Abstract
In contrast to classical optimization problems, in multiobjective optimization several objective functions are considered at the same time. For these problems, the solution is not a single optimum but a set of optimal compromises, the so-called Pareto set. In this work, we consider multiobjective optimization problems that additionally depend on an external parameter \({\lambda \in \mathbb{R}}\), so-called parametric multiobjective optimization problems. The solution of such a problem is given by the λ-dependent Pareto set. In this work we give a new definition that allows to characterize λ-robust Pareto points, meaning points which hardly vary under the variation of the parameter λ. To describe this task mathematically, we make use of the classical calculus of variations. A system of differential algebraic equations will turn out to describe λ-robust solutions. For the numerical solution of these equations concepts of the discrete calculus of variations are used. The new robustness concept is illustrated by numerical examples.
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Witting, K., Ober-Blöbaum, S. & Dellnitz, M. A variational approach to define robustness for parametric multiobjective optimization problems. J Glob Optim 57, 331–345 (2013). https://doi.org/10.1007/s10898-012-9972-6
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DOI: https://doi.org/10.1007/s10898-012-9972-6