Designing of a mat-heuristic algorithm for solving bi-level optimization problems

In this paper, a new algorithm for solving bi-level optimization problems is presented. This algorithm can obtain the optimal or near-optimal solution for any bi-level optimization problem. The decision variables of the first and second level models can be both integers and continuous. In this method, by solving a certain number of the bi-objective programming model and then solving the corresponding second-level model, a bi-level feasible solution that is either optimal or near-optimal is identified. To evaluate the efficiency of the algorithm, the value of the objective function, as well as its computation time in different instances, are compared with exact methods as well as evolution-based methods. The numerical results confirm the high efficiency of the proposed algorithm.