A New Formulation of the Set Covering Problem for Metaheuristic Approaches
Bibliographic record
Abstract
Two difficulties arise when solving the set covering problem (SCP) with metaheuristic approaches: solution infeasibility and set redundancy. In this paper, we first present a review and analysis of the heuristic approaches that have been used in the literature to address these difficulties. We then present a new formulation that can be used to solve the SCP as an unconstrained optimization problem and that eliminates the need to address the infeasibility and set redundancy issues. We show that all local optimums with respect to the new formulation and a 1-flip neighbourhood structure are feasible and free of redundant sets. In addition, we adapt an existing greedy heuristic for the SCP to the new formulation and compare the adapted heuristic to the original heuristic using 88 known test problems for the SCP. Computational results show that the adapted heuristic finds better results than the original heuristic on most of the test problems in shorter computation times.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".