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Given the counters of vehicles that traverse the roads of a traffic network, we reconstruct the travel demand that generated them expressed in terms of the number of origin-destination trips made by users. We model the problem as a bi-level optimization problem. At the inner-level, given a tentative demand, we solve a Dynamic Traffic Assignment (DTA) problem to decide the routing of the users between their origins and destinations. Finally, we adjust the number of trips and their origins and destinations at the outer-level to minimize the discrepancy between the counters generated at the inner-level and the given vehicle counts measured by sensors in the traffic network. We solve the DTA problem by employing a mesoscopic model implemented by the traffic simulator SUMO. Thus, the outer problem becomes an optimization problem that minimizes a black-box Objective Function (OF) determined by the results of the simulation, which is a costly computation. We study different approaches to the outer-level problem categorized as gradient-based and derivative-free approaches. Among the gradient-based approaches, we look at an assignment matrix-based approach and an assignment matrix-free approach that uses the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm. Among the derivative-free approaches, we investigate Machine Learning (ML) algorithms to learn a model of the simulator that can then be used as a surrogate OF in the optimization problem. We compare these approaches computationally on an artificial network. The gradient-based approaches perform the best in terms of solution quality and computational requirements. In contrast, the results obtained by the ML approach are currently less satisfactory but provide an interesting avenue for future research.