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

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

European Journal of Operational Research, 2020, vol. 282, issue 2, 453-463

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.

Keywords: Multiple objective programming; Non-dominated set; Pareto set; ϵ-constraint method; Unbounded Knapsack Problem; Algebraic test sets (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:282:y:2020:i:2:p:453-463

DOI: 10.1016/j.ejor.2019.09.032

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