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Given a transportation network with node and edge capacity constraints, initial node occupancy, destination locations, and the conflict resolution parameter k, the Conflict-Free Evacuation Route Planner (CF-ERP) problem finds evacuation routes that can minimize the evacuation time and the number of movement conflicts along the routes. CF-ERP is important for many societal applications, such as evacuation management and preparation in case of natural or man-made disasters. The problem is computationally challenging due to the large size of the transportation network and the constraints. Related work has considered the evacuation routing problem either solely as a network flow optimization problem or a conflict minimization problem, but not both. In this paper, we propose novel approaches that can produce evacuation routes to minimize the evacuation time and the number of movement conflicts. Experiments and a case study on real-world datasets from Florida show the effectiveness and efficiency of the proposed approaches.