Multi objective constrained optimisation of data envelopment analysis by differential evolution

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.