rvb-sub

binary set_partitioning knapsack

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
S. Weider	33765	225	1.29542e-01	hard	–	16.08499802	rvb-sub.mps.gz

Set partitioning instance resulting from a column generation algorithm used for duty scheduling in public transportation 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	33765	33763
Constraints	225	225
Binaries	33763	33763
Integers	0	0
Continuous	2	0
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.129542	0.129549
Nonzeroes	984143	984141

Constraint Classification Properties
	Original	Presolved
Total	225	225
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	0	0
Set Partitioning	223	223
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	2
Integer Knapsack	0	0
Mixed Binary	2	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	0.301030
Constraint %		0.888889	0.888889	0.888889	0.888889
Variable %		98.631600	98.631600	98.631600	98.631600
Score	0.000122

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	Int. Viol	Cons. Viol	Obj. Viol	Submitter	Date	Description
2	16.08500		0	0	0	Edward Rothberg	2020-02-05	Solved with Gurobi 9.0 within 8 hours
1	16.70222		0	0	0	-	2018-10-12	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to rvb-sub 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
ivu52	hard	157591	157591	0	2116	2179476	S. Weider	ivu	481.0068	binary set_partitioning invariant_knapsack knapsack mixed_binary
square47	easy	95030	94987	43	61591	27329856	Sascha Kurz	square	15.9999999997877	benchmark benchmark_suitable set_partitioning general_linear
square41	easy	62234	62197	37	40160	13566426	Sascha Kurz	square	15	benchmark benchmark_suitable set_partitioning general_linear
eilC76-2	easy	28599	28599	0	75	314837	J. Linderoth	eil	762.514781999996	binary benchmark_suitable set_partitioning
eilA101-2	easy	65832	65832	0	100	959373	J. Linderoth	eil	880.9201079999999	benchmark binary benchmark_suitable set_partitioning

Reference

@inproceedings{BorndoerferLoebelWeider2008,
 author = {Ralf Bornd{\"o}rfer and Andreas L{\"o}bel and Steffen
Weider},
 booktitle = {Computer-aided Systems in Public Transport},
 editor = {Mark Hickman and Pitu Mirchandani and Stefan Voß},
 pages = {3--24},
 series = {Lecture Notes in Economics and Mathematical Systems},
 title = {A Bundle Method for Integrated Multi-Depot Vehicle and
Duty Scheduling in Public Transit},
 volume = {600},
 year = {2008}
}

@phdthesis{Weider2007,
 author = {Steffen Weider},
 school = {Technische Universit{\"a}t Berlin},
 title = {Integration of Vehicle and Duty Scheduling in Public
Transport},
 year = {2007}
}