presolved
Total 16895 16895
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 0 0
Set Partitioning 4607 4607
Set Packing 12288 12288
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 % 18.1829 18.1829 18.1829 18.1829
Variable % 25.0000 25.0000 25.0000 25.0000
Score 0.545487

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 chromaticindex256-8 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
chromaticindex128-5 9216 9216 0 0 8447 33780 Pierre Le Bodic chromaticindex easy 4
chromaticindex512-7 36864 36864 0 0 33791 135156 Pierre Le Bodic chromaticindex easy 4
chromaticindex1024-7 73728 73728 0 0 67583 270324 Pierre Le Bodic chromaticindex easy 4
chromaticindex32-8 2304 2304 0 0 2111 8436 Pierre Le Bodic chromaticindex easy 4
netdiversion 129180 129180 0 0 119589 615282 Chris Cullenbine easy 242

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 "
}

Last Update Nov 09, 2018 by Gregor Hendel
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