Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

摘要

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(xu27)u3e=f_j(x) for all j and fj(xu27)u3efj(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.