Learning to handle parameter perturbations in Combinatorial Optimization: An application to facility location
Bibliographic record
Abstract
We present an approach to couple the resolution of Combinatorial Optimization problems with methods from Machine Learning. Specifically, our study is framed in the context where a reference discrete optimization problem is given and there exist data for many variations of such reference problem (historical or simulated) along with their optimal solution. Those variations can be originated by disruption but this is not necessarily the case. We study how one can exploit these to make predictions about an unseen new variation of the reference instance. The methodology is composed by two steps. We demonstrate how a classifier can be built from these data to determine whether the solution to the reference problem still applies to a perturbed instance. In case the reference solution is only partially applicable, we build a regressor indicating the magnitude of the expected change, and conversely how much of it can be kept for the perturbed instance. This insight, derived from a priori information, is expressed via an additional constraint in the original mathematical programming formulation. We present the methodology through an application to the classical facility location problem and we provide an empirical evaluation and discuss the benefits, drawbacks and perspectives of such an approach. Although it cannot be used in a black-box manner, i.e., it has to be adapted to the specific application at hand, we believe that the approach developed here is general and explores a new perspective on the exploitation of past experience in Combinatorial Optimization.
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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 | 0.006 | 0.027 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.003 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 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".