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Multi objective constrained optimisation of data envelopment analysis by differential evolution

Multi objective constrained optimisation of data envelopment analysis by differential evolution Traditional data envelopment analysis (DEA) has serious shortcomings: 1) linear programming is run as many times as the number of decision making units (DMUs) resulting in no common set of weights for them; 2) maximising efficiency, a nonlinear optimisation problem, is approximated by a linear programming problem (LPP); 3) the efficiencies obtained by DEA are only relative. Hence, we propose multi objective DEA (MODEA) solved by differential evolution. Here, we maximise the efficiencies of all the DMUs simultaneously. We developed two variants of the MODEA using: 1) scalar optimisation; 2) Max-Min approach. The effectiveness of the proposed methods is demonstrated on eight datasets taken from literature. We also applied NSGA-II to solve the nonlinear optimisation problem in the strict multi objective sense. It was found that MODEA1, MODEA2 and NSGA-II are comparable, as evidenced by Spearman's rank correlation coefficient test. However, MODEA1, MODEA2, and NSGA-II yielded better discrimination among the DMUs compared to the traditional DEA. Keywords: data envelopment analysis; DEA; differential evolution; multi objective optimisation; absolute efficiency; fractional programming; nonlinear programming. Reference to this paper should be made as follows: Ankaiah, N. and Ravi, V. (2015) `Multi objective constrained optimisation of data envelopment analysis by differential evolution', http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Information and Decision Sciences Inderscience Publishers

Multi objective constrained optimisation of data envelopment analysis by differential evolution

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Publisher
Inderscience Publishers
Copyright
Copyright © 2015 Inderscience Enterprises Ltd.
ISSN
1756-7017
eISSN
1756-7025
DOI
10.1504/IJIDS.2015.074131
Publisher site
See Article on Publisher Site

Abstract

Traditional data envelopment analysis (DEA) has serious shortcomings: 1) linear programming is run as many times as the number of decision making units (DMUs) resulting in no common set of weights for them; 2) maximising efficiency, a nonlinear optimisation problem, is approximated by a linear programming problem (LPP); 3) the efficiencies obtained by DEA are only relative. Hence, we propose multi objective DEA (MODEA) solved by differential evolution. Here, we maximise the efficiencies of all the DMUs simultaneously. We developed two variants of the MODEA using: 1) scalar optimisation; 2) Max-Min approach. The effectiveness of the proposed methods is demonstrated on eight datasets taken from literature. We also applied NSGA-II to solve the nonlinear optimisation problem in the strict multi objective sense. It was found that MODEA1, MODEA2 and NSGA-II are comparable, as evidenced by Spearman's rank correlation coefficient test. However, MODEA1, MODEA2, and NSGA-II yielded better discrimination among the DMUs compared to the traditional DEA. Keywords: data envelopment analysis; DEA; differential evolution; multi objective optimisation; absolute efficiency; fractional programming; nonlinear programming. Reference to this paper should be made as follows: Ankaiah, N. and Ravi, V. (2015) `Multi objective constrained optimisation of data envelopment analysis by differential evolution',

Journal

International Journal of Information and Decision SciencesInderscience Publishers

Published: Jan 1, 2015

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