Geodesic
Application of a direct generalization of scalar algorithms in vector optimization on graphs
Diskretnaya Matematika, Tome 13 (2001) no. 3, pp. 110-124

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We consider the problem of searching optimal paths on directed graphs with vector weights of edges. As the criterion of efficiency we use the lockout condition with respect to a binary preference relation defined on the set of paths. As the basic algorithm of vector optimisation we use the scheme of direct generalisation of scalar prototypes to the vector case. We give sufficient conditions of correctness of application of such approach. We suggest two algorithms constructed by the direct generalisation, for arbitrary graphs and graphs without cycles, prove their efficiency under the condition of asymmetry and transitivity of the preference relation. In addition, we describe a method of regulation of the cardinality of the set of effective solutions produced by the algorithm with regard to the preferences of the decision-maker. 
@article{DM_2001_13_3_a7,
     author = {Yu. V. Bugaev},
     title = {Application of a direct generalization of scalar algorithms in vector optimization on graphs},
     journal = {Diskretnaya Matematika},
     pages = {110--124},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2001_13_3_a7/}
}
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Yu. V. Bugaev. Application of a direct generalization of scalar algorithms in vector optimization on graphs. Diskretnaya Matematika, Tome 13 (2001) no. 3, pp. 110-124. http://geodesic.mathdoc.fr/item/DM_2001_13_3_a7/