stp3d

binary decomposition aggregations precedence variable_bound set_partitioning set_packing cardinality

Submitter Variables Constraints Density Status Group Objective MPS File
T. Koch 204880 159488 2.02635e-05 hard 493.71965 stp3d.mps.gz

Steiner tree packing instance in a 3 dimensional grid-graph, LP relaxation is highly degenerate. Alkis Vazacopoulos reports finding the first feasible solution of this instance using XPRESS 2006B. This instance was solved by a first implementation of ParaSCIP using up to 2048 cores of HLRN-II(http://www.hlrn.de). ParaSCIP, mainly developed by Yuji Shinano, is an extension of SCIP and realizes a parallelization on a distributed memory computing environment. For being able to interrupt and warmstart the computations, ParaSCIP has a checkpoint mechanism. Therefore, selected subproblems are stored as warm start information, which allows to virtually run ParaSCIP, although the HLRN-II environment imposes a time limit of 48 hours per run. The problem was presolved several times with SCIP presolving techniques. After that, it took approximately 114 hours to solve this instance.

Imported from MIPLIB2010.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 204880 179062
Constraints 159488 139386
Binaries 204880 179062
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 2.02635e-05 2.33948e-05
Nonzeroes 662128 583904
Constraint Classification Properties
Original Presolved
Total 159488 139386
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 94
Precedence 129232 112973
Variable Bound 0 50
Set Partitioning 82 23
Set Packing 2171 1965
Set Covering 0 0
Cardinality 28003 24281
Invariant Knapsack 0 0
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 0 0
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 1.672098
Constraint % 0.00215 2.14327 2.39622 12.05640
Variable % 0.00223 2.17372 3.06850 9.25909
Score 0.934837

Best Known Solution(s)

No solution available for stp3d .

Similar instances in collection

The following instances are most similar to stp3d 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-631710 easy 167056 167056 0 0 169576 834166 NEOS Server Submission neos-pseudoapplication-75 203 benchmark binary benchmark_suitable precedence set_partitioning set_packing binpacking
ns1828997 open 27275 27275 0 0 81725 190670 NEOS Server Submission neos-pseudoapplication-13 20* binary precedence variable_bound cardinality invariant_knapsack
neos-4295773-pissa open 85126 85124 0 2 210116 552408 Jeff Linderoth neos-pseudoapplication-6 0.0490931664* decomposition aggregations precedence variable_bound set_partitioning cardinality invariant_knapsack knapsack mixed_binary
neos-4300652-rahue hard 33003 20900 0 12103 76992 183616 Jeff Linderoth neos-pseudoapplication-13 2.1416 benchmark decomposition benchmark_suitable aggregations precedence variable_bound set_partitioning cardinality knapsack mixed_binary
supportcase29 easy 12050 12050 0 0 12441 96050 Domenico Salvagnin Infeasible infeasible binary decomposition benchmark_suitable precedence set_packing invariant_knapsack binpacking knapsack mixed_binary

Reference

@phdthesis{Koch2004,
 author = {Thorsten Koch},
 language = {English},
 school = {Technische {Universit\"at} Berlin},
 title = {Rapid Mathematical Programming},
 year = {2004}
}

Last Update Okt 02, 2019 by Gregor Hendel
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