The Diesel Submarine Flaming Datum Problem

Military Operations Research, 6(4), 2001, pp. 19-30.The Flaming Datum problem is one of relocating an enemy target that is fleeing after momentarily reveling its position. A diesel submarine faces this problem after attacking a ship, since the ship creates a visible marker of where the submarine must once have been. The tactical problem has been studied before under the assumption that the submarine's motion is constrained only by a top speed. Here we add the constraint that the battery's capacity is also finite. The problem is bounded rather than solved. Techniques used include two-person zero-sum game theory and optimal control theory

A Framework for Delivering Contextually Appropriate Opportunities for Warfighter Practice

Computer-based modeling and simulation has been a training staple in the military domain since the first aircraft simulators were adopted. More recently, virtual environments based on modeling, simulation and serious games, have introduced relatively low-cost, yet high value additions to the learning environment. As these virtual environments have proliferated, many researchers have investigated the relationship between theoretical foundations of learning, learner development and content delivery, and applied their findings in an attempt to bolster learning, yet performance deficiencies continue to exist. This study asserts that performance deficiencies exist in part because of insufficient contextually appropriate opportunities to practice. This work is multi-disciplinary in nature. Its foundation is modeling and simulation engineering; the use of technology to deliver training. Educational psychology and human factors concepts explain the theoretical basis for modeling and simulation as an effective training delivery agent. The study\u27s thesis is that a framework for delivering contextually appropriate opportunities for warfighter practice can be applied to discover whether modeling, simulation and game-based virtual environments have the potential to improve individual performance for learners beyond the Novice Stage (e.g., Competent Stage) of skills acquisition. Furthermore, this conceptually appropriate practice (CAP) framework can be used to assess the potential of low fidelity virtual environments to provide targeted practice and to improve individual performance, not only during training in high-fidelity virtual environments (near transfer) but also in the live environment (far transfer). To evaluate the thesis, this study investigates the relationship of technology and learning science, and features an empirical evaluation of training effectiveness afforded by delivering additional training repetitions using both low-fidelity virtual environment simulator systems and high-fidelity aircraft simulators

Considerations for Cross Domain / Mission Resource Allocation and Replanning

NPS NRP Technical ReportNaval platforms are inherently multi-mission - they execute a variety of missions simultaneously. Ships, submarines, and aircraft support multiple missions across domains, such as integrated air and missile defense, ballistic missile defense, anti-submarine warfare, strike operations, naval fires in support of ground operations, and intelligence, surveillance, and reconnaissance. Scheduling and position of these multi-mission platforms is problematic since one warfare area commander desires one position and schedule, while another may have a completely different approach. Commanders struggle to decide and adjudicate these conflicts, because there is plenty of uncertainty about the enemy and the environment. This project will explore emerging innovative data analytic technologies to optimize naval resource allocation and replanning across mission domains. NPS proposes a study that will evaluate the following three solution concepts for this application: (1) game theory, (2) machine learning, and (3) wargaming. The study will first identify a set of operational scenarios that involve distributed and diverse naval platforms and resources and a threat situation that requires multiple concurrent missions in multiple domains. The NPS team will use these scenarios to evaluate the three solution concepts and their applicability to supporting resource allocation and replanning. This project will provide valuable insights into innovative data analytic solution concepts to tackle the Navy's challenge of conducing multiple missions with cross-domain resources.N2/N6 - Information WarfareThis research is supported by funding from the Naval Postgraduate School, Naval Research Program (PE 0605853N/2098). https://nps.edu/nrpChief of Naval Operations (CNO)Approved for public release. Distribution is unlimited.

ARTIFICIAL INTELLIGENCE-ENABLED MULTI-MISSION RESOURCE ALLOCATION TACTICAL DECISION AID

The Department of Defense supports many military platforms that execute multiple missions simultaneously. Platforms such as watercraft, aircraft, and land convoys support multiple missions over domains such as air and missile defense, anti-submarine warfare, strike operations, fires in support of ground operations, intelligence sensing and reconnaissance. However, major challenges to the human decision-maker exist in allocating these multi-mission resources such as the growth in battle-tempo, scale, and complexity of available platforms. This capstone study seeks to apply systems engineering to analyze the multi-mission resource allocation (MMRA) problem set to further enable artificial intelligence (AI) and machine learning tools to aid human decision-makers for initial and dynamic re-planning. To approach this problem, the study characterizes inputs and outputs of a potential MMRA process, then analyzes the scalability and complexity across three unique use cases: directed energy convoy protection, aviation support, and a carrier strike group. The critical findings of these diverse use cases were then assessed for similarities and differences to further understand commonalities for a joint AI-enabled MMRA tool.Civilian, Department of the ArmyCivilian, Department of the ArmyCivilian, Department of the NavyApproved for public release. Distribution is unlimited

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http://archive.org/details/effectoffalsecon00walsNAN

Games for the Optimal Deployment of Security Forces

In this thesis, we develop mathematical models for the optimal deployment of security forces addressing two main challenges: adaptive behavior of the adversary and uncertainty in the model. We address several security applications and model them as agent-intruder games. The agent represents the security forces which can be the coast guard, airport control, or military assets, while the intruder represents the agent's adversary such as illegal fishermen, terrorists or enemy submarines. To determine the optimal agent's deployment strategy, we assume that we deal with an intelligent intruder. This means that the intruder is able to deduce the strategy of the agent. To take this into account, for example by using randomized strategies, we use game theoretical models which are developed to model situations in which two or more players interact. Additionally, uncertainty may arise at several aspects. For example, there might be uncertainty in sensor observations, risk levels of certain areas, or travel times. We address this uncertainty by combining game theoretical models with stochastic modeling, such as queueing theory, Bayesian beliefs, and stochastic game theory. This thesis consists of three parts. In the first part, we introduce two game theoretical models on a network of queues. First, we develop an interdiction game on a network of queues where the intruder enters the network as a regular customer and aims to route to a target node. The agent is modeled as a negative customer which can inspect the queues and remove intruders. By modeling this as a queueing network, stochastic arrivals and travel times can be taken into account. The second model considers a non-cooperative game on a queueing network where multiple players decide on a route that minimizes their sojourn time. We discuss existence of pure Nash equilibria for games with continuous and discrete strategy space and describe how such equilibria can be found. The second part of this thesis considers dynamic games in which information that becomes available during the game plays a role. First, we consider partially observable agent-intruder games (POAIGs). In these types of games, both the agent and the intruder do not have full information about the state space. However, they do partially observe the state space, for example by using sensors. We prove the existence of approximate Nash equilibria for POAIGs with an infinite time horizon and provide methods to find (approximate) solutions for both POAIGs with a finite time horizon and POAIGs with an infinite time horizon. Second, we consider anti-submarine warfare operations with time dependent strategies where parts of the agent's strategy becomes available to the intruder during the game. The intruder represents an enemy submarine which aims to attack a high value unit. The agent is trying to prevent this by the deployment of both frigates and helicopters. In the last part of this thesis we discuss games with restrictions on the agent's strategy. We consider a special case of security games dealing with the protection of large areas for a given planning period. An intruder decides on which cell to attack and an agent selects a patrol route visiting multiple cells from a finite set of patrol routes, such that some given operational conditions on the agent's mobility are met. First, this problem is modeled as a two-player zero-sum game with probabilistic constraints such that the operational conditions are met with high probability. Second, we develop a dynamic variant of this game by using stochastic games. This ensures that strategies are constructed that consider both past actions and expected future risk levels. In the last chapter, we consider Stackelberg security games with a large number of pure strategies. In order to construct operationalizable strategies we limit the number of pure strategies that is allowed in the optimal mixed strategy of the agent. We investigate the cost of these restrictions by introducing the price of usability and develop algorithmic approaches to calculate such strategies efficiently

The Third Battle

Since the beginning of the twentieth century, submarines have been the weapon of choice for weaker naval powers that wish to contest a dominant power\u27s control of the seas or its ability to project power ashore from the sea. This is because submarines have been and are likely to remain the weapon system with the highest leverage in a battle for control of the ocean surface. Hence, antisubmarine warfare (ASW) will always re-main the most important element of the U.S. Navy\u27s core mission-sea control.https://digital-commons.usnwc.edu/usnwc-newport-papers/1017/thumbnail.jp