Optimal deployment for anti-submarine operations with time-dependent strategies

In this paper, we consider the optimal deployment of multiple assets in anti-submarine warfare (ASW) operations with time-dependent strategies. We model this as a zero-sum game that takes place over a finite time horizon. An agent, representing multiple assets, in an ASW operation, decides on the allocation of these assets (e.g., one or more frigates and helicopters) to prevent an intruder, an enemy submarine, from attacking a moving high-value unit (HVU), e.g., a tanker ship. Hereby, the agent aims to prevent an intruder, an enemy submarine, from attacking a moving HVU, e.g., a tanker ship. The intruder is deciding on a route that minimizes the detection probability given the agent’s strategy. We first consider a game model where a part of the agent’s strategy, namely the complete strategy of a frigate, is known to the intruder; and second, we consider a sequential game approach where the exact location of the frigate becomes known to the intruder at the start of each time interval. For both approaches, we construct (integer) linear programs, give complexity results, and use an algorithmic approach to determine optimal strategies. Finally, we explore the added value of this approach in comparison to a traditional ASW simulation model.