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Optimal Toll Design in Second-Best Link-Based Congestion Pricing

In the traffic assignment literature, it is well known that a marginal-cost toll is charged on each link to drive a user equilibrium flow pattern toward a system optimum in a general network. Although this principle is theoretically reasonable, it is not practically appealing for many reasons. In real life, a second-best pricing scheme is more attractive, where only a subset of links is subject to toll charge. Previously most studies in the research area of second-best pricing concern the determination of optimal toll levels on predetermined toll links, whereas very little attention has been devoted to the selection of toll locations. The second-best link-based pricing scheme that involves optimal selection of both toll levels and toll locations is described here. Travel cost minimization or social welfare maximization with and without inclusion of the implementation cost of the toll charge is sought in general networks. Optimization models with mixed (integer and continuous) variables are formulated for determining toll levels and toll locations simultaneously. A binary genetic algorithm is used to search optimal toll locations dynamically and a simulated annealing method is used to search optimal toll levels.