Submitter Variables Constraints Density Status Group Objective MPS File
Pierre Le Bodic 2304 2111 1.73447e-03 easy chromaticindex 4 chromaticindex32-8.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 2304 2304
Constraints 2111 2111
Binaries 2304 2304
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.00173447 0.00173447
Nonzeroes 8436 8436
Constraint Classification Properties
Original Presolved
Total 2111 2111
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 0 0
Variable Bound 0 0
Set Partitioning 575 575
Set Packing 1536 1536
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 % 18.1904 18.1904 18.1904 18.1904
Variable % 25.0000 25.0000 25.0000 25.0000
Score 0.545713

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 chromaticindex32-8 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
chromaticindex256-8 18432 18432 0 0 16895 67572 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
neos-691058 3006 1755 0 1251 2667 30837 NEOS Server Submission neos-pseudoapplication-110 easy 297

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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