The Traffic Alert and Collision Avoidance System (TCAS) uses an on-board beacon radar to monitor the local air traffic and logic to determine when to alert pilots to potential conflict. The current TCAS logic was the result of many years of development and involved the careful engineering of many heuristic rules specified in pseudocode. Unfortunately, due to the complexity of the logic, it is difficult to revise the pseudocode to accommodate the evolution of the airspace and the introduction of new technologies and procedures. This report summarizes recent advances in computational techniques for automatically deriving the optimal logic with respect to a probabilistic model and a set of performance metrics. Simulations demonstrate how this new approach results in logic that significantly outperforms TCAS according to the standard safety and operational performance metrics.