The controlled estimation method in the multiobjective linear fractional problem

This paper introduces a new method to estimate the weakly efficient set for the Multiobjective Linear Fractional Programming problem. The main idea is based on the procedure proposed by Tzeng and Hsu (In: G.H. Tzeng, H.F. Wang, U.P. Wen, L. Yu (Eds.), Multiple Criteria Decision Making, Springer, New York, 1994, pp. 459–470), called CONNISE. However, as we will explain in this paper, the CONNISE method is not always convergent for problems with more than two objectives. For this reason, we have developed a new method, called “The Controlled Estimation Method”, based on the same concept as CONNISE regarding the decision-maker being able to control distances between points from the estimation set he/she wants to find, while ensuring the method is convergent with problems with more than two objectives. Thus, we propose an algorithm able to calculate a discrete estimation of the weakly efficient set that verifies this property of the CONNISE method, but further, improves it thanks to its convergence and the fact that it satisfies the three good properties suggested by Sayin (Math. Programming 87(3) (2000) 543): Coverage, Uniformity, and Cardinality.