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Branch‐Price‐and‐Cut Algorithms

2011· other· en· W1605874004 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueWiley Encyclopedia of Operations Research and Management Science · 2011
Typeother
Languageen
FieldEngineering
TopicVehicle Routing Optimization Methods
Canadian institutionsHEC Montréal
Fundersnot available
KeywordsColumn generationBranch and cutLinear programming relaxationDiscretizationBranch and boundBranch and priceInteger programmingRelaxation (psychology)Branching (polymer chemistry)Integer (computer science)Cutting-plane methodMathematicsTree (set theory)PolyhedronColumn (typography)Mathematical optimizationAlgorithmDecompositionComputer scienceCombinatoricsGeometry

Abstract

fetched live from OpenAlex

Abstract In many mixed integer programs there is some embedded problem structure which can be exploited, often by a decomposition. When the relaxation in each node of a branch‐and‐bound tree is solved by column generation, one speaks of branch‐and‐price. Optionally, cutting planes can be added in order to strengthen the relaxation, and this is called branch‐price‐and‐cut . We introduce the common concepts of convexification and discretization to arrive at a Dantzig–Wolfe type reformulation of a mixed integer program. The relation between the original and the extended formulations helps us understand how cutting planes should be formulated and how branching decisions can be taken while keeping the column generation subproblems manageable.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: Not applicable
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.451
Threshold uncertainty score0.654

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0010.001
Science and technology studies0.0000.001
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.034
GPT teacher head0.325
Teacher spread0.291 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it