polygonpack4-10

numerics set_packing invariant_knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Antonio Frangioni	20537	65935	2.50376e-04	open	polygonpack	-53594508.70758325*	polygonpack4-10.mps.gz

Given a set P of polygons, not necessarily convex, and a rectangle, we want to find the subset S of P with largest possible total area and a position every p in S so that there are no overlaps and they are all included in the rectangle. We allow a small set of rotations (0, 90, 180, 270 degrees) for every polygon. The problem is simplified w.r.t. the real application because the polygons do not have (fully encircled) “holes”, which are supposedly filled-in separately, although they can have “bays”. Models are saved as .lp. Instance LpPackingModel_Dim means that we are trying to pack polygons taken from set ; there are currently 5 different sets, and is 7, 10 or 15.

Location of instance in collection

Instance Statistics

Detailed explanation of the following tables can be found here.

Size Related Properties
	Original	Presolved
Variables	20537	20537
Constraints	65935	65905
Binaries	20517	20517
Integers	0	0
Continuous	20	20
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000250376	0.000250387
Nonzeroes	339036	338896

Constraint Classification Properties
	Original	Presolved
Total	65935	65905
Empty	0	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	0
Variable Bound	0	0
Set Partitioning	0	0
Set Packing	10	10
Set Covering	0	0
Cardinality	0	0
Invariant Knapsack	720	720
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	65205	65175
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	1.041393
Constraint %		0.001520	0.001520	0.001520	0.001520
Variable %		0.019477	0.019477	0.019477	0.019477
Score	0.000152

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	Cons. Viol	Obj. Viol	Submitter	Date	Description
2	-53594509		0	1e-06	0	Michael Winkler	2023-11-14	new incumbents found with Gurobi 10.0.2 on AMD EPYC 7313P 16-Core Processor with 264075352 kB memory running with default except for MIPGAP=0
1	-53594066	-53594066	0	0e+00	0	-	2018-10-13	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to polygonpack4-10 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
polygonpack4-7	open	10788	10774	14	34529	178591	Antonio Frangioni	polygonpack	-51837712.9799564*	numerics set_packing invariant_knapsack mixed_binary
polygonpack4-15	open	44237	44207	30	144478	731949	Antonio Frangioni	polygonpack	-63613612.41121812*	numerics set_packing invariant_knapsack mixed_binary
polygonpack3-15	open	44237	44207	30	144478	731949	Antonio Frangioni	polygonpack	-55055595.32367724*	numerics precedence variable_bound set_packing invariant_knapsack mixed_binary
polygonpack5-15	open	48163	48133	30	163429	804740	Antonio Frangioni	polygonpack	-55494686.5559904*	numerics precedence variable_bound set_packing invariant_knapsack mixed_binary
glass4	easy	322	302	20	396	1815	I. Luzzi	–	1200012599.972384	benchmark benchmark_suitable precedence set_partitioning mixed_binary

Reference

No bibliographic information available