%0 Journal Article %1 perny2006dta %A Perny, P. %A Spanjaard, O. %A Storme, L.X. %D 2006 %I Springer %J Annals of Operations Research %K equitable graph_theory multicriteria %N 1 %P 317--341 %T A decision-theoretic approach to robust optimization in multivalued graphs %V 147 %X Abstract This paper is devoted to the search of robust solutions in finite graphs when costs depend on scenar- ios. We first point out similarities between robust optimization and multiobjective optimization. Then, we present axiomatic requirements for preference compatibility with the intuitive idea of robustness in a multiple scenarios decision context. This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination of Lorenz optima, we show how the search can be embedded in algorithms designed to enumerate k best solutions. Then, we apply it in order to enumerate Lorenz optimal spanning trees and paths. We investigate possible refinements of Lorenz dominance and we propose an axiomatic justification of OWA operators in this context. Finally, the results of numerical experiments on randomly generated graphs are provided. They show the numerical efficiency of the suggested approach. Key words robust optimization, multicriteria optimization, Lorenz optima, k best solutions, minimum spanning tree, shortest path

@article{perny2006dta, abstract = {Abstract This paper is devoted to the search of robust solutions in finite graphs when costs depend on scenar- ios. We first point out similarities between robust optimization and multiobjective optimization. Then, we present axiomatic requirements for preference compatibility with the intuitive idea of robustness in a multiple scenarios decision context. This leads us to propose the Lorenz dominance rule as a basis for robustness analysis. Then, after presenting complexity results about the determination of Lorenz optima, we show how the search can be embedded in algorithms designed to enumerate k best solutions. Then, we apply it in order to enumerate Lorenz optimal spanning trees and paths. We investigate possible refinements of Lorenz dominance and we propose an axiomatic justification of OWA operators in this context. Finally, the results of numerical experiments on randomly generated graphs are provided. They show the numerical efficiency of the suggested approach. Key words robust optimization, multicriteria optimization, Lorenz optima, k best solutions, minimum spanning tree, shortest path }, added-at = {2008-05-06T13:31:47.000+0200}, author = {Perny, P. and Spanjaard, O. and Storme, L.X.}, biburl = {https://www.bibsonomy.org/bibtex/2c263b49619bd0cf98bd4fa6063a6b30e/krz}, interhash = {8d4b843f20bdc73c953052e219d6fc71}, intrahash = {c263b49619bd0cf98bd4fa6063a6b30e}, journal = {Annals of Operations Research}, keywords = {equitable graph_theory multicriteria}, number = 1, pages = {317--341}, publisher = {Springer}, timestamp = {2008-05-06T13:33:17.000+0200}, title = {{A decision-theoretic approach to robust optimization in multivalued graphs}}, volume = 147, year = 2006 }