Verified 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—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.
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