Using scalarizations for the approximation of multiobjective optimization problems: towards a general theory

Abstract We study the approximation of general multiobjective optimization problems with help scalarizations. Existing results state that minimization can be approximated well by norm-based However, for maximization problems, only impossibility are known so far. Countering this, we show all can, in principle, equally In this context, introduce a transformation theory scalarizations establishes following: Suppose there exists scalarization yields an certain quality arbitrary instances given decomposition specifying which objective functions to minimized/maximized. Then, each other decomposition, our another same decomposition. sense, existing about via carry over any decomposition—in particular, problems—when suitably adapting employed scalarization. further provide necessary and sufficient conditions on such its optimal solutions achieve constant quality. give upper bound best achievable applies is tight majority applied context optimization. As consequence, none these induce sets objectives, unifies generalizes concerning problems.