Low rank quadratic assignment problem: Formulations and experimental analysis
Bibliographic record
Abstract
In this thesis, we study the quadratic assignment problem (QAP) with a special emphasis on the case where the associated cost matrix is of rank r (QAP(r)), for small values of r.We first consider different representations of the cost matrix Q which were shown to be beneficial for the quadratic set covering problem (QSCP).Unlike QSCP, these representations were unable to solve QAP of size n ≥ 20 and had a behaviour different from that of QSCP.To reconfirm this, additional experiments were carried out using the quadratic knapsack problem (QKP).We did notice statistically significant preferred representations for QKP and QAP, but were different from what was observed and known for QSCP.Next we consider four different mixed integer linear programming (MILP) formulations of QAP(r), extending the known case of r = 1.Extensive experimental results are provided for r = 2, 3, 4. One of our new formulations was shown to be very effective in solving large size QAP(r) for r = 2, 3, 4.The performance of the model is observed to deteriorate as the rank is increased.Finally, we present theoretical and experimental comparisons of the linear programming relaxations of our MILP formulations of QAP(r).Our MILP formulations for QAP(r) could be used as a heuristic for QAP by computing a low-rank approximation of the data matrix Q.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.020 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.001 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".