On the computation of the Omega invariant of a numerical semigroup by optimizing over an efficient integer set

In this paper we present a mathematical formulation for the omega invariant of a numerical semigroup for each of its minimal generators. The model consists of solving a problem of optimizing a linear function over the efficient set of a multiobjective linear integer program. We offer a methodology to solve this problem and we provide some computational experiments to show the applicability of the proposed algorithm.