Submitter Variables Constraints Density Status Group Objective MPS File
Antonio Frangioni 10788 34529 4.7944e-04 open polygonpack -51837707.95* polygonpack4-7.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 10788 10788
Constraints 34529 34508
Binaries 10774 10774
Integers 0 0
Continuous 14 14
Implicit Integers 0 0
Fixed Variables 0 0
Nonzero Density 0.000479440 0.000479469
Nonzeroes 178591 178493
Constraint Classification Properties
Original Presolved
Total 34529 34508
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 7 7
Set Covering 0 0
Cardinality 0 0
Invariant Knapsack 336 336
Equation Knapsack 0 0
Bin Packing 0 0
Knapsack 0 0
Integer Knapsack 0 0
Mixed Binary 34186 34165
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 0.903090
Constraint % 0.0029000 0.0029000 0.0029000 0.0029000
Variable % 0.0370782 0.0370782 0.0370782 0.0370782
Score 0.000203

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 -51837708 -51837708 0 0 0 - 2018-10-13 Solution found during MIPLIB2017 problem selection.

Similar instances in collection

The following instances are most similar to polygonpack4-7 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
polygonpack4-10 20537 20517 0 20 65935 339036 Antonio Frangioni polygonpack open -53594065.703*
polygonpack4-15 44237 44207 0 30 144478 731949 Antonio Frangioni polygonpack open -52235913.799*
polygonpack3-15 44237 44207 0 30 144478 731949 Antonio Frangioni polygonpack open -48143434.86572*
polygonpack5-15 48163 48133 0 30 163429 804740 Antonio Frangioni polygonpack open -46870192.424*
glass4 322 302 0 20 396 1815 I. Luzzi easy 1200012600

Reference

No bibliographic information available

Last Update Nov 19, 2018 by Gregor Hendel
generated with R Markdown
© 2018 by Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB)
Imprint