Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

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-a set of all possible solutions x which cannot be improved in all categories (i.e., for which fj (x ) ≥ fj (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 (verified) algorithmic computability of maxima locations to show that Pareto sets can also be computed.