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1 International Journal of Applied Mathematics and Computer Science

1 2009

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Verified methods for computing Pareto sets: General algorithmic analysis

G.-Tóth B., Kreinovich V.

International Journal of Applied Mathematics and Computer Science

2009

Vol. 19, no 3

369-380

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.