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Verified methods for computing Pareto sets: General algorithmic analysis

Boglárka G. Tóth; Vladik Kreinovich — 2009

International Journal of Applied Mathematics and Computer Science

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 $f_{j} (x^{'}) \geq f_{j} (x)$ 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...

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