polygonpack5-15

numerics precedence variable_bound set_packing invariant_knapsack mixed_binary

Submitter	Variables	Constraints	Density	Status	Group	Objective	MPS File
Antonio Frangioni	48163	163429	1.02238e-04	open	polygonpack	-55494653.8357854*	polygonpack5-15.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	48163	43825
Constraints	163429	154960
Binaries	48133	43795
Integers	0	0
Continuous	30	30
Implicit Integers	0	0
Fixed Variables	0	0
Nonzero Density	0.000102238	0.000111108
Nonzeroes	804740	754548

Constraint Classification Properties
	Original	Presolved
Total	163429	154960
Empty	2	0
Free	0	0
Singleton	0	0
Aggregations	0	0
Precedence	0	999
Variable Bound	0	1
Set Partitioning	0	0
Set Packing	15	14
Set Covering	0	0
Cardinality	0	0
Invariant Knapsack	1680	1568
Equation Knapsack	0	0
Bin Packing	0	0
Knapsack	0	0
Integer Knapsack	0	0
Mixed Binary	161732	152378
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	1.255273
Constraint %		0.000645	0.0384919	0.000645	0.434951
Variable %		0.004560	0.0118117	0.009130	0.034227
Score	0.006541

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
5	-55494654		7e-07	7e-07	0.00000	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
4	-54950356		0e+00	0e+00	0.00000	Edward Rothberg	2019-12-13	Obtained with Gurobi 9.0
3	-54836088	-54836101	0e+00	0e+00	0.62253	Frederic Didier	2020-01-22	Obtained with Google OR-tools using 8 Threads through generating subproblems by fixing part of the current solution and trying to solve them with a sub CP-SAT solver
2	-50940915		0e+00	0e+00	0.00000	Robert Ashford and Alkis Vazacopoulus	2019-12-18	Found using ODH\|CPlex
1	-46870192	-46870192	0e+00	0e+00	0.00000	-	2018-10-13	Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to polygonpack5-15 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
polygonpack3-15	open	44237	44207	30	144478	731949	Antonio Frangioni	polygonpack	-55055595.32367724*	numerics precedence variable_bound 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
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	-51837707.95034043*	numerics set_packing invariant_knapsack mixed_binary
rocII-10-11	open	22968	22616	352	52692	604216	Joerg Rambau	rocI	-11.78958471072697*	aggregations precedence variable_bound set_partitioning set_packing mixed_binary

Reference

No bibliographic information available