Submitter Variables Constraints Density Status Group Objective MPS File
Antonio Frangioni 48163 163429 1.02238e-04 open polygonpack -46870192.424* 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.

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.

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.

ID Objective Exact Int. Viol Cons. Viol Obj. Viol Submitter Date Description
1 -46870192 -46870192 0 0 0 - 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 Variables Binaries Integers Continuous Constraints Nonz. Submitter Group Status Objective
polygonpack3-15 44237 44207 0 30 144478 731949 Antonio Frangioni polygonpack open -48143434.86572*
polygonpack4-15 44237 44207 0 30 144478 731949 Antonio Frangioni polygonpack open -52235913.799*
polygonpack4-10 20537 20517 0 20 65935 339036 Antonio Frangioni polygonpack open -53594065.703*
polygonpack4-7 10788 10774 0 14 34529 178591 Antonio Frangioni polygonpack open -51837707.95*
rocII-10-11 22968 22616 0 352 52692 604216 Joerg Rambau rocI open -8.736476098504*

Reference

No bibliographic information available

Last Update Nov 19, 2018 by Gregor Hendel
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