A Strong Class of Lifted Valid Inequalities for the Shortest Path Problem in Digraphs with Negative Cost Cycles
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Bibliographic record
Abstract
In this paper, we address a strong class of lifted valid inequalities for the shortest path problem in digraphs with possibly negative cost cycles. We call these lifted inequalities the $incident \ lifted \ valid \ inequalities$ ($ILI$) as they are based on the incident arcs of a given vertex. The $ILI$ inequalities are close in spirit of the so-called \textit{simple lifted valid inequalities} ($SLI$) and $cocycle \ lifted \ valid \ inequalities$ ($CLI$) introduced in Ibrahim et al. (2015). However, as we will see the $ILI$ inequalities are stronger than the first ones in term of linear relaxation strengthening. Indeed, contrary to $SLI$ and $CLI$ inequalities, consider the same instances, in a cutting plane algorithm, the computational results prove that the $ILI$ inequalities provide the optimal integer solution for all the considered instances within no more than three iterations except one case for which after the first strengthening iteration, there exists no generated inequality.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.006 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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