Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

In many engineering problems, we face multi-objective optimization, with several objective functions f₁, …, f_n. 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 f^j (x') ≥ f_j(x) for all j and f_j(x') > f_j(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.