Ponente
Descripción
Real world problems are often affected by diverse types of uncertainty, which we have to take into account in mathematical modelling of the problems. Uncertain data can be represented by various ways, depending on the source and type of uncertainty. In our presentation, we make use of the concept of interval analysis, which assumes that we obtain only nominal values with a given accuracy, so that we have intervals covering the true values. In contrast to stochastic or fuzzy programming, we have no additional information on the distribution on intervals. More concretely, we consider linear programming problems with multiple objective functions. Multiple objectives are usually scalarized by using appropriate weights, which are provided by a user or estimated. In our model, we suppose that the objective function coefficients and the weights are not known exactly and only interval outer approximations are known. These two types of interval values naturally lead to several concepts of definitions of efficient (Pareto) optimal solutions. We discuss these concepts in detail and compare them to each other. For each of them, we attempt to characterize the corresponding kind efficiency either for a general feasible solution, or for a basic solution. We also address the problem of computational complexity of deciding whether a given solution is efficient. We classify which concepts are polynomially decidable and which are NP-hard.
Keywords: multiobjective linear programming, interval analysis, robust optimization, weighted scalarization
