<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml">In many engineering problems, we face multi-objective optimization, with several objective functions <italic>f</italic>1, …, <italic>f</italic><italic>n</italic>. We want to provide the user with the Pareto set—a set of all possible solutions <italic>x</italic> which cannot be improved in all categories (i.e., for which <italic>fj</italic> (<italic>x</italic>') ≥ <italic>f</italic><italic>j</italic>(<italic>x</italic>) for all <italic>j</italic> and <italic>f</italic><italic>j</italic>(<italic>x</italic>') > <italic>f</italic><italic>j</italic>(<italic>x</italic>) for some <italic>j</italic> 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.</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 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.

Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

Department of Differential Equations, Institute of Mathematics, Budapest University of Technology and Economics (BME), Egry József u. 1, 1111 Budapest, Hungary

Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, Texas 79968, USA

International Journal of Applied Mathematics and Computer Science

{"article-title":"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...

Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

Published Online: Sep 24, 2009

Page range: 369 - 380

DOI: https://doi.org/10.2478/v10006-009-0031-5

Keywords
multi-objective optimization, Pareto set, verified computing

This content is open access.

Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

Published Online: Sep 24, 2009

Page range: 369 - 380

DOI: https://doi.org/10.2478/v10006-009-0031-5

Keywordsmulti-objective optimization, Pareto set, verified computing

This content is open access.

Keywords
multi-objective optimization, Pareto set, verified computing