sp98ir

decomposition benchmark_suitable precedence variable_bound set_covering binpacking knapsack mixed_binary general_linear

Submitter Variables Constraints Density Status Group Objective MPS File
J. Goessens, S. v. Hoessel, L. Kroon 1680 1531 2.78778e-02 easy sp9 219676790.4 sp98ir.mps.gz

Railway line planning instance

Imported from MIPLIB2010.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 1680 1557
Constraints 1531 1420
Binaries 992 869
Integers 688 688
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 121 0
Nonzero Density 0.0278778 0.0306598
Nonzeroes 71704 67787
Constraint Classification Properties
Original Presolved
Total 1531 1420
Empty 0 0
Free 0 0
Singleton 70 0
Aggregations 0 0
Precedence 82 82
Variable Bound 1112 1079
Set Partitioning 0 0
Set Packing 0 0
Set Covering 0 5
Cardinality 0 0
Invariant Knapsack 0 0
Equation Knapsack 0 0
Bin Packing 7 5
Knapsack 35 35
Integer Knapsack 0 0
Mixed Binary 55 44
General Linear 170 170
Indicator 0 0

Structure

Available nonzero structure and decomposition information. Further information can be found here.

value min median mean max
Components 2.593286
Constraint % 0.0704225 0.209106 0.211268 0.211268
Variable % 0.1282870 0.254606 0.256575 0.256575
Score 0.815513

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 219676790 219676790 0 0 0 - 2018-10-11 Solution found during MIPLIB2017 problem selection.
1 219676790 219676790 0 0 0 - 2018-10-11 Solution imported from MIPLIB2010.

Similar instances in collection

The following instances are most similar to sp98ir 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
bley_xs2 easy 2515 1632 883 0 2257 20861 A. Bley bley_x 1051266.38 numerics aggregations variable_bound set_partitioning set_packing set_covering invariant_knapsack knapsack mixed_binary general_linear
bley_xs1 open 3243 2360 883 0 3290 25762 A. Bley bley_x 3974033.21* numerics aggregations variable_bound set_partitioning set_packing set_covering invariant_knapsack knapsack mixed_binary general_linear
neos859080 easy 160 80 80 0 164 1280 NEOS Server Submission neos-pseudoapplication-96 Infeasible benchmark infeasible benchmark_suitable variable_bound general_linear
comp12-2idx open 11863 11820 43 0 16803 73677 Matias Sørensen coursetimetabling 391* decomposition precedence variable_bound set_partitioning cardinality invariant_knapsack mixed_binary general_linear
comp21-2idx hard 10863 10792 71 0 14038 57301 Matias Sørensen coursetimetabling 74 benchmark decomposition benchmark_suitable precedence variable_bound set_partitioning cardinality invariant_knapsack mixed_binary general_linear

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}
}

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