Hartillo Hermoso, IsabelJiménez Tafur, HaydeeUcha Enríquez, José María2021-02-042021-02-042020Hartillo Hermoso, I., Jiménez Tafur, H. y Ucha Enríquez, J.M. (2020). An exact algebraic ϵ-constraint method for bi-objective linear integer programming based on test sets. European Journal of Operational Research, 282 (2), 453-463.0377-2217https://hdl.handle.net/11441/104592A new exact algorithm for bi-objective linear integer problems is presented, based on the classic - constraint method and algebraic test sets for single-objective linear integer problems. Our method pro- vides 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. Al- though we use Gröbner bases for the computation of test sets, which may provoke a bottleneck in princi- ple, 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 algorithmcan be considered as a potentially faster alternative to IP-based methods when test sets are available.application/pdf11engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Multiple objective programmingNon-dominated setPareto setϵ-constraint methodUnbounded Knapsack ProblemAlgebraic test setsinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.ejor.2019.09.032