The most representative composite rank ordering of multi-attribute objects by the particle swarm optimization
Rank-ordering of individuals or objects on multiple criteria has many important practical applications. A reasonably representative composite rank ordering of multi-attribute objects/individuals or multi-dimensional points is often obtained by the Principal Component Analysis, although much inferior but computationally convenient methods also are frequently used. However, such rank ordering – even the one based on the Principal Component Analysis – may not be optimal. This has been demonstrated by several numerical examples. To solve this problem, the Ordinal Principal Component Analysis was suggested some time back. However, this approach cannot deal with various types of alternative schemes of rank ordering, mainly due to its dependence on the method of solution by the constrained integer programming. In this paper we propose an alternative method of solution, namely by the Particle Swarm Optimization. A computer program in FORTRAN to solve the problem has also been provided. The suggested method is notably versatile and can take care of various schemes of rank ordering, norms and types or measures of correlation. The versatility of the method and its capability to obtain the most representative composite rank ordering of multi-attribute objects or multi-dimensional points have been demonstrated by several numerical examples. It has also been found that rank ordering based on maximization of the sum of absolute values of the correlation coefficients of composite rank scores with its constituent variables has robustness, but it may have multiple optimal solutions. Thus, while it solves the one problem, it gives rise to the other problem. The overall ranking of objects by maximin correlation principle performs better if the composite rank scores are obtained by direct optimization with respect to the individual ranking scores.
|Date of creation:||12 Jan 2009|
|Date of revision:|
|Contact details of provider:|| Postal: Ludwigstraße 33, D-80539 Munich, Germany|
Web page: https://mpra.ub.uni-muenchen.de
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Korhonen, Pekka & Siljamaki, Aapo, 1998. "Ordinal principal component analysis theory and an application," Computational Statistics & Data Analysis, Elsevier, vol. 26(4), pages 411-424, February.
When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:12723. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joachim Winter)
If references are entirely missing, you can add them using this form.