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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/4539 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/4539 http://eprints.org/relation/isCoversheetVersionOf https://pure.iiasa.ac.at/id/document/4539 archive 351 disk0/00/00/56/35 2016-01-15 02:10:31 2021-08-27 17:16:31 2016-01-15 02:10:31 monograph show 2 Korhonen P. 7606 Karaivanova J. An Algorithm for Projecting a Reference Direction onto the Nondominated Set of Given Points pub iis_met iis_sys prog_das In this paper, we consider the problem of searching nondominated alternatives in a discrete multiple criteria problem. The search procedure is based on the use of a reference direction. A reference direction reflects the desire of the decision maker (DM) to specify a search direction. To find a set of given alternatives related somehow to the reference direction specified by the DM, the reference direction has to be projected onto the set of nondominated alternatives. Our purpose is to develop an efficient algorithm for making this projection. The projection of each given reference direction determines a nondominated ordered subset. The set is provided to a decision maker for evaluation. The decision maker will choose the most preferred alternative from this subset and continues the search from this alternative with a new reference direction. The search will end when no direction of of improvement is found. A critical point in the procedure is the efficiency of the projection operation. This efficiency of our algorithm is considered theoretically and numerically. The projection is made by parametrizing an achievement scalarizing function originally proposed by Wierzbicki (1980) to project any single point onto the nondominated set. 1998-03 published IR-98-011 IR-98-011 2062 public interim_report IIASA, Laxenburg, Austria 23 FALSE info:eu-repo/semantics/book