Quantitative comparison of approximate solution sets for multicriteria optimization problems with weighted tchebycheff preference function

Bilge Bozkurt, John Fowler, Esma Gel, Bosun Kim, Murat Köksalan, Jyrki Wallenius

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

We consider the problem of evaluating the quality of solution sets generated by heuristics for multiple-objective combinatorial optimization problems. We extend previous research on the integrated preference functional (IPF), which assigns a scalar value to a given discrete set of nondominated points so that the weighted Tchebycheff function can be used as the underlying implicit value function. This extension is useful because modeling the decision maker's value function with the weighted Tchebycheff function reflects the impact of unsupported points when evaluating sets of nondominated points. We present an exact calculation method for the IPF measure in this case for an arbitrary number of criteria. We show that every nondominated point has its optimal weight interval for the weighted Tchebycheff function. Accordingly, all nondominated points, and not only the supported points in a set, contribute to the value of the IPF measure when using the weighted Tchebycheff function. Two- and three-criteria numerical examples illustrate the desirable properties of the weighted Tchebycheff function, providing a richer measure than the original IPF based on a convex combination of objectives.

Original languageEnglish (US)
Pages (from-to)650-659
Number of pages10
JournalOperations Research
Volume58
Issue number3
DOIs
StatePublished - May 1 2010

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research

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