polygonpack4-15

numerics set_packing invariant_knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Antonio Frangioni	44237	144478	1.14523e-04	open	polygonpack	-63613612.41121812*	polygonpack4-15.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	44237	44237
Constraints	144478	144433
Binaries	44207	44207
Integers	0	0
Continuous	30	30
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000114523	0.000114526
Nonzeroes	731949	731739

Constraint Classification Properties
	Original	Presolved
Total	144478	144433
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	15	15
Set Covering	0	0
Cardinality	0	0
Invariant Knapsack	1680	1680
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	142783	142738
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	1.204120
Constraint %		0.000692	0.000692	0.000692	0.000692
Variable %		0.009040	0.009040	0.009040	0.009040
Score	0.000104

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	Submitter	Date	Description
4	-63613612	-63613612	0.0e+00	1e-07	Edward Rothberg	2020-11-25	Found with Gurobi 9.1 NoRel heuristics
3	-59923296	-59923263	4.3e-06	0e+00	Edward Rothberg	2020-05-15	Obtained with Gurobi 9.0 using the solution improvement heuristic
2	-59349778		0.0e+00	0e+00	Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	-52235914	-52235914	0.0e+00	0e+00	-	2018-10-13	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to polygonpack4-15 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
polygonpack4-10	open	20537	20517	20	65935	339036	Antonio Frangioni	polygonpack	-53594508.70758325*	numerics set_packing invariant_knapsack mixed_binary
polygonpack4-7	open	10788	10774	14	34529	178591	Antonio Frangioni	polygonpack	-51837712.9799564*	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
rocII-10-11	open	22968	22616	352	52692	604216	Joerg Rambau	rocI	-11.79399274280434*	aggregations precedence variable_bound set_partitioning set_packing mixed_binary

Reference

No bibliographic information available