mkc

decomposition precedence variable_bound set_packing invariant_knapsack binpacking mixed_binary

Submitter Variables Constraints Density Status Group Objective MPS File
J. Kalagnanam, M. Dawande 5325 3411 9.38031e-04 hard -563.8460100132 mkc.mps.gz

Multiple knapsack problem with color constraints. John Forrest, Laszlo Ladanyi and Jayant Kalagnanam solved this instance by reformulation in 1999.

Imported from MIPLIB2010.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 5325 5199
Constraints 3411 3212
Binaries 5323 5197
Integers 0 0
Continuous 2 2
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.000938031 0.000989030
Nonzeroes 17038 16516
Constraint Classification Properties
Original Presolved
Total 3411 3212
Empty 0 0
Free 0 0
Singleton 132 0
Aggregations 0 0
Precedence 2922 2855
Variable Bound 55 55
Set Partitioning 0 0
Set Packing 252 252
Set Covering 0 0
Cardinality 0 0
Invariant Knapsack 24 24
Equation Knapsack 0 0
Bin Packing 0 24
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 26 2
General Linear 0 0
Indicator 0 0

Structure

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

value min median mean max
Components 2.537819
Constraint % 0.0311333 0.286172 0.249066 2.11706
Variable % 0.0384689 0.289244 0.192345 1.53876
Score 0.979256

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 -563.846 -563.846 7e-07 7e-07 0 - 2018-10-11 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to mkc 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
gus-sch easy 5475 2736 2736 3 5984 33135 Alexandra M. Newman -1167 decomposition aggregations precedence variable_bound set_packing set_covering cardinality invariant_knapsack integer_knapsack mixed_binary general_linear
mkc1 easy 5325 3087 0 2238 3411 17038 MIPLIB submission pool -607.20703 decomposition benchmark_suitable precedence variable_bound invariant_knapsack mixed_binary
neos-1337307 easy 2840 2840 0 0 5687 30799 NEOS Server Submission neos-pseudoapplication-13 -202319 binary decomposition benchmark_suitable precedence set_partitioning invariant_knapsack knapsack mixed_binary
ab71-20-100 easy 6689 6689 0 0 6380 41961 MIPLIB submission pool ab -10420305975 binary decomposition numerics precedence set_packing
ab72-40-100 easy 12370 12370 0 0 11671 72137 MIPLIB submission pool ab -11186620442 binary decomposition numerics precedence set_packing

Reference

@techreport{DawandeKalagnanam1998,
 author = {M. Dawande and J. Kalagnanam},
 institution = {IBM},
 language = {English},
 number = {RC 21138},
 title = {The multiple knapsack problem with color constraints},
 type = {Research Report},
 year = {1998}
}

@article{ForrestKalagnanamLadanyi2006,
 author = {Forrest, John J. H. and Kalagnanam, Jayant and Ladanyi, Laszlo},
 journal = {{INFORMS} Journal on Computing},
 number = {1},
 pages = {129-134},
 title = {A Column-Generation Approach to the Multiple Knapsack Problem with
Color Constraints},
 volume = {18},
 year = {2006}
}

Last Update Aug 28, 2019 by Gregor Hendel
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