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An exact algebraic ϵ-constraint method for bi-objective linear integer programming based on test sets

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  • Hartillo-Hermoso, María Isabel
  • Jiménez-Tafur, Haydee
  • Ucha-Enríquez, José María

Abstract

A new exact algorithm for bi-objective linear integer problems is presented, based on the classic ϵ-constraint method and algebraic test sets for single-objective linear integer problems. Our method provides the complete Pareto frontier N of non-dominated points and, for this purpose, it considers exactly |N| single-objective problems by using reduction with test sets instead of solving with an optimizer. Although we use Gröbner bases for the computation of test sets, which may provoke a bottleneck in principle, the computational results are shown to be promising, especially for unbounded knapsack problems, for which any usual branch-and-cut strategy could be much more expensive. Nevertheless, this algorithm can be considered as a potentially faster alternative to IP-based methods when test sets are available.

Suggested Citation

  • Hartillo-Hermoso, María Isabel & Jiménez-Tafur, Haydee & Ucha-Enríquez, José María, 2020. "An exact algebraic ϵ-constraint method for bi-objective linear integer programming based on test sets," European Journal of Operational Research, Elsevier, vol. 282(2), pages 453-463.
    • Handle: RePEc:eee:ejores:v:282:y:2020:i:2:p:453-463
    DOI: 10.1016/j.ejor.2019.09.032
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    References listed on IDEAS

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