A new approach to solving multi-follower multi-objective linear bilevel programming problems
الموضوعات :
Habibe Sadeghi
1
(Faculty of mathematical science and computer, shahid chamran university of ahvaz, Ahvaz, Iran)
Farzaneh Anis Hosseini
2
(Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran)
الکلمات المفتاحية: Pareto-optimal solutions, Multi-objective programming, Multi-follower linear bilevel programming, Feasible set,
ملخص المقالة :
In this paper, we present a suitable extension of the approach described by Pieume et al. (2011) for solving multi-follower multi-objective linear bilevel programming problems. This problem is a special case of multi-follower bilevel linear programming problems, where each decision maker possesses several objective functions that in some cases, conflict with one another. We construct a multi-objective linear programming problem. Furthermore, we show that the multi-follower multi-objective linear bilevel programming problem can be reduced to optimize the top-level multi-objective linear programming problem over an efficient set. The proposed approach uses a Pareto-filter scheme, and obtains an approximate discrete representation efficient set unlike the fuzzy approaches that only obtain one efficient solution. Ultimately, a numerical example is presented to illustrate the efficiency of the proposed approach.
Ansari, E., & Zhiani Rezai, H. (2011). Solving Multi-objective Linear Bilevel Multi-follower Programming Problem. Journal of Industrial Mathematics, 3(4), 303-316.
Baky, I.A. (2009). Fuzzy Goal Programming Algorithm for Solving Decentralized Bilevel Multi-objective Programming Problems. Fuzzy sets system, 160, 2701-2713.
Bard, J.F. (1998). Practical Bilevel Optimization, Algorithms and Applications. Kluwer Academic Publishers, Dordrecht, Netherlands.
Dempe, S. (2003). Foundations of Bilevel Programming. Kluwer Academic, Dordrecht.
Farahi, M.H., & Ansari, E. (2010). A New Approach to Solve Multi-objective Linear Bilevel Programming Problems. Journal of Mathematics and Computer Science, 1(4), 313-320.
Habibpoor, M. (2016). A New Method for Solving Linear Bilevel Multi-Objective Multi-Follower Programming Problem. International Journal of Applied Operational Research, 6(4), 13-26.
Lachhwani, K. C. (2018). On Solving Multi-Objective Linear Bi-Level Multi-Follower Programming Problem. International Journal of Operational Research, 31(4), 442-460.
Matroud, F., & Sadeghi, H. (2013). Solving Bi-Level Programming with Multiple Linear Objectives at Lower Level Using Particle Swarm Optimization, Journal of Mathematics and Computer Science, 7, 221-229
Ma, W., Wang, M., & Zhu, X. (2014). Improved Particle Swarm Optimization Based Approach for Bilevel Programming Problem-an Application on Supply Chain Model. International Journal of Machine Learning and Cybernetics, 5, 281-292.
Mattson, C.A., Mullur, A.A. & Messac, A. (2004). Smart Pareto Filter: Obtaining a Minimal Representation of Multiobjective Design Space. Engineering Optimization, 36(6), 721-740.
Messac, A., & Mattson, C.A. (2002). Generating Well Distributed Sets of Pareto Points for Engineering Using Physical Programming. Optimization and Engineering, 3(4), 431-450.
Messac, A., & Mattson, C.A. (2004). Normal Constraint Method with Guarantee of Even Representation of Complete Pareto Frontier. American Institute of Aeronautics and Astronautics journal, 42(10).
Mehdizadeh, E., & Mohammadizadeh, M. R., (2013). A Multi-Level Capacitated Lot-Sizing Problem with Safety Stock Deficit and Production Manners: A Revised Simulated Annealing. Journal of Optimization in Industrial Engineering, 6(3), 55-64.
Mohagheghian, E., Rasti, M., & Sahraeian, R. (2018). Two-echelon Supply Chain Considering Multiple Retailers with Price and Promotional Effort Sensitive Non-Linear Demand. Journal of Optimization in Industrial Engineering, 11(2), 57-64.
Moslemi, F., & Sadeghi, H., (2022). On Solving Uncooperative Linear Bi-Level Multi-Follower Programming Problem. Pakistan Journal of Statistics and operation Research, 18 (1), 1-12.
Pieume, C.O., Marcotte, P., Fotso, L.P., & Siarry, P. (2011). Solving Bilevel Linear Multi-objective Programming Problems. American Journal of Operations Research, 1, 214-219.
Safaei, A.S., Farsad, S., & Paydar, M.M. (2018). Robust Bi-level Optimization of Relief Logistics Operations. Applied Mathematical Modelling, 56, 359-380
Sayin, S. (2003). A Procedure to Find Discrete Representation of the Efficient Set with Specified Cover Errors. Operations Research, 51(3), 427-436.
Shi, X., & Xia, H.S. (2001). Model and Interactive Algorithm of Bi-Level Multi-Objective Decision-Making with Multiple Interconnected Decision Makers. Journal of Multi-Criteria Decision Analysis, 10, 27-34.
Taran, M., & Roghanian, E. (2013). A Fuzzy Multi-Objective Multi-follower Linear Bi-level Programming Problem to Supply Chain Optimization. J. Uncertain Supply Chain Management, 1(4), 193-206.
Von Stackelberg, H. (1952). The Theory of the Market Economy: Oxford University Press, York, Oxford.
Yin, Y. (2000). Multiobjective Bilevel Optimization for Transportation Planning and Management Problems. Journal of Advanced Transportation, 36(1), 93-105.
Zhang, G., Lu, J., & Gao, Y. (2008). Fuzzy Bilevel Programming: Multi-Objective and Multi-Follower with Shared Variables. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16, 105-133.
Zhang, G., & Lu, J. C. (2010). Fuzzy Bilevel Programming with Multiple Objectives and Cooperative Multiple Followers. Journal of Global Optimization, 47(1), 403-419.
Zhang, G., Lu, J., & Gao, Y. (2016). Multi-Level Decision Making: Models, Methods and Applications, Springer-Verlag Berlin AN.
