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We determine the power of the weighted sum scalarization with respect to thecomputation of approximations for general multiobjective minimization andmaximization problems. Additionally, we introduce a new multi-factor notion ofapproximation that is specifically tailored to the multiobjective case and itsinherent trade-offs between different objectives.  For minimization problems, we provide an efficient algorithm that computes anapproximation of a multiobjective problem by using an exact or approximatealgorithm for its weighted sum scalarization. In case that an exact algorithmfor the weighted sum scalarization is used, this algorithm comes arbitrarilyclose to the best approximation quality that is obtainable by supportedsolutions - both with respect to the common notion of approximation and withrespect to the new multi-factor notion. Moreover, the algorithm yields thecurrently best approximation results for several well-known multiobjectiveminimization problems. For maximization problems, however, we show that apolynomial approximation guarantee can, in general, not be obtained in morethan one of the objective functions simultaneously by supported solutions.

The Power of the Weighted Sum Scalarization for Approximating Multiobjective Optimization Problems