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

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Abstract
Rankordering of individuals or objects on multiple criteria has many important practical applications. A reasonably representative composite rank ordering of multiattribute objects/individuals or multidimensional 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 multiattribute objects or multidimensional 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 

Original Title:  The most representative composite rank ordering of multiattribute objects by the particle swarm optimization 
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 
Item ID:  12723 
Depositing User:  Sudhanshu Kumar Mishra 
Date Deposited:  14. Jan 2009 07:19 
Last Modified:  13. Feb 2013 05:01 
References:  Bauer, J.M. (2002): “Harnessing the Swarm: Communication Policy in an Era of Ubiquitous Networks and Disruptive Technologies”, Communications and Strategies, 45. Bradley, C. (1985) “The Absolute Correlation”, The Mathematical Gazette, 69(447): 1217. Dawkins, R. (1976) The Selfish Gene. Oxford University Press, Oxford. Eberhart R.C. and Kennedy J. (1995): “A New Optimizer using Particle Swarm Theory”, Proceedings Sixth Symposium on Micro Machine and Human Science: 39–43. IEEE Service Center, Piscataway, NJ. Fleischer, M. (2005): “Foundations of Swarm Intelligence: From Principles to Practice”, Swarming Network Enabled C4ISR, arXiv:nlin.AO/0502003 v1. Hayek, F. A. (1948) Individualism and Economic Order, The University of Chicago Press, Chicago. Hayek, F. A. (1952) The Sensory Order: An Inquiry into the Foundations of Theoretical Psychology, University of Chicago Press, Chicago. Hotelling, H. (1936) “Relations Between Two Sets of Variates”, Biometrica, 28: 321377. Kendall, M.G. and Stuart, A. (1968): The Advanced Theory of Statistics, vol. 3, Charles Griffin & Co. London. Korhonen, P. (1984) Ordinal Principal Component Analysis, HSE Working Papers, Helsinki School of Economics, Helsinki, Finland. Korhonen, P. and Siljamaki, A. (1998) Ordinal Principal Component Analysis. Theory and an Application”, Computational Statistics & Data Analysis, 26(4): 411424. Li, J. and Li, Y. (2004) Multivariate Mathematical Morphology based on Principal Component Analysis: Initial Results in Building Extraction”, http://www.cartesia.org/geodoc/isprs2004/comm7/papers/223.pdf Liang, J.J. and Suganthan, P.N. (2005) “Dynamic MultiSwarm Particle Swarm Optimizer”, International Swarm Intelligence Symposium, IEEE # 0780389166/05/$20.00. : 124129. Mishra, S.K. (2006) “Global Optimization by Differential Evolution and Particle Swarm Methods: Evaluation on Some Benchmark Functions”, available at SSRN: http://ssrn.com/abstract=933827 Mishra, S. K. (2008a) “On Construction of Robust Composite Indices by Linear Aggregation”, available at SSRN: http://ssrn.com/abstract=1147964 Mishra, S. K. (2008b) “A Note on the SubOptimality of Rank Ordering of Objects on the Basis of the Leading Principal Component Factor Scores”, available at http://ssrn.com/abstract=1321369 Ong Y. S., Lim M. H., Zhu N. and Wong K. W. (2006). "Classification of Adaptive Memetic Algorithms: A Comparative Study". IEEE Transactions on Systems Man and Cybernetics  Part B. 36 (1): 141152. Shevlyakov, G.L. (1997) “On Robust Estimation of a Correlation Coefficient”, Journal of Mathematical Sciences, 83(3): 434438. Simon, H.A.(1982): Models of Bounded Rationality, Cambridge Univ. Press, Cambridge, MA. Spearman, C. (1904) "The Proof and Measurement of Association between Two Things", American. Journal of Psychology, 15: 8893. Urfalioglu, O. (2004) “Robust Estimation of Camera Rotation, Translation and Focal Length at High Outlier Rates”, Proceedings of the 1st Canadian Conference on Computer and Robot Vision, IEEE Computer Society Washington, DC, USA: 464 – 471. Wikipedia (2008a) “Ranking”, available at Wikipedia http://en.wikipedia.org/wiki/Rank_order Wikipedia (2008b) “Least absolute deviations”: http://en.wikipedia.org/wiki/Least_absolute_deviations Wikipedia (2008c) “Particle Swarm Optimization”, available at Wikipedia http://en.wikipedia.org/wiki/Particle_swarm_optimization 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/12723 