Solving transportation bi-level programs with Differential Evolution

Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. These problems are recognized as one of the most difficult and challenging problems in transportation systems management. Several problems within the transportation literature can be cast in the bi-level programming framework. At the same time, significant advances have been made in the deployment of stochastic heuristics for function optimization. This paper reports on the use of Differential Evolution (DE) for solving bi-level programming problems with applications in the field of transportation planning. After illustrating our solution algorithm with some mathematical functions, we then apply this method to two control problems facing the transportation network manager. DE is integrated with conventional traffic assignment techniques to solve the resulting bi-level program. Numerical computations of this DE based algorithm (known as DEBLP) are presented and compared with existing results. Our numerical results augment the view that DE is a suitable contender for solving these types of problems.