Instance - core2586-950


	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.

Decomposed These decomposed images were created by GCG.
Name	pythago7824 [MIPLIB]	v150d30-2hopcds [MIPLIB]	scpj4scip [MIPLIB]	pythago7825 [MIPLIB]	core2536-691 [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 / 0.902	2 / 0.902	3 / 0.925	4 / 0.928	5 / 0.929
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIC top 5.

Decomposed These decomposed images were created by GCG.
Name	core2536-691 [MIPLIB]	core4284-1064 [MIPLIB]	core4872-1529 [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.	5 / 0.929	9 / 0.982	15 / 1.067	20 / 1.096	157 / 1.990
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIPLIB top 5.

Instance Summary

The table below contains summary information for core2586-950, the five most similar instances to core2586-950 according to the MIC, and the five most similar instances to core2586-950 according to MIPLIB 2017.

	INSTANCE	SUBMITTER	DESCRIPTION	ISS	RANK
Parent Instance	core2586-950 [MIPLIB]	A. Caprara, M. Fischetti, P. Toth	Set covering instance coming from Italian railway models	0.000000	-
MIC Top 5	pythago7824 [MIPLIB]	Felix J. L. Willamowski	2-coloring of Pythagorean triples	0.901885	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.	0.902380	2
	scpj4scip [MIPLIB]	Shunji Umetani	This is a random test instance generator for SCP using the scheme of the following paper, namely the column cost c[j] are integer randomly generated from [1,100]; every column covers at least one row; and every row is covered by at least two columns. see reference: E. Balas and A. Ho, Set covering algorithms using cutting planes, heuristics, and subgradient optimization: A computational study, Mathematical Programming, 12 (1980), 37-60. We have newly generated Classes I-N with the following parameter values, where each class has five instances. We have also generated reduced instances by a standard pricing method in the following paper: S. Umetani and M. Yagiura, Relaxation heuristics for the set covering problem, Journal of the Operations Research Society of Japan, 50 (2007), 350-375. You can obtain the instance generator program from the following web site. https://sites.google.com/site/shunjiumetani/benchmark	0.924961	3
	pythago7825 [MIPLIB]	Felix J. L. Willamowski	2-coloring of Pythagorean triples	0.928290	4
	core2536-691 [MIPLIB]	A. Caprara, M. Fischetti, P. Toth	Set covering instance coming from Italian railway models	0.928663	5
MIPLIB Top 5	core2536-691 [MIPLIB]	A. Caprara, M. Fischetti, P. Toth	Set covering instance coming from Italian railway models	0.928663	5
	core4284-1064 [MIPLIB]	A. Caprara, M. Fischetti, P. Toth	Set covering instance coming from Italian railway models	0.982304	9
	core4872-1529 [MIPLIB]	A. Caprara, M. Fischetti, P. Toth	Set covering instance coming from Italian railway models	1.067499	15
	rail507 [MIPLIB]	A. Caprara, M. Fischetti, P. Toth	Railway crew scheduling	1.096474	20
	ex1010-pi [MIPLIB]	M. Winkler	Logic synthesis problem from the 2010 SAT conference pseudo-Boolean competition	1.990402	157

These are model group composite (MGC) images for the MIC top 5 model groups.
Name	iis	neos-pseudoapplication-106	2hopcds	assign1	neos-pseudoapplication-103
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 / 1.187	2 / 1.205	3 / 1.211	4 / 1.361	5 / 1.390

Model Group Summary

The table below contains summary information for the five most similar model groups to core2586-950 according to the MIC.

	MODEL GROUP	SUBMITTER	DESCRIPTION	ISS	RANK
MIC Top 5	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.	1.187090	1
	neos-pseudoapplication-106	Hans Mittelmann	Collection of anonymous submissions to the NEOS Server for Optimization	1.204763	2
	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.	1.210583	3
	assign1	Robert Fourer	Imported from the MIPLIB2010 submissions.	1.360679	4
	neos-pseudoapplication-103	Hans Mittelmann	Collection of anonymous submissions to the NEOS Server for Optimization	1.390354	5

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

Model Group Assignment from MIPLIB:	core
Assigned Model Group Rank/ISS in the MIC:	42 / 2.055

core2586-950: Instance-to-Instance Comparison Results

Parent Instance (core2586-950)

MIC Top 5 Instances

MIPLIB Top 5 Instances

Instance Summary

core2586-950: Instance-to-Model Comparison Results

MIC Top 5 Model Groups

Model Group Summary