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.

Location of instance in collection

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.

Nonzero entries of original problem

Nonzero entries after trivial presolving

Decomposed structure of original problem (dec-file)

Decomposed structure after trivial presolving (dec-file)

	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	Constraints	Nonz.	Submitter	Group	Objective	Tags
opm2-z10-s4	hard	6250	6250	160633	371240	Daniel Espinoza	opm2	-33269	benchmark binary benchmark_suitable precedence knapsack
opm2-z8-s0	easy	3200	3200	63608	152793	Daniel Espinoza	opm2	-15775	binary benchmark_suitable precedence knapsack
rmine13	open	23980	23980	197155	485784	Daniel Espinoza	rmine	-3495.3706624382535*	binary precedence mixed_binary
rmine15	open	42438	42438	358395	879732	Daniel Espinoza	rmine	-5018.819990999996*	binary precedence mixed_binary
opm2-z7-s8	easy	2023	2023	31798	79756	Daniel Espinoza	opm2	-11242	binary benchmark_suitable precedence knapsack

Reference

No bibliographic information available