rail02

benchmark binary benchmark_suitable aggregations set_partitioning set_packing cardinality

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Thomas Schlechte	270869	95791	2.91453e-05	easy	rail0	-200.4499077	rail02.mps.gz

Track allocation problem modeled as arc coupling problem Imported from MIPLIB2010.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	270869	270867
Constraints	95791	95786
Binaries	270869	270867
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	2.91453e-05	2.91447e-05
Nonzeroes	756228	756166

Constraint Classification Properties
	Original	Presolved
Total	95791	95786
Empty	0	0
Free	0	0
Singleton	2	0
Aggregations	39086	39088
Precedence	0	0
Variable Bound	0	0
Set Partitioning	31181	33575
Set Packing	2700	2700
Set Covering	0	0
Cardinality	22819	20423
Invariant Knapsack	0	0
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	3	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.

Nonzero entries of original problem

Nonzero entries after trivial presolving

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving (dec-file)

	value	min	median	mean	max
Components	1.690196
Constraint %		0.0636836	1.58041	0.426994	38.7802
Variable %		0.0646069	1.93445	0.446895	42.6560
Score	0.583826

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	-200.4499	-200.4499	0	0	0	-	2018-10-12	Solution imported from MIPLIB2010.
1	-200.4499	-200.4499	0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to rail02 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	Constraints	Nonz.	Submitter	Group	Objective	Tags
rail03	hard	758775	758775	0	253905	1728451	Thomas Schlechte	rail0	-867.093965444446	binary numerics aggregations variable_bound set_partitioning set_packing cardinality knapsack
rail01	easy	117527	117527	0	46843	392086	Thomas Schlechte	rail0	-70.5699643	benchmark binary benchmark_suitable aggregations variable_bound set_partitioning set_packing cardinality knapsack
neos-780889	easy	182700	182700	0	73910	497210	NEOS Server Submission	neos-pseudoapplication-94	3421500	binary benchmark_suitable aggregations set_partitioning cardinality mixed_binary
bab6	hard	114240	114240	0	29904	1283181	Elmar Swarat	bab	-284248.2307000001	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	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}
}