A Toll-Setting Optimization Approach for Transportation Networks

In this manuscript, we consider a toll-setting optimization problem (TOP) in transportation networks. The model can be formulated as a bilevel programming problem (BLPP) where two levels of decision makers are involved. In the model some lower-level variables are restricted into the integer set such that the resulting model is too hard to solve by usual optimization techniques. In order to overcome the shortcoming, a genetic algorithm based on an approximate technique is proposed. First, for most of lower-level problems, only approximate solutions, instead of the optimal solutions, are fed back to the upper level, and each of these approximate solutions can be obtained simply by solving the relaxed one of the lower-level problem as well as an additional 0–1 program. Then, a heuristic crossover operator is developed by using the information of some better points, which is expected to generate potential high-quality offspring. Finally, the proposed algorithm is tested on some computational examples in two multi-commodity networks, and the experimental results show that the algorithm is feasible and effective.