“Elastic Multi-User Stochastic Equilibrium Toll Design with Direct Search Meta-Heuristics”

Here is the abstract of a sadly under-cited piece (pdf), by Dimitriou and Tsekeris, which is only now receiving some trial implementation attempts:

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.