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a2864-99blp: Instance-to-Instance Comparison Results
| Type: | Instance |
| Submitter: | Daniel Heinlein |
| Description: | Clique problems arising from a selection problem of subspaces in the PG(7,2) with different prescribed variables and numerically instable linear programming relaxation. |
| MIPLIB Entry |
Parent Instance (a2864-99blp)
All other instances below were be compared against this "query" instance.  |
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Raw
This is the CCM image before the decomposition procedure has been applied.
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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.
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Composite of MIC Top 5
Composite of the five decomposed CCM images from the MIC Top 5.
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Composite of MIPLIB Top 5
Composite of the five decomposed CCM images from the MIPLIB Top 5.
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Model Group Composite Image
Composite of the decomposed CCM images for every instance in the same model group as this query.
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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.
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| Name | neos-4760493-puerua [MIPLIB] | v150d30-2hopcds [MIPLIB] | air04 [MIPLIB] | air05 [MIPLIB] | fast0507 [MIPLIB] | |
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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.
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1 / 1.344 | 2 / 1.395 | 3 / 1.397 | 4 / 1.398 | 5 / 1.404 | |
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Raw
These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIC top 5.
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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.
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| Name | sorrell7 [MIPLIB] | sorrell3 [MIPLIB] | cod105 [MIPLIB] | cdc7-4-3-2 [MIPLIB] | z26 [MIPLIB] | |
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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.
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28 / 1.644 | 49 / 1.827 | 67 / 2.014 | 72 / 2.067 | 73 / 2.077 | |
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Raw
These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIPLIB top 5.
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Instance Summary
The table below contains summary information for a2864-99blp, the five most similar instances to a2864-99blp according to the MIC, and the five most similar instances to a2864-99blp according to MIPLIB 2017.
| INSTANCE | SUBMITTER | DESCRIPTION | ISS | RANK | |
|---|---|---|---|---|---|
| Parent Instance | a2864-99blp [MIPLIB] | Daniel Heinlein | Clique problems arising from a selection problem of subspaces in the PG(7,2) with different prescribed variables and numerically instable linear programming relaxation. | 0.000000 | - |
| MIC Top 5 | neos-4760493-puerua [MIPLIB] | Hans Mittelmann | Collection of anonymous submissions to the NEOS Server for Optimization | 1.344420 | 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. | 1.394731 | 2 | |
| air04 [MIPLIB] | G. Astfalk | Airline crew scheduling set partitioning problem | 1.397458 | 3 | |
| air05 [MIPLIB] | G. Astfalk | Airline crew scheduling set partitioning problem | 1.398163 | 4 | |
| fast0507 [MIPLIB] | MIPLIB submission pool | Imported from the MIPLIB2010 submissions. | 1.404050 | 5 | |
| MIPLIB Top 5 | sorrell7 [MIPLIB] | Toni Sorrell | These instances are based on Neil Sloane's Challenge problems: Independent Sets in Graphs. | 1.644407 | 28 |
| sorrell3 [MIPLIB] | Toni Sorrell | These instances are based on Neil Sloane's Challenge problems: Independent Sets in Graphs. | 1.827124 | 49 | |
| cod105 [MIPLIB] | MIPLIB submission pool | Imported from the MIPLIB2010 submissions. | 2.013539 | 67 | |
| cdc7-4-3-2 [MIPLIB] | Sascha Kurz | Codes for Networkcoding A constant dimension code with parameters n, k, d and q is a collection of k-dimensional subspaces of the n-dimensional vector space \\(GF(q)^n\\) over a finite field with q elements, called codewords, such that the dimension of the intersection of each pair of different k-dimensional subspaces is at most \\(k-d/2\\). Let \\(A_q(n,d;k)\\) denote the maximum number of codewords. For instance cdc6-4-3-2 \\(A_2(6,4;3)=77\\) is known , while \\(333 \\le A_2(7,4;3) \\le 381\\) for instance cdc7-4-3-2 are the tightest known bounds, see e.g. . A code of size 381 would correspond to a putative binary q-analog of the Fano plane (finite projective plane of order 2 with 7 points and lines). More bounds are available at http://subspacecodes.uni-bayreuth.de. | 2.066876 | 72 | |
| 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. | 2.076868 | 73 |
a2864-99blp: Instance-to-Model Comparison Results
| Model Group Assignment from MIPLIB: | selofsubspaces |
| Assigned Model Group Rank/ISS in the MIC: | 1 / 0.0 |
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.
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| Name | selofsubspaces | neos-pseudoapplication-23 | 2hopcds | neos-pseudoapplication-103 | iis | |
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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.
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1 / 0.000 | 2 / 1.554 | 3 / 1.672 | 4 / 1.686 | 5 / 1.708 |
Model Group Summary
The table below contains summary information for the five most similar model groups to a2864-99blp according to the MIC.
| MODEL GROUP | SUBMITTER | DESCRIPTION | ISS | RANK | |
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| MIC Top 5 | selofsubspaces | Daniel Heinlein | Clique problems arising from a selection problem of subspaces in the PG(7,2) with different prescribed variables and numerically instable linear programming relaxation. | 0.000000 | 1 |
| neos-pseudoapplication-23 | NEOS Server Submission | Imported from the MIPLIB2010 submissions. | 1.553601 | 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. | 1.672127 | 3 | |
| neos-pseudoapplication-103 | Hans Mittelmann | Collection of anonymous submissions to the NEOS Server for Optimization | 1.685859 | 4 | |
| 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. | 1.707676 | 5 |
