The most representative composite rank ordering of multi-attribute objects by the particle swarm optimization

Mishra, SK (2009): The most representative composite rank ordering of multi-attribute objects by the particle swarm optimization.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Rank ordering, standard; modified; competition; fractional; dense; ordinal; principal component; integer programming; repulsive particle swarm; maximin; absolute; correlation; FORTRAN; program
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63 - Computational Techniques ; Simulation Modeling; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C87 - Econometric Software; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C45 - Neural Networks and Related Topics; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis

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