rail01

benchmark binary benchmark_suitable aggregations variable_bound set_partitioning set_packing cardinality knapsack

Submitter Variables Constraints Density Status Group Objective MPS File
Thomas Schlechte 117527 46843 7.12195e-05 easy rail0 -70.5699643 rail01.mps.gz

Track allocation problem modeled as arc coupling problem

Imported from MIPLIB2010.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 117527 117526
Constraints 46843 46840
Binaries 117527 117526
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 7.12195e-05 7.12170e-05
Nonzeroes 392086 392044
Constraint Classification Properties
Original Presolved
Total 46843 46840
Empty 0 0
Free 0 0
Singleton 1 0
Aggregations 20791 20792
Precedence 0 0
Variable Bound 1 1
Set Partitioning 14412 15283
Set Packing 1321 1321
Set Covering 0 0
Cardinality 10305 9433
Invariant Knapsack 0 0
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 12 10
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 1.612784
Constraint % 0.207088 1.92544 0.866781 9.51964
Variable % 0.218673 2.31432 0.968288 12.19720
Score 0.723363

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 1 -70.56996 -70.56996 0 0 0 - 2018-10-13 Solution found during MIPLIB2017 problem selection.
1 2 -70.56996 -70.56996 0 0 0 - 2018-10-13 Solution imported from MIPLIB2010.

Similar instances in collection

The following instances are most similar to rail01 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
rail03 hard 758775 758775 0 0 253905 1728450 Thomas Schlechte rail0 -867.093965444446 binary numerics aggregations variable_bound set_partitioning set_packing cardinality knapsack
rail02 easy 270869 270869 0 0 95791 756228 Thomas Schlechte rail0 -200.4499077 benchmark binary benchmark_suitable aggregations set_partitioning set_packing cardinality
neos-780889 easy 182700 182700 0 0 73910 497210 NEOS Server Submission neos-pseudoapplication-94 3421500 binary benchmark_suitable aggregations set_partitioning cardinality mixed_binary
bab6 hard 114240 114240 0 0 29904 1283180 Elmar Swarat bab -284248.2307 benchmark binary benchmark_suitable aggregations precedence set_partitioning set_packing set_covering cardinality invariant_knapsack equation_knapsack knapsack mixed_binary
neos-555001 easy 3855 3782 73 0 3474 16649 NEOS Server Submission neos-pseudoapplication-94 1210625 decomposition numerics aggregations precedence set_partitioning invariant_knapsack mixed_binary general_linear

Reference

@inproceedings{BorndoerferSchlechte2007,
 author = {Ralf Bornd{\"o}rfer and Thomas Schlechte},
 booktitle = {7th Workshop on Algorithmic Approaches for
Transportation Modeling, Optimization, and Systems},
 editor = {Christian Liebchen and Ravindra K. Ahuja and Juan A. Mesa},
 publisher = {Dagstuhl Publishing},
 title = {Models for Railway Track Allocation},
 year = {2007}
}

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