t1722

binary set_partitioning

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
R. Borndörfer	36630	338	1.07501e-02	open	–	108953.0*	t1722.mps.gz

Vehicle scheduling set partitioning problem from Berlin’s Telebus handicapped people’s transportation system 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	36630	36630
Constraints	338	338
Binaries	36630	36630
Integers	0	0
Continuous	0	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.0107501	0.0107501
Nonzeroes	133096	133096

Constraint Classification Properties
	Original	Presolved
Total	338	338
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	0	0
Set Partitioning	338	338
Set Packing	0	0
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.

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	0.30103
Constraint %		100	100	100	100
Variable %		100	100	100	100
Score	0.00000

Best Known Solution(s)

Find solutions below. Download the archive containing all solutions from the Download page.

## Warning in lapply(df["exactobjval"], as.numeric): NAs introduced by coercion

ID	Objective	Exact	Submitter	Date	Description
5	108953	108953	Ed Rothberg	2022-12-08	Found with Gurobi 10.0 using the NoRel heuristic.
4	109137	109137	Edward Rothberg	2020-03-03	Obtained with Gurobi 9.0 using the solution improvement heuristic
3	109473		Kengo Nakamura	2020-02-06	Obtained with weighting local search with exploiting variable associations (WLS) ([1]) [1] Umetani, Shunji. “Exploiting variable associations to configure efficient local search algorithms in large-scale binary integer programs.” European Journal of Operational Research 263.1 (2017): 72-81.
2	111256		Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
1	114245	114245	-	2018-10-11	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to t1722 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	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
t1717	open	73885	73885	0	551	325689	R. Borndörfer	–	158260*	binary set_partitioning
h80x6320	easy	12640	6320	6320	79	6320	MIPLIB submission pool	fixed-cost-network-flow	3700	binary decomposition set_partitioning
eil33-2	easy	4516	4516	0	32	44243	J. Linderoth	eil	934.007915999999	benchmark binary benchmark_suitable set_partitioning
eilC76-2	easy	28599	28599	0	75	314837	J. Linderoth	eil	762.514781999996	binary benchmark_suitable set_partitioning
ds	hard	67732	67732	0	656	1024059	MIPLIB submission pool	–	93.52	binary set_partitioning

Reference

@book{Borndoerfer1998,
 address = {Aachen},
 author = {Ralf Bornd{\"o}rfer},
 instance = {t1717},
 language = {English},
 note = {Ph.D. thesis, Technische Universit{\"a}t Berlin},
 publisher = {Shaker Verlag},
 title = {Aspects of Set Packing, Partitioning, and Covering},
 year = {1998}
}

@inproceedings{BorndoerferGroetschelKlostermeierKuettner1999,
 address = {Berlin},
 author = {Ralf Bornd{\"o}rfer and Martin Gr{\"o}tschel and
Fridolin
Klostermeier and Christian K{\"u}ttner},
 booktitle = {Proceedings of the 7th International Workshop on
Computer-Aided Transit Scheduling},
 editor = {Nigel Wilson},
 language = {English},
 pages = {391--422},
 publisher = {Springer Verlag},
 series = {Lecture Notes in Economics and Mathematical Systems},
 title = {Telebus {B}erlin: Vehicle Scheduling in a Dial-a-Ride
System},
 volume = {471},
 year = {1999}
}