Title: Normalisation in multiobjective optimisation: a general overview

Authors: Willem Karel Brauers

Addresses: Faculty of Applied Economics and Institute for Development Policy and Management, University of Antwerp, Birontlaan, 97, Berchem-Antwerpen B2600, Belgium

Abstract: This paper shows the application of normalisation in multiobjective optimisation. Methods of partial aggregation or with pairwise comparisons, given the Condorcet Paradox, are from the beginning excluded, as also normalisation would only be partially. Instead, general aggregative methods are discussed, either in a discrete or in a continuous way. For the discrete methods, the additive linear method with weights obtains bad points. Multiplicative theory is of importance for production economics, but less for consumption economics, whereas the other methods, namely reference point theory and ratio systems are preferred. For the continuous way, the methods of application are more restricted. Fractional programming can be mentioned, but mainly linear programming with a rank of priorities of objectives. Indifference curve analysis influences the continuous case too, whereas the reference point theory can be used. For this occasion, the name of utopian reference point is changed into |desirable point|.

Keywords: normalisation; decision making; continuous methods; discrete methods; additive linear methods; weights; economic law; decreasing marginal utility; indifference curve analysis; reference point theory; multiplicative method; ratio systems; linear programming; objectives priority; multiobjective optimisation.

DOI: 10.1504/IJMDM.2007.013412

International Journal of Management and Decision Making, 2007 Vol.8 No.5/6, pp.461 - 474

Available online: 27 Apr 2007 *

Full-text access for editors Access for subscribers Purchase this article Comment on this article