Verified methods for computing Pareto sets: general algorithmic analysis

Authors

Boglarka G.-Toth
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

9-2008

Comments

Technical Reports: UTEP-CS-08-35a

Published in International Journal of Applied Mathematics and Computer Science AMCS, 2009, Vol. 19, No. 3, pp. 369-380.

Abstract

In many engineering problems, we face multi-objective optimization, with several objective functions f1,...,fn. We want to provide the user with the Pareto set -- set of all possible solutions x which cannot be improved in all categories (i.e., for which fj(x')>=f_j(x) for all j and fj(x')>fj(x) for some j is impossible). The user should be able to select an appropriate trade-off between, say, cost and durability. We extend the general results about the (verified) algorithmic computability of maxima locations to show that Pareto sets can also computed.