seymour: Instance-to-Instance Comparison Results

Type: Instance
Submitter: W. Cook, P. Seymour
Description: A set-covering problem that arose from work related to the proof of the 4-color theorem.
MIPLIB Entry

Parent Instance (seymour)

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

seymour Raw seymour Decomposed seymour Composite of MIC top 5 seymour Composite of MIPLIB top 5 seymour 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.
seymour1 decomposed neos5 decomposed f2gap401600 decomposed f2gap801600 decomposed ta2-UUE decomposed
Name seymour1 [MIPLIB] neos5 [MIPLIB] f2gap401600 [MIPLIB] f2gap801600 [MIPLIB] ta2-UUE [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 / 1.246 2 / 1.452 3 / 1.467 4 / 1.484 5 / 1.503
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIC top 5.
seymour1 raw neos5 raw f2gap401600 raw f2gap801600 raw ta2-UUE 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.
glass-sc decomposed iis-glass-cov decomposed iis-hc-cov decomposed ramos3 decomposed v150d30-2hopcds decomposed
Name glass-sc [MIPLIB] iis-glass-cov [MIPLIB] iis-hc-cov [MIPLIB] ramos3 [MIPLIB] v150d30-2hopcds [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.
31 / 1.696 37 / 1.727 52 / 1.778 132 / 1.958 313 / 2.108
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIPLIB top 5.
glass-sc raw iis-glass-cov raw iis-hc-cov raw ramos3 raw v150d30-2hopcds raw

Instance Summary

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

INSTANCE SUBMITTER DESCRIPTION ISS RANK
Parent Instance seymour [MIPLIB] W. Cook, P. Seymour A set-covering problem that arose from work related to the proof of the 4-color theorem. 0.000000 -
MIC Top 5 seymour1 [MIPLIB] MIPLIB submission pool Imported from the MIPLIB2010 submissions. 1.245523 1
neos5 [MIPLIB] NEOS Server Submission Imported from the MIPLIB2010 submissions. 1.451997 2
f2gap401600 [MIPLIB] Salim Haddadi Restrictions of well-known hard generalized assignment problem instances (D10400,D20400,D40400,D15900,D30900,D60900,D201600,D401600,D801600) 1.466811 3
f2gap801600 [MIPLIB] Salim Haddadi Restrictions of well-known hard generalized assignment problem instances (D10400,D20400,D40400,D15900,D30900,D60900,D201600,D401600,D801600) 1.483749 4
ta2-UUE [MIPLIB] MIPLIB submission pool Imported from the MIPLIB2010 submissions. 1.502643 5
MIPLIB Top 5 glass-sc [MIPLIB] Marc Pfetsch Set covering problems arising from a Benders algorithm for finding maximum feasible subsystems. More details on the generation is given in the README file in the tarball. 1.695984 31
iis-glass-cov [MIPLIB] Marc Pfetsch 23 "middlehard" Set-Covering Instances for MIPLIB: they have a small number of variables compared to the number of constraints and CPLEX 12.1 needs about one hour to solve them.For more information, have a look into the readme file which explains how the instances can be created. 1.727279 37
iis-hc-cov [MIPLIB] Marc Pfetsch 23 "middlehard" Set-Covering Instances for MIPLIB: they have a small number of variables compared to the number of constraints and CPLEX 12.1 needs about one hour to solve them.For more information, have a look into the readme file which explains how the instances can be created. 1.778229 52
ramos3 [MIPLIB] F. Ramos Set covering problem from a product manufacturing application 1.957550 132
v150d30-2hopcds [MIPLIB] Austin Buchanan A problem in wireless networks. The objective is to select a minimum number of relay nodes so that any two nonadjacent nodes can communicate by way of the chosen relay nodes in at most s hops, where s is a problem input. The 2-hop case of this problem can be formulated as a set cover/hitting set problem with n binary variables and n^2 constraints: _{ k N(i) N(j) } x_k 1 for nonadjacent node pairs {i,j}. Despite the formulation's simplicity, instances with as few as 120 variables are left unsolved after one hour using Gurobi 7.0.2. 2.108225 313


seymour: Instance-to-Model Comparison Results

Model Group Assignment from MIPLIB: no model group assignment
Assigned Model Group Rank/ISS in the MIC: N.A. / N.A.

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: neos-pseudoapplication-21 Model group: generated Model group: independentset Model group: neos-pseudoapplication-66 Model group: neos-pseudoapplication-101
Name neos-pseudoapplication-21 generated independentset neos-pseudoapplication-66 neos-pseudoapplication-101
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 / 1.850 2 / 1.857 3 / 1.924 4 / 1.985 5 / 2.024

Model Group Summary

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

MODEL GROUP SUBMITTER DESCRIPTION ISS RANK
MIC Top 5 neos-pseudoapplication-21 NEOS Server Submission Imported from the MIPLIB2010 submissions. 1.849657 1
generated Simon Bowly Randomly generated integer and binary programming models. These results are part of an early phase of work aimed at generating diverse and challenging MIP models for experimental testing. We have aimed to produce small integer and binary programming models which are reasonably difficult to solve and have varied structure, eliciting a range of behaviour in state of the art algorithms. 1.856920 2
independentset Toni Sorrell These models are based on Neil Sloane's Challenge problems: Independent Sets in Graphs. 1.924055 3
neos-pseudoapplication-66 NEOS Server Submission Imported from the MIPLIB2010 submissions. 1.985293 4
neos-pseudoapplication-101 NEOS Server Submission Model coming from the NEOS Server with unknown application. Infeasibility claimed by CPLEX 12.6 and CPLEX 12.6.1 with extreme numerical caution emphasi after 4 and 2 hours computation, respectively. 2.023645 5


Updated August 16, 2019