sp97ar

benchmark binary benchmark_suitable variable_bound set_packing set_covering mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
J. Goessens, S. v. Hoessel, L. Kroon	14101	1761	1.17175e-02	easy	sp9	660705645.759	sp97ar.mps.gz

Railway line planning instance. Solved with Gurobi 4.5.1 on a 12-core Linux system in 2678.77 sec. 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	14101	14101
Constraints	1761	1739
Binaries	14101	14101
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.0117175	0.0118648
Nonzeroes	290968	290945

Constraint Classification Properties
	Original	Presolved
Total	1761	1739
Empty	0	0
Free	0	0
Singleton	22	0
Aggregations	0	0
Precedence	0	0
Variable Bound	52	52
Set Partitioning	0	0
Set Packing	1140	1140
Set Covering	129	130
Cardinality	0	0
Invariant Knapsack	0	0
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	418	417
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	3.075912
Constraint %		0.0575043	0.0576010	0.0575043	0.172513
Variable %		0.0141834	0.0839025	0.0921920	0.141834
Score	0.684877

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	660705646	660705646	0	0	1e-07	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to sp97ar 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	Constraints	Nonz.	Submitter	Group	Objective	Tags
sp98ar	easy	15085	15085	1435	426148	J. Goessens, S. v. Hoessel, L. Kroon	sp9	529740623.2	benchmark binary benchmark_suitable variable_bound set_packing set_covering mixed_binary
sp98ic	easy	10894	10894	825	316317	J. Goessens, S. v. Hoessel, L. Kroon	sp9	449144758.4	binary decomposition benchmark_suitable variable_bound set_packing set_covering mixed_binary
sp97ic	easy	12497	12497	1033	316629	J. Goessens, S. v. Hoessel, L. Kroon	sp9	427684487.6799999	binary decomposition benchmark_suitable variable_bound set_packing set_covering mixed_binary
neos-1516309	easy	4500	4500	489	30400	NEOS Server Submission	neos-pseudoapplication-26	35954	binary decomposition set_packing set_covering knapsack
n3div36	easy	22120	22120	4484	340740	R. Meirich	nseq	130800	benchmark binary decomposition benchmark_suitable set_packing set_covering mixed_binary

Reference

@article{FischettiLodi2003,
 author = {Fischetti, Matteo and Lodi, Andrea},
 issn = {0025-5610},
 issue = {1},
 journal = {Mathematical Programming},
 keyword = {Mathematics and Statistics},
 pages = {23-47},
 publisher = {Springer},
 title = {Local branching},
 volume = {98},
 year = {2003}
}

@article{GoossensHoeselKroon2004,
 author = {J.-W. Goossens and S. van Hoesel and L. G. Kroon},
 journal = {Transportation Science},
 language = {English},
 number = {3},
 pages = {379--393},
 title = {A Branch-and-Cut Approach for Solving Railway Line-Planning Problems},
 volume = {38},
 year = {2004}
}