Monday, 16:15 - 16:40 h, Room: H 1029

 

Kai-Simon Goetzmann
Compromise solutions

Coauthors: Christina B├╝sing, Jannik Matuschke, Sebastian Stiller

 

Abstract:
The most common concept in multicriteria optimization is Pareto optimality. However, in general the number of Pareto optimal solutions is exponential. To choose a single, well-balanced Pareto optimal solution, Yu (1973) proposed compromise solutions.
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A compromise solution is a feasible solution closest to the ideal point. The ideal point is the component-wise optimum over all feasible solutions in objective space.
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Compromise solutions are always Pareto optimal. Using different weighted norms, the compromise solution can attain any point in the Pareto set.
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The concept of compromise solutions (and the slightly more general reference point methods) are widely used in state-of-the-art software tools. Still, there are very few theoretical results backing up these methods.
We establish a strong connection between approximating the Pareto set and approximating compromise solutions. In particular, we show that an approximate Pareto set always contains an approximate compromise solution. The converse is also true if we allow to substitute the ideal point by a sub-ideal reference point. Compromise solutions thus neatly fit with the concept of Pareto optimality.

 

Talk 3 of the invited session Mon.3.H 1029
"Multi-objective optimization" [...]
Cluster 15
"Multi-objective optimization" [...]

 

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