A new approach to solve Multi-objective linear bilevel programming problems

Many problems in sciences and industry such as signal optimization, traffic assignment, economic market,… have been modeled, or their mathematical models can be approximated, by linear bilevel programming (LBLP) problems, where in each level one must optimize some objective functions. In this paper, we use fuzzy set theory and fuzzy programming to convert the multi-objective linear bilevel programming (MOLBLP) problem to a linear bilevel programming problem, then we extend the Kth-best method to solve the final LBLP problem. The existence of optimal solution, and the convergence of this approach, are important issues that are considered in this article. A numerical example is illustrated to show the efficiency of the new approach.