Abstract
In this paper, an approach of hybrid technique is presented to derive Pareto optimal solutions of a multi-objective linear fractional programming problem (MOLFPP). Taylor series approximation along with the use of a hybrid technique comprising both weighting and \( \epsilon \)-constraint method is applied to solve the MOLFPP. It maintains both priority and achievement of possible aspired values of the objectives by the decision maker (DM) while producing Pareto optimal solutions. An illustrative numerical example is discussed to demonstrate the proposed method and to justify the effectiveness, the results so obtained are compared with existing fuzzy max–min operator method.
Keywords
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Martos, B.: Hyperbolic programming. Publ. Res. Inst. Math. Sci. 5, 386–407 (1960)
Charnes, A., Cooper, W.W.: Programming with linear fractional functionals. Naval Res. logist. Q. 9, 181–186 (1962)
Stancu-Minasian, I.M.: Fractional programming: Theory, Methods and Applications. Kluwer Academic Publishers (1997)
Costa, J.P.: Computing non-dominated solutions in MOLFP. Eur. J. Oper. Res. 181, 1464–1475 (2007)
Mishra, S.: Weighting method for bi-level linear fractional programming problems. Eur. J. Oper. Res. 183, 296–302 (2007)
Toksar, M.D.: Taylor series approach to fuzzy multiobjective linear fractional programming. Inform. Sci. 178, 1189–1204 (2008)
Ojha, A.K., Ota, R.R.: A hybrid method for solving multi-objective geometric programming problem. Int. J. Math. Oper. Res. 7, 119–137 (2015)
Valipour, E., Yaghoobi, M.A., Mashinchi, M.: An iterative approach to solve multiobjective linear fractional programming problems. Appl. Math. Model. 38, 38–49 (2014)
Ojha, A.K., Biswal, K.K.: Multi-objective geometric programming problem with ϵ-constraint method. Appl. Math. Model. 38, 747–758 (2014)
Collette, Y., Siarry, P.: Multiobjective optimization: principles and case studies. Springer (2003)
Miettinen, K.M.: Nonlinear multiobjective optimization. Kluwer Academic Publisher (2004)
Ehrgott, M.: Multicriteria optimization. Springer (2005)
Haimes, Y.Y., Ladson, L.S., Wismer, D.A.: On a Bicriterion formulation of problems of integrated system identification and system optimization. IEEE Trans. Syst., Man, Cybern., Syst. 1, 296–297 (1971)
Zimmermann, H.-J.: Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst. 1, 45–55, (1978)
Bellman, R.E., Zadeh, L.A.: Decision-making in a fuzzy environment. Mang. Sci. 17, B-141 (1970)
Acknowledgments
Authors are grateful to the Editor and anonymous referees for their valuable comments and suggestions to improve the quality of presentation of the paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer Science+Business Media Singapore
About this paper
Cite this paper
Suvasis Nayak, Ojha, A.K. (2016). An Approach to Solve Multi-objective Linear Fractional Programming Problem. In: Pant, M., Deep, K., Bansal, J., Nagar, A., Das, K. (eds) Proceedings of Fifth International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 436. Springer, Singapore. https://doi.org/10.1007/978-981-10-0448-3_59
Download citation
DOI: https://doi.org/10.1007/978-981-10-0448-3_59
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-0447-6
Online ISBN: 978-981-10-0448-3
eBook Packages: EngineeringEngineering (R0)