stockholm

variable_bound mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Paul Rubin	20644	57346	1.44508e-04	open	–	120.9999950202855*	stockholm.mps.gz

Toll booth placement 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	20644	20644
Constraints	57346	57346
Binaries	962	962
Integers	0	0
Continuous	19682	19682
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000144508	0.000144508
Nonzeroes	171076	171076

Constraint Classification Properties
	Original	Presolved
Total	57346	57346
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	962	962
Set Partitioning	0	0
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	56384	56384
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 %		98.3225	98.3225	98.3225	98.3225
Variable %		95.3401	95.3401	95.3401	95.3401
Score	0.045818

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	Submitter	Date	Description
4	121	1e+100	8.9e-06	Michael Winkler	2024-07-16	Gurobi 11.0.1 on AMD EPYC 7313P 16-Core Processor with 264075352 kB memory
3	122		0.0e+00	Mars Davletshin	2023-12-28	The solution was obtained with Huawei OptVerse solver (0.7.0) using neural primal heuristic.
2	125		0.0e+00	Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	126	0e+00	0.0e+00	-	2018-10-11	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to stockholm 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
neos-3754224-navua	open	150228	3574	0	146654	232387	652974	Jeff Linderoth	neos-pseudoapplication-83	157909.0677610051*	numerics aggregations precedence variable_bound set_partitioning mixed_binary
eva1aprime5x5opt	open	1712	400	0	1312	11929	57162	Yoshihiro Kanno	evaprime	-17.94807560443689*	aggregations variable_bound set_packing mixed_binary
neos-619167	easy	3452	400	0	3052	6800	20020	NEOS Server Submission	neos-pseudoapplication-83	1.664893618589958	decomposition numerics precedence variable_bound mixed_binary
eva1aprime6x6opt	open	3514	836	0	2678	34872	161558	Yoshihiro Kanno	evaprime	-16.31528287738903*	aggregations variable_bound set_packing mixed_binary
neos-5018451-chiese	easy	265713	1222	244	264247	170175	1249955	Jeff Linderoth	neos-pseudoapplication-69	-147988824.81	numerics aggregations variable_bound mixed_binary general_linear

Reference

@article{BaiRubin2009,
 author = {Lihui Bai and Paul A. Rubin},
 journal = {Operations Research},
 number = {6},
 pages = {1510--1522},
 title = {Combinatorial {B}enders Cuts for the Minimum Tollbooth Problem},
 volume = {57},
 year = {2009}
}

@inproceedings{BaiStampsHarwoodKollmann2006,
 author = {Lihui Bai and Matthew T. Stamps and R. Corban Harwood and
Christopher J. Kollmann},
 booktitle = {Proceedings of the 2006 Meeting of the Decision Sciences
Institute},
 title = {A Genetic Algorithm for the Minimum Tollbooth Problem},
 year = {2006}
}