All large transport aircraft are required to be equipped with a collision avoidance system that instructs pilots how to maneuver to avoid collision with other aircraft. The uncertainty in the behavior of the intruding aircraft makes developing a robust collision avoidance logic challenging. This paper presents an automated approach for optimizing collision avoidance logic based on probabilistic models of aircraft behavior and a performance metric that balances the competing objectives of maximizing safety and minimizing alert rate. The approach involves framing the problem of collision avoidance as a Markov decision process that is solved using dynamic programming. Although this paper focuses on airborne collision avoidance for manned aircraft, the methods may be applied to collision avoidance for other categories of vehicles, both manned and unmanned.