Instance - air05

air05: Instance-to-Instance Comparison Results

Type:	Instance
Submitter:	G. Astfalk
Description:	Airline crew scheduling set partitioning problem
	MIPLIB Entry


	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	v150d30-2hopcds [MIPLIB]	core2536-691 [MIPLIB]	air04 [MIPLIB]	core4284-1064 [MIPLIB]	fast0507 [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 / 0.901	2 / 0.907	3 / 0.916	4 / 0.958	5 / 0.972
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	air04 [MIPLIB]	mod010 [MIPLIB]	10teams [MIPLIB]	air03 [MIPLIB]	ds [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.	3 / 0.916	63 / 1.651	136 / 2.250	193 / 2.497	264 / 2.697
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 air05, the five most similar instances to air05 according to the MIC, and the five most similar instances to air05 according to MIPLIB 2017.

	INSTANCE	SUBMITTER	DESCRIPTION	ISS	RANK
Parent Instance	air05 [MIPLIB]	G. Astfalk	Airline crew scheduling set partitioning problem	0.000000	-
MIC Top 5	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.	0.900828	1
	core2536-691 [MIPLIB]	A. Caprara, M. Fischetti, P. Toth	Set covering instance coming from Italian railway models	0.906697	2
	air04 [MIPLIB]	G. Astfalk	Airline crew scheduling set partitioning problem	0.915764	3
	core4284-1064 [MIPLIB]	A. Caprara, M. Fischetti, P. Toth	Set covering instance coming from Italian railway models	0.958317	4
	fast0507 [MIPLIB]	MIPLIB submission pool	Imported from the MIPLIB2010 submissions.	0.972239	5
MIPLIB Top 5	air04 [MIPLIB]	G. Astfalk	Airline crew scheduling set partitioning problem	0.915764	3
	mod010 [MIPLIB]	MIPLIB submission pool	Imported from the MIPLIB2010 submissions.	1.651317	63
	10teams [MIPLIB]	MIPLIB submission pool	Imported from the MIPLIB2010 submissions.	2.249775	136
	air03 [MIPLIB]	G. Astfalk	Airline crew scheduling set partitioning problem	2.497183	193
	ds [MIPLIB]	MIPLIB submission pool	Imported from MIPLIB2003.	2.696610	264

air05: Instance-to-Model Comparison Results

Model Group Assignment from MIPLIB:	air
Assigned Model Group Rank/ISS in the MIC:	4 / 1.265

These are model group composite (MGC) images for the MIC top 5 model groups.
Name	iis	neos-pseudoapplication-106	2hopcds	air	assign1
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 / 1.021	2 / 1.057	3 / 1.116	4 / 1.266	5 / 1.297

Model Group Summary

The table below contains summary information for the five most similar model groups to air05 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.	1.021100	1
	neos-pseudoapplication-106	Hans Mittelmann	Collection of anonymous submissions to the NEOS Server for Optimization	1.056805	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.	1.116288	3
	air	G. Astfalk	Airline crew scheduling set partitioning problem	1.265727	4
	assign1	Robert Fourer	Imported from the MIPLIB2010 submissions.	1.297475	5

air05: Instance-to-Instance Comparison Results

Parent Instance (air05)

MIC Top 5 Instances

MIPLIB Top 5 Instances

Instance Summary

air05: Instance-to-Model Comparison Results

MIC Top 5 Model Groups

Model Group Summary