Seeking the Optimal Solution to Bilevel Linear Programming by Dual Problem

Abstract

In view of the linear feature of the upper-level and lower-level objective function of the bilevel programming as well as its constraint conditions, this paper presented a global optimization method. Replaced low-level sub-problem of the bilevel linear programming problem with dual problem, and then added the duality gap of the lower-level problem to the upper-level objective function, as a penalty function, and solved single level mathematical programming problem as an alternative to seek the optimal solution of the original problem. Numerical experiments show that the proposed algorithm is effective and feasible. This paper avoided the complexity with solving the dual problem's constraint domain pole, thus saved computing time and energy.