# “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.

You will find some further results here.