Estimation of Pareto sets in the mixed control problem

Abstract

Multiobjective design problems give rise to a well-defined object: the Pareto-set. This paper proposes some verifiable conditions that are applicable to sets with finite number of elements, to ^corroborate or ^falsify the ^hypothesis of the elements of that set being samples of the Pareto set. These conditions lead to several generic criteria that can be employed in the evaluation of algorithms as multiobjective optimization mechanisms. A conceptual multiobjective genetic algorithm is proposed, exploiting the group properties of the intermediate Pareto-set estimates to generate a consistent final estimate. The methodology is applied to the case of a mixed control design. Recent dedicated multiobjective algorithms are evaluated under the proposed methodology, and it is shown that they can generate sub-optimal or non-consistent solution sets. It is shown that the proposed synthesis methodology can lead to both enhanced objectives and enhanced consistency in the Pareto-set estimate.

Acknowledgements

This research has been supported in part by grants from CNPq and CAPES, Brazil.

Notes

¹ An arbitrary algorithm that is used as a comparison basis for the evaluation of .

² The following assumption is made: