Optimal road user charging cordon design: A heuristic optimization approach

This article addresses the optimal design problem of selecting a charging cordon in a general traffic network. A charging cordon is a set of tolled links surrounding a designated area so that all travelers entering or passing through this area will be tolled. Travelers in the network are assumed to respond to the tolls imposed by adjusting their behaviors to achieve a new equilibrium following Wardrop's equilibrium condition. The necessity of this equilibrium condition is imposed as one of the constraints in the optimal charging cordon design problem. This problem can be categorized as a Mathematical Program with Equilibrium Constraints. This article presents an innovative Genetic Algorithm (GA) based method to tackle the problem. A new framework, called branch-tree framework, is developed to represent a closed charging cordon so that the method of GA can be used. The method is tested with a network of Edinburgh. Although the proposed algorithm is a heuristic-based method, the optimization result in the test is very promising. The optimal closed charging cordon as found by the algorithm produces a significantly higher benefit than that of judgmental cordons.