set3-09

precedence variable_bound mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Kerem Akartunali	4019	3747	9.12864e-04	open	set3	176497.15*	set3-09.mps.gz

This is joint work with Andrew J. Miller, Universite de Bordeaux 1; RealOpt, INRIA Bordeaux Sud-Ouest, France. Andrew.Miller@math.u-bordeaux1.fr. These are five hard instances chosen from our library MULTILSB (Multi-item Lot-Sizing with Backlogging), which is fully available at (incl. documentation and mosel file):http://personal.strath.ac.uk/kerem.akartunali/research/multi-lsb/ For these 5 instances, gaps remain in the range of >50% after 30 min. (using latest version of FICO on a laptop with i7 processor and 4GB RAM): (first two columns indicate the 30 min-runs, and the last column indicates the best solutions we know at the moment). Computational results for these instances as well as for others of MULTILSB can be found on the website. Imported from the MIPLIB2010 submissions.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	4019	3347
Constraints	3747	3390
Binaries	1424	752
Integers	0	0
Continuous	2595	2595
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000912864	0.001093130
Nonzeroes	13747	12403

Constraint Classification Properties
	Original	Presolved
Total	3747	3390
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	576	891
Variable Bound	654	612
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	0	0
Integer Knapsack	0	0
Mixed Binary	2517	1887
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	1.230449
Constraint %		0.0294985	4.05973	3.95280	9.58702
Variable %		0.0746454	3.23619	3.11023	8.16123
Score	0.624521

Best Known Solution(s)

Find solutions below. Download the archive containing all solutions from the Download page.

## Warning in lapply(df["exactobjval"], as.numeric): NAs introduced by coercion

ID	Objective	Exact	Int. Viol	Submitter	Date	Description
3	176497.2	176497.2	0e+00	Edward Rothberg	2020-06-11	Obtained with Gurobi 9.0 using the solution improvement heuristic
2	178576.4		2e-07	Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
1	178701.6		0e+00	Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex

Similar instances in collection

The following instances are most similar to set3-09 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	Continuous	Constraints	Nonz.	Submitter	Group	Objective	Tags
set3-15	hard	4019	1424	2595	3747	13747	Kerem Akartunali	set3	124886	precedence variable_bound mixed_binary
set3-10	hard	4019	1424	2595	3747	13747	Kerem Akartunali	set3	185179.043049708	precedence variable_bound mixed_binary
set3-16	open	4019	1424	2595	3747	13747	Kerem Akartunali	set3	134040.4097522878*	precedence variable_bound mixed_binary
set3-20	hard	4019	1424	2595	3747	13747	Kerem Akartunali	set3	159462.572721458	precedence variable_bound mixed_binary
neos-5041822-cockle	open	227668	149313	78355	546733	1362468	Jeff Linderoth	neos-pseudoapplication-25	5724245.704467608*	aggregations precedence variable_bound set_packing mixed_binary

Reference

No bibliographic information available