Mishra, SK (2012): A note on construction of heuristically optimal Pena’s synthetic indicators by the particle swarm method of global optimization.

PDF
MPRA_paper_37625.pdf Download (157kB)  Preview 
Abstract
Pena’s method of construction of a synthetic indicator is very sensitive to the order in which the constituent variables (whose linear aggregation yields the synthetic indicator) are arranged. Due to this, Pena’s method can at present give only an arbitrary synthetic indicator whose representativeness is indeterminate and uncertain, especially when the number of constituent variables is not very small. This paper uses discrete global optimization method based on the Particle Swarms to obtain a heuristically optimal order in which the constituent variables can be arranged so as to yield Pena’s synthetic indicator that maximizes the minimal absolute (or squared) correlation with its constituent variables.
Item Type:  MPRA Paper 

Original Title:  A note on construction of heuristically optimal Pena’s synthetic indicators by the particle swarm method of global optimization 
Language:  English 
Keywords:  Synthetic indicators, Pena’s distance, Particle swarm, Discrete Global Optimization, Composite indices, Maximin absolute correlation 
Subjects:  C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C43  Index Numbers and Aggregation C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C44  Operations Research; Statistical Decision Theory C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63  Computational Techniques; Simulation Modeling C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C61  Optimization Techniques; Programming Models; Dynamic Analysis 
Item ID:  37625 
Depositing User:  Sudhanshu Kumar Mishra 
Date Deposited:  25. Mar 2012 02:28 
Last Modified:  02. Mar 2013 16:45 
References:  1. Banks, A., Vincent, J., & Anyakoha, C. (2008): “A Review of Particle Swarm Optimization. Part II: Hybridisation, Combinatorial, Multicriteria and Constrained Optimization, and Indicative Applications”, Natural Computing, 7(1): 109–124. 2. Dorigo, M. (1992) Optimization, Learning and Natural Algorithms, PhD thesis, Politecnico di Milano, Italie, 1992. 3. García, E.C., Rodríguez Martín, J.A. & Pabsdorf, M.N. (2010): “The Features of Development in the Pacific Countries of the African, Caribbean and Pacific Group”, Social Indicators Research 99(3): 469485. 4. Glover, F. (1989). "Tabu Search  Part 1". ORSA Journal on Computing, 1(2): 190–206. 5. Glover, F. (1990). "Tabu Search  Part 2". ORSA Journal on Computing, 2(1): 4–32. 6. Holland, J.H. (1975) Adaptation in Natural and Artificial Systems, Ann Arbor: The U. of Michigan Press. 7. Kennedy, J. & Eberhart, R. (1995). “Particle Swarm Optimization”. Proceedings of IEEE International Conference on Neural Networks  IV : 1942–1948. doi:10.1109/ICNN.1995.488968. 8. Martína, J.A.R. & Fernández, J.A.S. (2011): “An Index of Maternal and Child Health in the Least Developed Countries of Asia”, Gac Sanit. 2011 [in press]; doi:10.1016/j.gaceta.2011.05.021. 9. Mishra, S.K. (2007): “A Note on Human Development Indices with Income Equalities”, http://ssrn.com/abstract=992854 or http://dx.doi.org/10.2139/ssrn.992854. 10. Mishra, S.K. (2010a): "Performance of Differential Evolution and Particle Swarm Methods on Some Relatively Harder Multimodal Benchmark Functions", The IUP Journal of Computational Mathematics, III(1): 718. 11. Mishra, S.K. (2010b): "Construction of an Index: A New Method", in Growth and Human Development in NorthEast India, Nayak, P. (ed.), Oxford University Press: 2435. 12. Mishra, S.K. (2011): "A Comparative Study of Various Inclusive Indices and the Index Constructed by the Principal Component Analysis", IUP Journal of Computational Mathematics, 4(2): 726. 13. Mishra, S.K. (2012): “A Note on the Indeterminacy and Arbitrariness of Pena’s Method of Construction of Synthetic Indicators”, (unpublished paper) http://mpra.ub.unimuenchen.de/37554/ 14. Montero, J.M., Chasco, C. & Lanaz, B. (2010): “Building an environmental quality index for a big city: a spatial interpolation approach combined with a distance indicator”, J. Geogr. Syst. 12: 435459. 15. Munda, G. & Nardo, M (2005): “Constructing Consistent Composite Indicators: The Issue of Weights”, EUR 21834 EN, Institute for the Protection and Security of the citizen, European Commission, Luxembourg. 16. Pena, J. B. (1977): Problemas de la medicio´n del bienestar y conceptos afines. Una aplicacio´n al Caso Espan˜ol. (I.N.E.: Madrid). 17. Sarker, S., Biswas, B. & Soundrs, P.J. (2006): “DistributionAugmented Human Development Index: A Principal Component Analysis”, GSP, College of Business, Utah State Univ., USA. www.usu.edu/cob/econ/graduatestudents/documents/papers/developmentpaper.pdf. (visited on April1 24, 2007). 18. Somarriba, N. & Pena, B. (2009): “Synthetic Indicators of Quality of Life in Europe”, Soc. Indic. Res. 94(1): 115–133. 19. Zarzosa, P. (1996): Aproximacio´n a la medicio´n del bienestar social. Valladolid: Secretario de Publicaciones. 20. Parsopoulos, K.E. & Vrahatis, M.N. (2006) “Studying the Performance of Unified Particle Swarm Optimization on the Single Machine Total Weighted Tardiness Problem” In: Sattar, A., Kang , B.H. (eds) AI 2006, LNAI 4304, SpringerVerlag: 1027–1031. 21. Tasgetiren, F., Sevkli, M., Lian, Y.C., & Gencyilmaz, G. (2004) “Particle Swarm Optimization Algorithm for Single Machine Weighted Tardiness Problem”, Proceedings of IEEE Congress on Evolutionary Computation: 1412–1419. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/37625 