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The Multi-Objective Mixed-Integer Programming (MOMIP) problem is one of themost challenging. To derive its Pareto optimal solutions one can use thewell-known Chebyshev scalarization and Mixed-Integer Programming (MIP) solvers.However, for a large-scale instance of the MOMIP problem, its scalarization maynot be solved to optimality, even by state-of-the-art optimization packages,within the time limit imposed on the optimization. If a MIP solver cannotderive the optimal solution within the assumed time limit, it provides theoptimality gap, which gauges the quality of the approximate solution. However,for the MOMIP case, no information is provided on the lower and upper bounds ofthe components of the Pareto optimal outcome. For the MOMIP problem with twoand three objective functions, an algorithm is proposed to provide theso-called interval representation of the Pareto optimal outcome designated bythe weighting vector when there is a time limit on solving the Chebyshevscalarization. Such interval representations can be used to navigate on thePareto front. The results of several numerical experiments on selectedlarge-scale instances of the multi-objective, multidimensional 0-1 knapsackproblem illustrate the proposed approach. The limitations and possibleenhancements of the proposed method are also discussed.

A general framework for providing interval representations of Pareto optimal outcomes for large-scale bi- and tri-criteria MIP problems