Quantitative Comparison of Approximate Solution Sets for Multicriteria Optimization Problems with Weighted Tchebycheff Preference Function

Bilge Bozkurt (), John W. Fowler (), Esma S. Gel (), Bosun Kim (), Murat Köksalan () and Jyrki Wallenius ()
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Bilge Bozkurt: Department of Industrial Engineering, Middle East Technical University, 06531 Ankara, Turkey
John W. Fowler: School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, Arizona 85287
Esma S. Gel: School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, Arizona 85287
Bosun Kim: School of Computing, Informatics, and Decision Systems Engineering, Arizona State University, Tempe, Arizona 85287
Murat Köksalan: Department of Industrial Engineering, Middle East Technical University, 06531 Ankara, Turkey
Jyrki Wallenius: Department of Business Technology, Helsinki School of Economics, FIN-00100 Helsinki, Finland

Operations Research, 2010, vol. 58, issue 3, 650-659

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.

Keywords: multiple objective combinatorial optimization; Tchebycheff function; multiple criteria metaheuristics (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (6)

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