A variational approach to define robustness for parametric multiobjective optimization problems

Katrin Witting (), Sina Ober-Blöbaum and Michael Dellnitz

Journal of Global Optimization, 2013, vol. 57, issue 2, 345 pages

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. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Multiobjective optimization; Robust Pareto points; Parameter dependent multiobjective optimization problems; Calculus of variations (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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DOI: 10.1007/s10898-012-9972-6

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