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This study addresses a new electric vehicle routing problem with time windows and recharging strategies (EVRPTW-RS), where two recharging policies (i.e., full or partial recharging) and three recharging technologies (i.e., normal, rapid, and ultra-rapid) are considered. For this problem, we first develop a mixed-integer linear programming model defined in a series of vertices including a depot, a series of recharging stations, and a set of customers. Due to the strong NP-hardness of EVRPTW-RS, a tailored adaptive large neighborhood search heuristic (ALNS) which contains a number of advanced efficient procedures tailored to handle the proposed problem is developed. Numerical experiments for benchmark instances generated based on the Greater Toronto Area and Ontario in Canada are conducted to evaluate the performance of the proposed model and ALNS. Computational results demonstrate that the ALNS is highly effective in solving EVRPTW-RS and outperforms commercial solver CPLEX. Moreover, the advantages of the proposed recharging strategies are illustrated and some recommendations are provided for stakeholders when using electric vehicles for delivery.