A variational approach to define robustness for parametric multiobjective optimization problems

作者：Witting Katrin^*; Ober Bloebaum Sina; Dellnitz Michael

来源：Journal of Global Optimization, 2013, 57(2): 331-345.

DOI：10.1007/s10898-012-9972-6

• Multiobjective optimization
• Robust Pareto points
• Parameter dependent multiobjective optimization problems
• Calculus of variations

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 , so-called parametric multiobjective optimization problems. The solution of such a problem is given by the lambda-dependent Pareto set. In this work we give a new definition that allows to characterize lambda-robust Pareto points, meaning points which hardly vary under the variation of the parameter lambda. 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 lambda-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.

• 出版日期2013-10