This study describes the use of a Direct Search (DS) meta-heuristic algorithm for solving the toll design problem, in terms of finding the optimum toll level, in private roads. The problem is formulated as a nonconvex, bilevel nonlinear mathematical program which seeks to maximize toll revenues while taking into account the travel responses of network users, through a multi-class stochastic user equilibrium traffic assignment model with elastic demand. The algorithm is implemented onto a real-life urban sub-network which includes a private highway. The results show the ability of the DS algorithm to relatively quickly find an optimal solution and signify its potential to provide a competitive alternative to the currently used genetic algorithm (GA) approach for solving such types of nonconvex bilevel programs in the sector of road transport services.
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