opm2-z12-s8

binary precedence knapsack

Submitter Variables Constraints Density Status Group Objective MPS File
Daniel Espinoza 10800 319508 2.10212e-04 hard opm2 -58540 opm2-z12-s8.mps.gz

Problems coming from precedence constrained knapsacks arising in mining applications. These are one-period problems with integer data but large root LP GAP

Imported from the MIPLIB2010 submissions. Solved with CPLEX 12.8, optimal objective confirmed with Gurobi and XPRESS.

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
Original Presolved
Variables 10800 10409
Constraints 319508 300349
Binaries 10800 10409
Integers 0 0
Continuous 0 0
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.000210212 0.000218765
Nonzeroes 725377 683931
Constraint Classification Properties
Original Presolved
Total 319508 300349
Empty 0 0
Free 0 0
Singleton 0 0
Aggregations 0 0
Precedence 319500 300341
Variable Bound 0 0
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 8 8
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 0.30103
Constraint % 99.998 99.998 99.998 99.998
Variable % 100.000 100.000 100.000 100.000
Score 0.00000

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 -58540 -58540 0 0 0 Gregor Hendel 2019-02-27 “Found with CPLEX 12.8 using 8 threads in 14 hours and 22802 B&B nodes.”
1 -58395 -58395 0 0 0 - 2018-10-13 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to opm2-z12-s8 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
opm2-z10-s4 hard 6250 6250 0 0 160633 371240 Daniel Espinoza opm2 -33269 benchmark binary benchmark_suitable precedence knapsack
opm2-z8-s0 easy 3200 3200 0 0 63608 152793 Daniel Espinoza opm2 -15775 binary benchmark_suitable precedence knapsack
rmine13 open 23980 23980 0 0 197155 485784 Daniel Espinoza rmine -3494.715232* binary precedence mixed_binary
rmine15 open 42438 42438 0 0 358395 879732 Daniel Espinoza rmine -5018.006238* binary precedence mixed_binary
opm2-z7-s8 easy 2023 2023 0 0 31798 79756 Daniel Espinoza opm2 -11242 binary benchmark_suitable precedence knapsack

Reference

No bibliographic information available

Last Update Mär 19, 2019 by Gregor Hendel
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