The growing number of man-made and natural disasters in recent years has made the disaster management a focal point of interest and research. To assist and streamline emergency evacuation, changing the directions of the roads (called contraflow, a traffic control measure) is proven to be an effective, quick and affordable scheme in the action list of the disaster management. The contraflow is computationally a challenging problem (known as NP-hard), hence developing an efficient method applicable to real-world and large-sized cases is a significant challenge in the literature. To cope with its complexities and to tailor to practical applications, a hybrid heuristic method based on a machine-learning model and bilevel optimization is developed. The idea is to try and test several contraflow scenarios providing a training dataset for a supervised learning (regression) model which is then used in an optimization framework to find a better scenario in an iterative process. This method is coded as a single computer program synchronized with GAMS (for optimization), MATLAB (for machine learning), EMME3 (for traffic simulation), MS-Access (for data storage) and MS-Excel (as an interface), and it is tested using a real dataset from Winnipeg, and Sioux-Falls as benchmarks. The algorithm managed to find globally optimal solutions for the Sioux-Falls example and improved accessibility to the dense and congested central areas of Winnipeg just by changing the direction of some roads.