Validated Methods for Computing Pareto Sets: General Algorithmic Analysis

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′) ≥ 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 the (validated) algorithmic computability of maxima locations to show that Pareto sets can also computed.