core4872-1529: Instance-to-Instance Comparison Results

Type: Instance
Submitter: A. Caprara, M. Fischetti, P. Toth
Description: Set covering instance coming from Italian railway models
MIPLIB Entry

Parent Instance (core4872-1529)

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

core4872-1529 Raw core4872-1529 Decomposed core4872-1529 Composite of MIC top 5 core4872-1529 Composite of MIPLIB top 5 core4872-1529 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.
core2586-950 decomposed v150d30-2hopcds decomposed core4284-1064 decomposed core2536-691 decomposed pythago7824 decomposed
Name core2586-950 [MIPLIB] v150d30-2hopcds [MIPLIB] core4284-1064 [MIPLIB] core2536-691 [MIPLIB] pythago7824 [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 / 1.067 2 / 1.093 3 / 1.141 4 / 1.160 5 / 1.163
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIC top 5.
core2586-950 raw v150d30-2hopcds raw core4284-1064 raw core2536-691 raw pythago7824 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.
core2586-950 decomposed core4284-1064 decomposed core2536-691 decomposed rail507 decomposed ex1010-pi decomposed
Name core2586-950 [MIPLIB] core4284-1064 [MIPLIB] core2536-691 [MIPLIB] rail507 [MIPLIB] ex1010-pi [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 / 1.067 3 / 1.141 4 / 1.160 21 / 1.289 174 / 2.135
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIPLIB top 5.
core2586-950 raw core4284-1064 raw core2536-691 raw rail507 raw ex1010-pi raw

Instance Summary

The table below contains summary information for core4872-1529, the five most similar instances to core4872-1529 according to the MIC, and the five most similar instances to core4872-1529 according to MIPLIB 2017.

INSTANCE SUBMITTER DESCRIPTION ISS RANK
Parent Instance core4872-1529 [MIPLIB] A. Caprara, M. Fischetti, P. Toth Set covering instance coming from Italian railway models 0.000000 -
MIC Top 5 core2586-950 [MIPLIB] A. Caprara, M. Fischetti, P. Toth Set covering instance coming from Italian railway models 1.067499 1
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. 1.093423 2
core4284-1064 [MIPLIB] A. Caprara, M. Fischetti, P. Toth Set covering instance coming from Italian railway models 1.140869 3
core2536-691 [MIPLIB] A. Caprara, M. Fischetti, P. Toth Set covering instance coming from Italian railway models 1.160475 4
pythago7824 [MIPLIB] Felix J. L. Willamowski 2-coloring of Pythagorean triples 1.163357 5
MIPLIB Top 5 core2586-950 [MIPLIB] A. Caprara, M. Fischetti, P. Toth Set covering instance coming from Italian railway models 1.067499 1
core4284-1064 [MIPLIB] A. Caprara, M. Fischetti, P. Toth Set covering instance coming from Italian railway models 1.140869 3
core2536-691 [MIPLIB] A. Caprara, M. Fischetti, P. Toth Set covering instance coming from Italian railway models 1.160475 4
rail507 [MIPLIB] A. Caprara, M. Fischetti, P. Toth Railway crew scheduling 1.289126 21
ex1010-pi [MIPLIB] M. Winkler Logic synthesis problem from the 2010 SAT conference pseudo-Boolean competition 2.135462 174


core4872-1529: Instance-to-Model Comparison Results

Model Group Assignment from MIPLIB: core
Assigned Model Group Rank/ISS in the MIC: 39 / 2.176

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-48 Model group: neos-pseudoapplication-106 Model group: iis Model group: neos-pseudoapplication-78 Model group: 2hopcds
Name neos-pseudoapplication-48 neos-pseudoapplication-106 iis neos-pseudoapplication-78 2hopcds
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 / 1.494 2 / 1.567 3 / 1.616 4 / 1.687 5 / 1.713

Model Group Summary

The table below contains summary information for the five most similar model groups to core4872-1529 according to the MIC.

MODEL GROUP SUBMITTER DESCRIPTION ISS RANK
MIC Top 5 neos-pseudoapplication-48 NEOS Server Submission Imported from the MIPLIB2010 submissions. 1.493946 1
neos-pseudoapplication-106 Hans Mittelmann Collection of anonymous submissions to the NEOS Server for Optimization 1.567107 2
iis Marc Pfetsch 23 "middlehard" Set-Covering Models 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 models can be created. 1.615609 3
neos-pseudoapplication-78 Jeff Linderoth (None provided) 1.687066 4
2hopcds 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, models with as few as 120 variables are left unsolved after one hour using Gurobi 7.0.2. 1.712615 5


Updated August 16, 2019