# Verified methods for computing Pareto sets: General algorithmic analysis

Boglárka G. Tóth; Vladik Kreinovich

International Journal of Applied Mathematics and Computer Science (2009)

- Volume: 19, Issue: 3, page 369-380
- ISSN: 1641-876X

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topBoglárka G. Tóth, and Vladik Kreinovich. "Verified methods for computing Pareto sets: General algorithmic analysis." International Journal of Applied Mathematics and Computer Science 19.3 (2009): 369-380. <http://eudml.org/doc/207942>.

@article{BoglárkaG2009,

abstract = {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 $f_j(x^\{\prime \}) ≥ f_j(x)$ 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.},

author = {Boglárka G. Tóth, Vladik Kreinovich},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {multi-objective optimization; Pareto set; verified computing},

language = {eng},

number = {3},

pages = {369-380},

title = {Verified methods for computing Pareto sets: General algorithmic analysis},

url = {http://eudml.org/doc/207942},

volume = {19},

year = {2009},

}

TY - JOUR

AU - Boglárka G. Tóth

AU - Vladik Kreinovich

TI - Verified methods for computing Pareto sets: General algorithmic analysis

JO - International Journal of Applied Mathematics and Computer Science

PY - 2009

VL - 19

IS - 3

SP - 369

EP - 380

AB - 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 $f_j(x^{\prime }) ≥ f_j(x)$ 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.

LA - eng

KW - multi-objective optimization; Pareto set; verified computing

UR - http://eudml.org/doc/207942

ER -

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