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Electric vehicles (EVs) have been highly favoured as a future transportation mode in the transportation section in recent years. EVs have many advantages compared to traditional transportation, especially the environmental aspect. However, despite many EVs' benefits, operating EVs has limitations in their usage. One of the significant issues is the uncertainty in their driving range. The driving range of EVs is closely related to their energy consumption, which is highly affected by exogenous and endogenous factors. Since those factors are unpredictable, uncertainty in EVs' energy consumption should be considered for efficient operation. This paper proposes an adaptive robust optimization framework for the electric vehicle routing problem. The objective is to minimize the worst-case energy consumption while guaranteeing that services are delivered at the appointed time windows without battery level deficiency. We postulate that EVs can be recharged en route, and the charging amount can be adjusted depending on the circumstance. The proposed problem is formulated as a two-stage adaptive robust problem. A column-and-constraint generation based heuristic algorithm, which is cooperated with variable neighborhood search and alternating direction algorithm, is proposed to solve the proposed model. The computational results show the economic efficiency and robustness of the proposed model, and that there is a tradeoff between the total required energy and the risk of failing to satisfy all customers' demand.