Verified Methods for Computing Pareto Sets: General Algorithmic Analysis

Authors:
BogláRka G.-TóTh;Vladik Kreinovich
Affiliations:
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
Venue:
International Journal of Applied Mathematics and Computer Science - Verified Methods: Applications in Medicine and Engineering
Year:
2009

Citing 3
Cited 1

Introduction to Precise Numerical Methods, Second Edition

Introduction to Precise Numerical Methods, Second Edition
Obtaining an outer approximation of the efficient set of nonlinear biobjective problems

Journal of Global Optimization
Obtaining the efficient set of nonlinear biobjective optimization problems via interval branch-and-bound methods

Computational Optimization and Applications

Convergence method, properties and computational complexity for Lyapunov games

International Journal of Applied Mathematics and Computer Science - SPECIAL SECTION: Efficient Resource Management for Grid-Enabled Applications

Quantified Score

Hi-index	0.00

Visualization

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') 茂戮驴 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.