A new approach to solving multi-follower multi-objective linear bilevel programming problems

Subject Areas : Design of Experiment

Habibe Sadeghi ¹ , Farzaneh Anis Hosseini ²

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Received: 2017-09-06 Accepted : 2022-10-16 Published : 2023-06-01

Keywords: Pareto-optimal solutions, Multi-objective programming, Multi-follower linear bilevel programming, Feasible set,

Abstract :

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.

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