square31: Instance-to-Instance Comparison Results

Type: Instance
Submitter: Sascha Kurz
Description: Squaring the square For a given integer n, determine the minimum number of squares in a tiling of an \\(n\\times n\\) square using using only integer sided squares of smaller size. (Although the models get quite large even for moderate n, they can be solved to optimality for all \\(n \\le 61\\), while challenging the MIP solver, especially the presolver.)
MIPLIB Entry

Parent Instance (square31)

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

square31 Raw square31 Decomposed square31 Composite of MIC top 5 square31 Composite of MIPLIB top 5 square31 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.
square37 decomposed square41 decomposed square47 decomposed square23 decomposed gsvm2rl3 decomposed
Name square37 [MIPLIB] square41 [MIPLIB] square47 [MIPLIB] square23 [MIPLIB] gsvm2rl3 [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 / 0.179 2 / 0.245 3 / 0.333 4 / 0.340 5 / 0.790
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIC top 5.
square37 raw square41 raw square47 raw square23 raw gsvm2rl3 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.
square37 decomposed square41 decomposed square47 decomposed square23 decomposed ivu52 decomposed
Name square37 [MIPLIB] square41 [MIPLIB] square47 [MIPLIB] square23 [MIPLIB] ivu52 [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 / 0.179 2 / 0.245 3 / 0.333 4 / 0.340 990 / 4.492
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIPLIB top 5.
square37 raw square41 raw square47 raw square23 raw ivu52 raw

Instance Summary

The table below contains summary information for square31, the five most similar instances to square31 according to the MIC, and the five most similar instances to square31 according to MIPLIB 2017.

INSTANCE SUBMITTER DESCRIPTION ISS RANK
Parent Instance square31 [MIPLIB] Sascha Kurz Squaring the square For a given integer n, determine the minimum number of squares in a tiling of an \\(n\\times n\\) square using using only integer sided squares of smaller size. (Although the models get quite large even for moderate n, they can be solved to optimality for all \\(n \\le 61\\), while challenging the MIP solver, especially the presolver.) 0.000000 -
MIC Top 5 square37 [MIPLIB] Sascha Kurz Squaring the square For a given integer n, determine the minimum number of squares in a tiling of an \\(n\\times n\\) square using using only integer sided squares of smaller size. (Although the models get quite large even for moderate n, they can be solved to optimality for all \\(n \\le 61\\), while challenging the MIP solver, especially the presolver.) 0.178914 1
square41 [MIPLIB] Sascha Kurz Squaring the square For a given integer n, determine the minimum number of squares in a tiling of an \\(n\\times n\\) square using using only integer sided squares of smaller size. (Although the models get quite large even for moderate n, they can be solved to optimality for all \\(n \\le 61\\), while challenging the MIP solver, especially the presolver.) 0.245068 2
square47 [MIPLIB] Sascha Kurz Squaring the square For a given integer n, determine the minimum number of squares in a tiling of an \\(n\\times n\\) square using using only integer sided squares of smaller size. (Although the models get quite large even for moderate n, they can be solved to optimality for all \\(n \\le 61\\), while challenging the MIP solver, especially the presolver.) 0.332586 3
square23 [MIPLIB] Sascha Kurz Squaring the square For a given integer n, determine the minimum number of squares in a tiling of an \\(n\\times n\\) square using using only integer sided squares of smaller size. (Although the models get quite large even for moderate n, they can be solved to optimality for all \\(n \\le 61\\), while challenging the MIP solver, especially the presolver.) 0.339758 4
gsvm2rl3 [MIPLIB] Toni Sorrell Suport vector machine with ramp loss. GSVM2-RL is the formulation found in Hess E. and Brooks P. (2015) paper, The Support Vector Machine and Mixed Integer Linear Programming: Ramp Loss SVM with L1-Norm Regularization 0.790408 5
MIPLIB Top 5 square37 [MIPLIB] Sascha Kurz Squaring the square For a given integer n, determine the minimum number of squares in a tiling of an \\(n\\times n\\) square using using only integer sided squares of smaller size. (Although the models get quite large even for moderate n, they can be solved to optimality for all \\(n \\le 61\\), while challenging the MIP solver, especially the presolver.) 0.178914 1
square41 [MIPLIB] Sascha Kurz Squaring the square For a given integer n, determine the minimum number of squares in a tiling of an \\(n\\times n\\) square using using only integer sided squares of smaller size. (Although the models get quite large even for moderate n, they can be solved to optimality for all \\(n \\le 61\\), while challenging the MIP solver, especially the presolver.) 0.245068 2
square47 [MIPLIB] Sascha Kurz Squaring the square For a given integer n, determine the minimum number of squares in a tiling of an \\(n\\times n\\) square using using only integer sided squares of smaller size. (Although the models get quite large even for moderate n, they can be solved to optimality for all \\(n \\le 61\\), while challenging the MIP solver, especially the presolver.) 0.332586 3
square23 [MIPLIB] Sascha Kurz Squaring the square For a given integer n, determine the minimum number of squares in a tiling of an \\(n\\times n\\) square using using only integer sided squares of smaller size. (Although the models get quite large even for moderate n, they can be solved to optimality for all \\(n \\le 61\\), while challenging the MIP solver, especially the presolver.) 0.339758 4
ivu52 [MIPLIB] S. Weider Set partitioning instance resulting from a column generation algorithm used for duty scheduling in public transportation. Solved in June 2014 using CPLEX 12.6 with 48 threads in about 25 days. 4.491994 990


square31: Instance-to-Model Comparison Results

Model Group Assignment from MIPLIB: square
Assigned Model Group Rank/ISS in the MIC: 1 / 0.639

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: square Model group: supportvectormachine Model group: drayage Model group: neos-pseudoapplication-2 Model group: neos-pseudoapplication-74
Name square supportvectormachine drayage neos-pseudoapplication-2 neos-pseudoapplication-74
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 / 0.639 2 / 1.292 3 / 1.300 4 / 1.378 5 / 1.382

Model Group Summary

The table below contains summary information for the five most similar model groups to square31 according to the MIC.

MODEL GROUP SUBMITTER DESCRIPTION ISS RANK
MIC Top 5 square Sascha Kurz Squaring the square For a given integer n, determine the minimum number of squares in a tiling of an \\(n\\times n\\) square using using only integer sided squares of smaller size. (Although the models get quite large even for moderate n, they can be solved to optimality for all \\(n \\le 61\\), while challenging the MIP solver, especially the presolver.) 0.639050 1
supportvectormachine Toni Sorrell Suport vector machine with ramp loss. GSVM2-RL is the formulation found in Hess E. and Brooks P. (2015) paper, The Support Vector Machine and Mixed Integer Linear Programming: Ramp Loss SVM with L1-Norm Regularization 1.292026 2
drayage F. Jordan Srour The .rar file contains three folders: 1) R_mps with all of the models (165, organized into 5 groups R0_, R25_, R50_, R75_, and R100_*), 2) results_and_runtimes with datafiles on the runtime and results, and 3) doc with documentation on the models in the form of a pdf. 1.300292 3
neos-pseudoapplication-2 NEOS Server Submission Imported from the MIPLIB2010 submissions. 1.377891 4
neos-pseudoapplication-74 Jeff Linderoth (None provided) 1.382399 5


Updated August 16, 2019