On scalarizing functions in multiobjective optimization

被引：178

作者：

Miettinen K. ^{[1
]}

Mäkelä M.M. ^{[1
]}

机构：

[1] Dept. of Math. Info. Technology, University of Jyväskylä, 40351 Jyväskylä

来源：

OR Spectrum | 2002年 / 24卷 / 2期

关键词：

Classification; Multiple criteria decision making (MCDM); Nonlinear optimization; Reference point; Scalarizing function;

D O I：

10.1007/s00291-001-0092-9

中图分类号：

学科分类号：

摘要：

Scalarizing functions play an essential role in solving multiobjective optimization problems. Many different scalarizing functions have been suggested in the literature based on different approaches. Here we concentrate on classification and reference point-based functions. We present a collection of functions that have been used in interactive methods as well as some modifications. We compare their theoretical properties and numerical behaviour. In particular, we are interested in the relation between the information provided and the results obtained. Our aim is to select some of them to be used in our WWW-NIMBUS optimization system.

引用

页码：193 / 213

页数：20

共 45 条

[1] Aksoy Y., Butler T.W., Minor III E.D., Comparative studies in interactive multiple objective mathematical programming, European Journal of Operational Research, 89, pp. 408-422, (1996)
[2] Benayoun R., De Montgolfier J., Tergny J., Laritchev O., Linear programming with multiple objective functions: Step method (STEM), Mathematical Programming, 1, pp. 366-375, (1971)
[3] Buchanan J., Gardiner L., A Comparison of Two Reference Point Methods in Multiple Objective Mathematical Programming, (2001)
[4] Buchanan J.T., A naïve approach for solving MCDM problems: The GUESS method, Journal of the Operational Research Society, 48, pp. 202-206, (1997)
[5] Buchanan J.T., Daellenbach H.G., A comparative evaluation of interactive solution methods for multiple objective decision models, European Journal of Operational Research, 29, pp. 353-359, (1987)
[6] Caballero R., Rey L., Ruiz F., Determination of satisfying and efficient solutions in convex multi-objective programming, Optimization, 37, pp. 125-137, (1996)
[7] Geoffrion A.M., Proper efficiency and the theory of vector maximization, Journal of Mathematical Analysis and Applications, 22, pp. 618-630, (1968)
[8] Granat J., Makowski M., Interactive specification and analysis of aspiration-based preferences, European Journal of Operational Research, 122, pp. 469-485, (2000)
[9] Gulati T.R., Islam M.A., Efficiency and proper efficiency in nonlinear vector maximum problems, European Journal of Operational Research, 44, pp. 373-382, (1990)
[10] Hwang C.-L., Masud A.S.M., Multiple Objective Decision Making - Methods and Applications: A State-of-the-art Survey, (1979)

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