Stability and accuracy functions in multicriteria combinatorial optimization problem with Σ-MINMAX and Σ-MINMIN partial criteria

Abstract: We consider a vector generic combinatorial optimization problem in which initial coefficients of objective functions are subject to perturbations. For Pareto and lexicographic principles of efficiency we introduce appropriate measures of quality of a given feasible solution from the point of view of its stability. These measures correspond to so-called stability and accuracy functions defined earlier for scalar optimization problems. Then we study properties of such functions and calculate the maximal norms of perturbations for which an efficient solution preserves the efficiency.