Submitter Variables Constraints Density Status Group Objective MPS File
Antonio Frangioni 44237 144478 1.14523e-04 open polygonpack -52235913.799* 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.

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.

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.

ID Objective Exact Int. Viol Cons. Viol Obj. Viol Submitter Date Description
1 -52235914 -52235914 0 0 0 - 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 Variables Binaries Integers Continuous Constraints Nonz. Submitter Group Status Objective
polygonpack4-10 20537 20517 0 20 65935 339036 Antonio Frangioni polygonpack open -53594065.703*
polygonpack4-7 10788 10774 0 14 34529 178591 Antonio Frangioni polygonpack open -51837707.95*
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*
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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