polygonpack5-15: Instance-to-Instance Comparison Results

Type: Instance
Submitter: Antonio Frangioni
Description: 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.
MIPLIB Entry

Parent Instance (polygonpack5-15)

All other instances below were be compared against this "query" instance.

polygonpack5-15 Raw polygonpack5-15 Decomposed polygonpack5-15 Composite of MIC top 5 polygonpack5-15 Composite of MIPLIB top 5 polygonpack5-15 Model Group Composite
Raw This is the CCM image before the decomposition procedure has been applied.
Decomposed This is the CCM image after a decomposition procedure has been applied. This is the image used by the MIC's image-based comparisons for this query instance.
Composite of MIC Top 5 Composite of the five decomposed CCM images from the MIC Top 5.
Composite of MIPLIB Top 5 Composite of the five decomposed CCM images from the MIPLIB Top 5.
Model Group Composite Image Composite of the decomposed CCM images for every instance in the same model group as this query.

MIC Top 5 Instances

These are the 5 decomposed CCM images that are most similar to decomposed CCM image for the the query instance, according to the ISS metric.

Decomposed These decomposed images were created by GCG.
neos-3209462-rhin decomposed rmatr200-p20 decomposed rmatr200-p10 decomposed rmatr200-p5 decomposed neos-4703857-ahuroa decomposed
Name neos-3209462-rhin [MIPLIB] rmatr200-p20 [MIPLIB] rmatr200-p10 [MIPLIB] rmatr200-p5 [MIPLIB] neos-4703857-ahuroa [MIPLIB]
Rank / ISS The image-based structural similarity (ISS) metric measures the Euclidean distance between the image-based feature vectors for the query instance and all other instances. A smaller ISS value indicates greater similarity.
1 / 0.235 2 / 0.236 3 / 0.248 4 / 0.260 5 / 0.304
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIC top 5.
neos-3209462-rhin raw rmatr200-p20 raw rmatr200-p10 raw rmatr200-p5 raw neos-4703857-ahuroa raw

MIPLIB Top 5 Instances

These are the 5 instances that are most closely related to the query instance, according to the instance statistic-based similarity measure employed by MIPLIB 2017

Decomposed These decomposed images were created by GCG.
polygonpack4-7 decomposed polygonpack4-15 decomposed polygonpack4-10 decomposed rocII-10-11 decomposed polygonpack3-15 decomposed
Name polygonpack4-7 [MIPLIB] polygonpack4-15 [MIPLIB] polygonpack4-10 [MIPLIB] rocII-10-11 [MIPLIB] polygonpack3-15* [MIPLIB]
Rank / ISS The image-based structural similarity (ISS) metric measures the Euclidean distance between the image-based feature vectors for the query instance and all model groups. A smaller ISS value indicates greater similarity.
10 / 0.392 12 / 0.403 14 / 0.437 594 / 1.608 12* / 0.403*
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIPLIB top 5.
polygonpack4-7 raw polygonpack4-15 raw polygonpack4-10 raw rocII-10-11 raw polygonpack3-15 raw

Instance Summary

The table below contains summary information for polygonpack5-15, the five most similar instances to polygonpack5-15 according to the MIC, and the five most similar instances to polygonpack5-15 according to MIPLIB 2017.

INSTANCE SUBMITTER DESCRIPTION ISS RANK
Parent Instance polygonpack5-15 [MIPLIB] Antonio Frangioni 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. 0.000000 -
MIC Top 5 neos-3209462-rhin [MIPLIB] Jeff Linderoth (None provided) 0.235424 1
rmatr200-p20 [MIPLIB] Dmitry Krushinsky Instance coming from a formulation of the p-Median problem using square cost matrices. Solved using ug[SCIP/spx], a distributed massively parallel version of SCIP run on 2,000 cores at the HLRN-II super computer facility. 0.235726 2
rmatr200-p10 [MIPLIB] Dmitry Krushinsky Instance coming from a formulation of the p-Median problem using square cost matrices. Solved by Gurobi 4.6.1 (12 threads) in 19644 seconds (January 2012). 0.247760 3
rmatr200-p5 [MIPLIB] Dmitry Krushinsky Instance coming from a formulation of the p-Median problem using square cost matrices 0.260176 4
neos-4703857-ahuroa [MIPLIB] Jeff Linderoth (None provided) 0.304198 5
MIPLIB Top 5 polygonpack4-7 [MIPLIB] Antonio Frangioni 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. 0.391971 10
polygonpack4-15 [MIPLIB] Antonio Frangioni 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. 0.402567 12
polygonpack4-10 [MIPLIB] Antonio Frangioni 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. 0.437259 14
rocII-10-11 [MIPLIB] Joerg Rambau Optimal control model in the deterministic dynamic system given by bounded-confidence dynamics in a system of opinions 1.608157 594
polygonpack3-15* [MIPLIB] Antonio Frangioni 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. 0.402567* 12*


polygonpack5-15: Instance-to-Model Comparison Results

Model Group Assignment from MIPLIB: polygonpack
Assigned Model Group Rank/ISS in the MIC: 3 / 0.649

MIC Top 5 Model Groups

These are the 5 model group composite (MGC) images that are most similar to the decomposed CCM image for the query instance, according to the ISS metric.

These are model group composite (MGC) images for the MIC top 5 model groups.
Model group: map Model group: rmatr Model group: polygonpack Model group: sp_product Model group: n37
Name map rmatr polygonpack sp_product n37
Rank / ISS The image-based structural similarity (ISS) metric measures the Euclidean distance between the image-based feature vectors for the query instance and all other instances. A smaller ISS value indicates greater similarity.
1 / 0.361 2 / 0.430 3 / 0.650 4 / 0.871 5 / 0.910

Model Group Summary

The table below contains summary information for the five most similar model groups to polygonpack5-15 according to the MIC.

MODEL GROUP SUBMITTER DESCRIPTION ISS RANK
MIC Top 5 map Kiyan Ahmadizadeh Land parcel selection problems motivated by Red-Cockaded Woodpecker conservation problem 0.361463 1
rmatr Dmitry Krushinsky Model coming from a formulation of the p-Median problem using square cost matrices 0.430441 2
polygonpack Antonio Frangioni 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. Model 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. 0.649994 3
sp_product MIPLIB submission pool Imported from the MIPLIB2010 submissions. 0.870924 4
n37 J. Aronson Fixed charge transportation problem 0.910295 5


* polygonpack3-15 is a duplicate of polygonpack4-15.

Updated August 16, 2019