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The school bus routing problem (SBRP) represents a variant of the well-known vehicle routing problem. The main goal of this study is to pick up students allocated to some bus stops and generate routes, including the selected stops, in order to carry students to school. In this paper, we have proposed a simple but effective metaheuristic approach that employs two features: first, it utilizes large neighborhood structures for a deeper exploration of the search space; second, the proposed heuristic executes an efficient transition between the feasible and infeasible portions of the search space. Exploration of the infeasible area is controlled by a dynamic penalty function to convert the unfeasible solution into a feasible one. Two metaheuristics, called N-ILS (a variant of the Nearest Neighbourhood with Iterated Local Search algorithm) and I-ILS (a variant of Insertion with Iterated Local Search algorithm) are proposed to solve SBRP. Our experimental procedure is based on the two data sets. The results show that N-ILS is able to obtain better solutions in shorter computing times. Additionally, N-ILS appears to be very competitive in comparison with the best existing metaheuristics suggested for SBRP