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.
Detailed explanation of the following tables can be found here.
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 |
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 |
Available nonzero structure and decomposition information. Further information can be found here.
Decomposed structure of original problem (dec-file)
Decomposed structure after trivial presolving (dec-file)
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 |
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. |
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 |
@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}
}