Abstract:

 Based on the bilevel linear multi-objective programming problem with multiple objectives at the lower level and the characteristic of the grey system, a grey bilevel linear multi-objective programming problem is put forward, and its model and theorem are given. Under the assumption of the constraint region of the proposed model nonempty and compactness, it is  shown that the optimal solution of the drifting grey bilevel linear multi-objective programming problem can be reached on the extreme point of the constraint region. Finally, an algorithm based on the k-th best method is developed and its global convergence is proven. Numerical examples show that the proposed algorithm is effective.

Key words:  bilevel linear multi-objective programming; grey system; constraint region; extreme point