We develop the Game-Theoretic ASW Mission Planner (G-TAMP), an operational-level planning aid for the tasking of anti-submarine warfare (ASW) platforms to protect a high-value unit (HVU) from attack by hostile submarines (SSKs). We first present a defender-attacker optimization model in which the defender tasks platforms to minimize the probability that the enemy can reach the HVU, while the enemy observes and reacts to these visible defenses by routing SSKs to maximize this probability. A defender-attacker/defender (D-A/D) model then extends the first model by adding a final "defender stage" to task potentially "secret" platforms. This model also prescribes the optimal sensor mode for platforms that can use passive sonar (for secrecy) or active sonar (for increased detection ranges), in effect, quantifying the value of secrecy for the defender. Five scenarios illustrate the D-A/D model's ability to "shape" the battle space to the defender's advantage using visible platforms in the first stage, and then to exploit the secrecy of hidden platforms for maximum benefit. Model instances are mixed-integer programs with up to 14,000 constraints and 12,000 variables. In each case, an optimal or near-optimal search plan coordinates the actions of multiple, heterogeneous ASW platforms to protect an HVU from an intelligent enemy.

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http://archive.org/details/trileveloptimiza109453911

US Navy (USN) author.

Outstanding Thesis