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The controlled estimation method in the multiobjective linear fractional problem. (English) Zbl 1073.90038

Summary: 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 Y. R. Tzeng and J. Hsu [in: G. H. Tzeng, H. F. Wang, U. P. Wen, L. Yu (Eds.), Multiple Criteria Decision Making, Springer, New York, 459–470 (1994)], 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 S. Sayin [Math. Program. 87, No. 3(A), 543–560 (2000; Zbl 0970.90090)]: Coverage, Uniformity, and Cardinality.

MSC:

90C29 Multi-objective and goal programming
90C32 Fractional programming
90C59 Approximation methods and heuristics in mathematical programming

Citations:

Zbl 0970.90090
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References:

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