Instance - sorrell4


	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	scpk4 [MIPLIB]	scpj4scip [MIPLIB]	eilC76-2 [MIPLIB]	core2536-691 [MIPLIB]	core4284-1064 [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 / 0.316	2 / 0.336	3 / 0.746	4 / 0.750	5 / 0.764
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	sorrell7 [MIPLIB]	sorrell3 [MIPLIB]	z26 [MIPLIB]	manna81 [MIPLIB]	sorrell8 [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.	52 / 1.411	83 / 1.692	91 / 1.744	228 / 2.309	610 / 2.764
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 sorrell4, the five most similar instances to sorrell4 according to the MIC, and the five most similar instances to sorrell4 according to MIPLIB 2017.

	INSTANCE	SUBMITTER	DESCRIPTION	ISS	RANK
Parent Instance	sorrell4 [MIPLIB]	Toni Sorrell	These instances are based on Neil Sloane's Challenge problems: Independent Sets in Graphs.	0.000000	-
MIC Top 5	scpk4 [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	0.315854	1
	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	0.336116	2
	eilC76-2 [MIPLIB]	J. Linderoth	Set partitioning problem approximation for capicated vehicle routing problem instance from TSPLIB Imported from the MIPLIB2010 submissions.	0.745788	3
	core2536-691 [MIPLIB]	A. Caprara, M. Fischetti, P. Toth	Set covering instance coming from Italian railway models	0.750026	4
	core4284-1064 [MIPLIB]	A. Caprara, M. Fischetti, P. Toth	Set covering instance coming from Italian railway models	0.764282	5
MIPLIB Top 5	sorrell7 [MIPLIB]	Toni Sorrell	These instances are based on Neil Sloane's Challenge problems: Independent Sets in Graphs.	1.410523	52
	sorrell3 [MIPLIB]	Toni Sorrell	These instances are based on Neil Sloane's Challenge problems: Independent Sets in Graphs.	1.692492	83
	z26 [MIPLIB]	Daniel Bienstock	Set packing problem arising from the ongoing "Frequency Spectrum Auction" in the U.S. Work is collaboration with Ion Media Networks, Inc.	1.744451	91
	manna81 [MIPLIB]	MIPLIB submission pool	Imported from the MIPLIB2010 submissions.	2.308858	228
	sorrell8 [MIPLIB]	Toni Sorrell	These instances are based on Neil Sloane's Challenge problems: Independent Sets in Graphs.	2.763618	610

These are model group composite (MGC) images for the MIC top 5 model groups.
Name	2hopcds	f2gap	neos-pseudoapplication-106	iis	independentset
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 / 0.759	2 / 0.984	3 / 1.006	4 / 1.018	5 / 1.050

Model Group Summary

The table below contains summary information for the five most similar model groups to sorrell4 according to the MIC.

	MODEL GROUP	SUBMITTER	DESCRIPTION	ISS	RANK
MIC Top 5	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.	0.759336	1
	f2gap	Salim Haddadi	Restrictions of well-known hard generalized assignment problem models (D10400,D20400,D40400,D15900,D30900,D60900,D201600,D401600,D801600)	0.983894	2
	neos-pseudoapplication-106	Hans Mittelmann	Collection of anonymous submissions to the NEOS Server for Optimization	1.006033	3
	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.	1.017682	4
	independentset	Toni Sorrell	These models are based on Neil Sloane's Challenge problems: Independent Sets in Graphs.	1.050325	5

Type:	Instance
Submitter:	Toni Sorrell
Description:	These instances are based on Neil Sloane's Challenge problems: Independent Sets in Graphs.
	MIPLIB Entry

sorrell4: Instance-to-Instance Comparison Results

Parent Instance (sorrell4)

MIC Top 5 Instances

MIPLIB Top 5 Instances

Instance Summary

sorrell4: Instance-to-Model Comparison Results

MIC Top 5 Model Groups

Model Group Summary

Model Group Assignment from MIPLIB:	independentset
Assigned Model Group Rank/ISS in the MIC:	5 / 1.050