8div-n59k10: Instance-to-Instance Comparison Results

Type: Instance
Submitter: Sascha Kurz
Description: Projective binary 8-divisible linear block codes A linear block code is called 8-divisible if the weights of its codewords are divisible by 8. It is called projective if there are no duplicate columns in the generator matrix. The possible lengths of 8-divisible linear block codes have been classified except for length n=59, where it is undecided whether such a linear code exists. The possible dimensions satisfy \\(10 \\le k \\le 20\\). Instance 8div_n59_kXX contains the corresponding feasibility problem. Projective binary 8-divisible linear block codes occur as hole configurations of so-called partial solid spreads in finite geometry. Binary 4-divisible linear block codes have applications in physics.
MIPLIB Entry

Parent Instance (8div-n59k10)

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

8div-n59k10 Raw 8div-n59k10 Decomposed 8div-n59k10 Composite of MIC top 5 8div-n59k10 Composite of MIPLIB top 5 8div-n59k10 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.
8div-n59k11 decomposed 8div-n59k12 decomposed prod1 decomposed fhnw-schedule-pairb400 decomposed fhnw-schedule-pairb200 decomposed
Name 8div-n59k11 [MIPLIB] 8div-n59k12 [MIPLIB] prod1 [MIPLIB] fhnw-schedule-pairb400 [MIPLIB] fhnw-schedule-pairb200 [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 / 0.258 2 / 0.259 3 / 0.653 4 / 0.846 5 / 0.894
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIC top 5.
8div-n59k11 raw 8div-n59k12 raw prod1 raw fhnw-schedule-pairb400 raw fhnw-schedule-pairb200 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.
8div-n59k11 decomposed 8div-n59k12 decomposed neos-3045796-mogo decomposed brazil3 decomposed neos-952987 decomposed
Name 8div-n59k11 [MIPLIB] 8div-n59k12 [MIPLIB] neos-3045796-mogo [MIPLIB] brazil3 [MIPLIB] neos-952987 [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 / 0.258 2 / 0.259 379 / 1.491 496 / 1.576 742 / 1.867
Raw These images represent the CCM images in their raw forms (before any decomposition was applied) for the MIPLIB top 5.
8div-n59k11 raw 8div-n59k12 raw neos-3045796-mogo raw brazil3 raw neos-952987 raw

Instance Summary

The table below contains summary information for 8div-n59k10, the five most similar instances to 8div-n59k10 according to the MIC, and the five most similar instances to 8div-n59k10 according to MIPLIB 2017.

INSTANCE SUBMITTER DESCRIPTION ISS RANK
Parent Instance 8div-n59k10 [MIPLIB] Sascha Kurz Projective binary 8-divisible linear block codes A linear block code is called 8-divisible if the weights of its codewords are divisible by 8. It is called projective if there are no duplicate columns in the generator matrix. The possible lengths of 8-divisible linear block codes have been classified except for length n=59, where it is undecided whether such a linear code exists. The possible dimensions satisfy \\(10 \\le k \\le 20\\). Instance 8div_n59_kXX contains the corresponding feasibility problem. Projective binary 8-divisible linear block codes occur as hole configurations of so-called partial solid spreads in finite geometry. Binary 4-divisible linear block codes have applications in physics. 0.000000 -
MIC Top 5 8div-n59k11 [MIPLIB] Sascha Kurz Projective binary 8-divisible linear block codes A linear block code is called 8-divisible if the weights of its codewords are divisible by 8. It is called projective if there are no duplicate columns in the generator matrix. The possible lengths of 8-divisible linear block codes have been classified except for length n=59, where it is undecided whether such a linear code exists. The possible dimensions satisfy \\(10 \\le k \\le 20\\). Instance 8div_n59_kXX contains the corresponding feasibility problem. Projective binary 8-divisible linear block codes occur as hole configurations of so-called partial solid spreads in finite geometry. Binary 4-divisible linear block codes have applications in physics. 0.258109 1
8div-n59k12 [MIPLIB] Sascha Kurz Projective binary 8-divisible linear block codes A linear block code is called 8-divisible if the weights of its codewords are divisible by 8. It is called projective if there are no duplicate columns in the generator matrix. The possible lengths of 8-divisible linear block codes have been classified except for length n=59, where it is undecided whether such a linear code exists. The possible dimensions satisfy \\(10 \\le k \\le 20\\). Instance 8div_n59_kXX contains the corresponding feasibility problem. Projective binary 8-divisible linear block codes occur as hole configurations of so-called partial solid spreads in finite geometry. Binary 4-divisible linear block codes have applications in physics. 0.258802 2
prod1 [MIPLIB] MIPLIB submission pool Imported from the MIPLIB2010 submissions. 0.653025 3
fhnw-schedule-pairb400 [MIPLIB] Simon Felix Continuous-time project scheduling and selection, inspired by an industry use-case. Each project has a value, the sum should be maximized. Each project has a deadline, and an earliest start date. Three formulations of the same problem ("Pair A", "Pair B" and "Slot") - we expect "Pair B" to be the best formulation. 0.845716 4
fhnw-schedule-pairb200 [MIPLIB] Simon Felix Continuous-time project scheduling and selection, inspired by an industry use-case. Each project has a value, the sum should be maximized. Each project has a deadline, and an earliest start date. Three formulations of the same problem ("Pair A", "Pair B" and "Slot") - we expect "Pair B" to be the best formulation. 0.893544 5
MIPLIB Top 5 8div-n59k11 [MIPLIB] Sascha Kurz Projective binary 8-divisible linear block codes A linear block code is called 8-divisible if the weights of its codewords are divisible by 8. It is called projective if there are no duplicate columns in the generator matrix. The possible lengths of 8-divisible linear block codes have been classified except for length n=59, where it is undecided whether such a linear code exists. The possible dimensions satisfy \\(10 \\le k \\le 20\\). Instance 8div_n59_kXX contains the corresponding feasibility problem. Projective binary 8-divisible linear block codes occur as hole configurations of so-called partial solid spreads in finite geometry. Binary 4-divisible linear block codes have applications in physics. 0.258109 1
8div-n59k12 [MIPLIB] Sascha Kurz Projective binary 8-divisible linear block codes A linear block code is called 8-divisible if the weights of its codewords are divisible by 8. It is called projective if there are no duplicate columns in the generator matrix. The possible lengths of 8-divisible linear block codes have been classified except for length n=59, where it is undecided whether such a linear code exists. The possible dimensions satisfy \\(10 \\le k \\le 20\\). Instance 8div_n59_kXX contains the corresponding feasibility problem. Projective binary 8-divisible linear block codes occur as hole configurations of so-called partial solid spreads in finite geometry. Binary 4-divisible linear block codes have applications in physics. 0.258802 2
neos-3045796-mogo [MIPLIB] Jeff Linderoth (None provided) 1.490926 379
brazil3 [MIPLIB] George Fonseca Educational timetabling problems from several real schools/universities around the world. These instances were originally expressed in the xhstt file format [1] and formulated as Integer Programming models as described at [2]. 1.576371 496
neos-952987 [MIPLIB] NEOS Server Submission Instance coming from the NEOS Server with unknown application 1.867290 742


8div-n59k10: Instance-to-Model Comparison Results

Model Group Assignment from MIPLIB: 8div
Assigned Model Group Rank/ISS in the MIC: 1 / 0.347

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: 8div Model group: neos-pseudoapplication-95 Model group: neos-pseudoapplication-74 Model group: scp Model group: stein
Name 8div neos-pseudoapplication-95 neos-pseudoapplication-74 scp stein
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 / 0.347 2 / 1.498 3 / 1.554 4 / 1.646 5 / 1.648

Model Group Summary

The table below contains summary information for the five most similar model groups to 8div-n59k10 according to the MIC.

MODEL GROUP SUBMITTER DESCRIPTION ISS RANK
MIC Top 5 8div Sascha Kurz Projective binary 8-divisible linear block codes A linear block code is called 8-divisible if the weights of its codewords are divisible by 8. It is called projective if there are no duplicate columns in the generator matrix. The possible lengths of 8-divisible linear block codes have been classified except for length n=59, where it is undecided whether such a linear code exists. The possible dimensions satisfy \\(10 \\le k \\le 20\\). Model 8div_n59_kXX contains the corresponding feasibility problem. Projective binary 8-divisible linear block codes occur as hole configurations of so-called partial solid spreads in finite geometry. Binary 4-divisible linear block codes have applications in physics. 0.347012 1
neos-pseudoapplication-95 NEOS Server Submission Imported from the MIPLIB2010 submissions. 1.498374 2
neos-pseudoapplication-74 Jeff Linderoth (None provided) 1.553987 3
scp Shunji Umetani This is a random test model 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 models. We have also generated reduced models 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 model generator program from the following web site. https://sites.google.com/site/shunjiumetani/benchmark 1.646027 4
stein MIPLIB submission pool Imported from the MIPLIB2010 submissions. 1.648113 5