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Computational Testing of Lifted Cover Inequalities with a Single Continuous Variable (Rapporti tecnici/preprint/working paper)

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Computational Testing of Lifted Cover Inequalities with a Single Continuous Variable (Rapporti tecnici/preprint/working paper) (literal)

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P. Avella, M. Boccia, S. Mattia (2013)
Computational Testing of Lifted Cover Inequalities with a Single Continuous Variable
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P. Avella, M. Boccia. Dipartimento di Ingegneria, Università del Sannio. S. Mattia. Istituto di Analisi dei Sistemi ed Informatica (IASI), Consiglio Nazionale delle Ricerche (CNR). (literal)

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Computational Testing of Lifted Cover Inequalities with a Single Continuous Variable (literal)

Abstract

Reformulating Mixed-Integer Programming (MIP) problems by cutting planes in order to speed up the solution process is a common practice. All the best known MIP solvers now offer built-in separation routines for generating inequalities to refine the formulation and speed-up the optimization. Mixed-Integer Rounding (MIR) cuts are recognized among the most effective cutting planes to reformulate general MIP problems. They can be derived from the binary knapsack set with a single continuous variable. Here we consider another family of cuts derived from the same knapsack set, namely the \emph{Lifted Cover Inequalities with a Single Continuous Variable} (LCISCV), and present an effective separation procedure, LCISCV-SEP. To validate the effectiveness of LCISCV-SEP, we exhibit a set of benchmark instances from MIPLIB 2010, where LCISCV-SEP leads to significant improvements in the lower bound, with little additional computational effort. (literal)

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