polygonpack4-7: 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 (polygonpack4-7)

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

polygonpack4-7 Raw polygonpack4-7 Decomposed polygonpack4-7 Composite of MIC top 5 polygonpack4-7 Composite of MIPLIB top 5 polygonpack4-7 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.
polygonpack4-10 decomposed polygonpack4-15 decomposed polygonpack5-15 decomposed neos-4703857-ahuroa decomposed fhnw-schedule-paira400 decomposed
Name polygonpack4-10 [MIPLIB] polygonpack4-15 [MIPLIB] polygonpack5-15 [MIPLIB] neos-4703857-ahuroa [MIPLIB] fhnw-schedule-paira400 [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 / 0.248 2 / 0.294 3 / 0.392 4 / 0.396 5 / 0.410
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIC top 5.
polygonpack4-10 raw polygonpack4-15 raw polygonpack5-15 raw neos-4703857-ahuroa raw fhnw-schedule-paira400 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.
polygonpack4-10 decomposed polygonpack4-15 decomposed polygonpack5-15 decomposed glass4 decomposed polygonpack3-15 decomposed
Name polygonpack4-10 [MIPLIB] polygonpack4-15 [MIPLIB] polygonpack5-15 [MIPLIB] glass4 [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.
1 / 0.248 2 / 0.294 3 / 0.392 110 / 0.868 2* / 0.294*
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIPLIB top 5.
polygonpack4-10 raw polygonpack4-15 raw polygonpack5-15 raw glass4 raw polygonpack3-15 raw

Instance Summary

The table below contains summary information for polygonpack4-7, the five most similar instances to polygonpack4-7 according to the MIC, and the five most similar instances to polygonpack4-7 according to MIPLIB 2017.

INSTANCE SUBMITTER DESCRIPTION ISS RANK
Parent Instance 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. 0.000000 -
MIC Top 5 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. 0.247584 1
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. 0.293792 2
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. 0.391971 3
neos-4703857-ahuroa [MIPLIB] Jeff Linderoth (None provided) 0.395737 4
fhnw-schedule-paira400 [MIPLIB] Simon Felix Continuous-time project scheduling and selection, inspired by an industry use-case. Each project has a value, the sum should be maximized. Each project has a deadline, and an earliest start date. Three formulations of the same problem ("Pair A", "Pair B" and "Slot") - we expect "Pair B" to be the best formulation. 0.410260 5
MIPLIB Top 5 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. 0.247584 1
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. 0.293792 2
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. 0.391971 3
glass4 [MIPLIB] I. Luzzi Nesting instance 0.868314 110
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. 0.293792* 2*


polygonpack4-7: Instance-to-Model Comparison Results

Model Group Assignment from MIPLIB: polygonpack
Assigned Model Group Rank/ISS in the MIC: 3 / 0.605

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 / 0.499 2 / 0.600 3 / 0.606 4 / 0.904 5 / 0.953

Model Group Summary

The table below contains summary information for the five most similar model groups to polygonpack4-7 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 0.498719 1
rmatr Dmitry Krushinsky Model coming from a formulation of the p-Median problem using square cost matrices 0.600124 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. 0.605692 3
sp_product MIPLIB submission pool Imported from the MIPLIB2010 submissions. 0.903952 4
n37 J. Aronson Fixed charge transportation problem 0.952523 5


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

Updated August 16, 2019