In this paper, we generated intelligent self-driving policies that minimize the injury severity in unexpected traffic signal violation scenarios at an intersection using the deep reinforcement learning. We provided guidance on reward engineering in terms of the multiplicity of objective function. We used a deep deterministic policy gradient method in the simulated environment to train self-driving agents. We designed two agents, one with a single-objective reward function of collision avoidance and the other with a multi-objective reward function of both collision avoidance and goal-approaching. We evaluated their performances by comparing the percentages of collision avoidance and the average injury severity against those of human drivers and an autonomous emergency braking (AEB) system. The percentage of collision avoidance of our agents were 78.89% higher than human drivers and 84.70% higher than the AEB system. The average injury severity score of our agents were only 8.92% of human drivers and 6.25% of the AEB system.