Using the Modified Artificial Bee Colony Algorithm to Find the Non-Archimedean Epsilon for Evaluating the Efficiency in DEA

Abstract

The artificial bee colony algorithm is one of the population-based optimization methods inspired by the evolutionary principles of the social behavior of bees. On the other hand, one of the sub-fields of operations research science is data envelopment analysis. There are some difficulties in DEA models for selecting the appropriate numerical value for an infinitesimal non-Archimedean epsilon. So far, various methods have been proposed to solve this problem and choose the suitable non-Archimedean epsilon. In order to solve the problem, the artificial bee colony algorithm (ABC), and modification of the original ABC algorithm (MABC) are adopted and proposed in this paper. The impacts of our proposed algorithms on the suitable non-Archimedean epsilon by solving only one linear programming (LP), instead of n LP are investigated. Finally, the performance of the proposed algorithms is evaluated by comparing the solutions obtained from GAMS software based on the presented examples.