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Separation algorithms for 0-1 knapsack polytopes

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Abstract

Valid inequalities for 0-1 knapsack polytopes often prove useful when tackling hard 0-1 Linear Programming problems. To generate such inequalities, one needs separation algorithms for them, i.e., routines for detecting when they are violated. We present new exact and heuristic separation algorithms for several classes of inequalities, namely lifted cover, extended cover, weight and lifted pack inequalities. Moreover, we show how to improve a recent separation algorithm for the 0-1 knapsack polytope itself. Extensive computational results, on MIPLIB and OR Library instances, show the strengths and limitations of the inequalities and algorithms considered.

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Authors and Affiliations

  1. School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

    Konstantinos Kaparis

  2. Department of Management Science, Lancaster University, Lancaster, LA1 4YX, UK

    Adam N. Letchford

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  1. Konstantinos Kaparis
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  2. Adam N. Letchford
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Correspondence to Adam N. Letchford.

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Kaparis, K., Letchford, A.N. Separation algorithms for 0-1 knapsack polytopes. Math. Program. 124, 69–91 (2010). https://doi.org/10.1007/s10107-010-0359-5

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  • DOI: https://doi.org/10.1007/s10107-010-0359-5

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