In the current work, we considered the problem of hazardous material distribution where the distributer chooses the routes on the network, and a regulatory agency controls the behaviour of the distributer to traverse the specified routes. In these circumstances, the distributer sets to select some routes to minimise the total distributing costs. Mostly, this occurs due to selecting risky arcs in which more individuals are exposed to risk. To prevent this and increase the capability to deal with the risk of hazardous material transportation through roads, the regulatory agency obliges carriers to traverse through the most secure arcs, though imposing more distribution costs. The problem is modelled as a bi-level routing problem. The bi-level model is difficult to solve and may be ill-posed. Two meta-heuristic algorithms are proposed to solve the bi-level model, and some randomly generated problems are applied to show the applicability and efficiency of the proposed algorithms.
