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| Názov: |
On the exact separation of cover inequalities of maximum-depth. |
| Autori: |
Catanzaro, Daniele, Coniglio, Stefano, Furini, Fabio |
| Zdroj: |
Optimization Letters; Mar2022, Vol. 16 Issue 2, p449-469, 21p |
| Abstrakt: |
We investigate the problem of separating cover inequalities of maximum-depth exactly. We propose a pseudopolynomial-time dynamic-programming algorithm for its solution, thanks to which we show that this problem is weakly N P -hard (similarly to the problem of separating cover inequalities of maximum violation). We carry out extensive computational experiments on instances of the knapsack and the multi-dimensional knapsack problems with and without conflict constraints. The results show that, with a cutting-plane generation method based on the maximum-depth criterion, we can optimize over the cover-inequality closure by generating a number of cuts smaller than when adopting the standard maximum-violation criterion. We also introduce the Point-to-Hyperplane Distance Knapsack Problem (PHD-KP), a problem closely related to the separation problem for maximum-depth cover inequalities, and show how the proposed dynamic programming algorithm can be adapted for effectively solving the PHD-KP as well. [ABSTRACT FROM AUTHOR] |
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