Low rank quadratic assignment problem: Formulations and experimental analysis
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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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Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it