Preferential defense strategies. :

Includes bibliographical references (p. 24-25).Cover title.Research supported by the Joint Directors of Laboratories. ONR-N00014-85-K-0782 Research supported by the Office of Naval Research. ONR-N00014-84-K-0519Patrick A. Hosein, Michael Athans

OPTIMIZING VLS FIRING POLICY: AN ENUMERATION OF HETEROGENEOUS SEQUENCES TO INFORM EXPENDITURE

The U.S. Navy (USN) utilizes the Vertical Launch System (VLS) to store and launch both their offensive and defensive missiles. Since the number of VLS silos on a given ship is fixed, to maximize offensive capability the USN needs to minimize the number of interceptors required to combat incoming anti-surface missiles. Current firing policies may be overly conservative and expend too many interceptors per incoming threat, which results in a substantial fraction of VLS silos dedicated to defensive missiles. Decision makers need an analysis tool to explore the trade-off between missile consumption and probability of raid annihilation (PRA) for various firing policies and would also benefit from a prescriptive algorithm to help inform missile expenditure. This thesis provides a model to optimize VLS firing policy using a set of multiple interceptor types while accounting for range limitations, travel time, multi-interceptor salvos, battle damage assessment, and range dependent probability of kill. Additionally, the thesis derives analytical results for the optimal, lowest-cost allocation of interceptors in the single interceptor case, which, in turn, generates insight into how to structure sequential salvos.N81, Washington DCEnsign, United States NavyApproved for public release. Distribution is unlimited

Operations Research in the High Tech Military Environment: A Survey

The use of operations research as a technology to solve many of the problems of government and industry has become a major field of study within the very short span of the last fifty years. In the paper entitled, Operations Research in the High Tech Military Environment: A Survey, the reader is provided with a better understanding of the tenets of operations research through an examination of a representative sample of the latest operations research applications developed for the high tech environment. Initially, this involves providing the reader with some fundamental insights into what operations research is, what its practitioners do, and how the state-of-the-art has evolved to its present form. It then involves providing a brief description of what is meant by the term, high tech military environment. A survey, which constitutes the bulk of the material presented, focuses on how various operations research methodologies are being used within that environment. The paper concludes with a discussion of the possible directions operations research will take in the future, based on the present state-of-the-art

A Game Theoretic Model for the Optimal Disposition of Integrated Air Defense System Assets

We examine the optimal allocation of Integrated Air Defense System (IADS) resources to protect a country\u27s assets, formulated as a Defender-Attacker-Defender three-stage sequential, perfect information, zero-sum game between two opponents. We formulate a trilevel nonlinear integer program for this Defender-Attacker-Defender model and seek a subgame perfect Nash equilibrium, for which neither the defender nor the attacker has an incentive to deviate from their respective strategies. Such a trilevel formulation is not solvable via conventional optimization software and an exhaustive enumeration of the game tree based on the discrete set of strategies is intractable for large problem sizes. As such, we test and evaluate variants of a tree pruning algorithm and a customized heuristic, which we benchmark against an exhaustive enumeration. Our tests demonstrate that the pruning strategy is not efficient enough to scale up to a larger problem. We then demonstrate the scalability of the heuristic to show that the model can be applied to a realistic size problem

Approximate Dynamic Programming for Military Resource Allocation

This research considers the optimal allocation of weapons to a collection of targets with the objective of maximizing the value of destroyed targets. The weapon-target assignment (WTA) problem is a classic non-linear combinatorial optimization problem with an extensive history in operations research literature. The dynamic weapon target assignment (DWTA) problem aims to assign weapons optimally over time using the information gained to improve the outcome of their engagements. This research investigates various formulations of the DWTA problem and develops algorithms for their solution. Finally, an embedded optimization problem is introduced in which optimization of the multi-stage DWTA is used to determine optimal weaponeering of aircraft. Approximate dynamic programming is applied to the various formulations of the WTA problem. Like many in the field of combinatorial optimization, the DWTA problem suffers from the curses of dimensionality and exact solutions are often computationally intractability. As such, approximations are developed which exploit the special structure of the problem and allow for efficient convergence to high-quality local optima. Finally, a genetic algorithm solution framework is developed to test the embedded optimization problem for aircraft weaponeering

Game Theory and Prescriptive Analytics for Naval Wargaming Battle Management Aids

NPS NRP Technical ReportThe Navy is taking advantage of advances in computational technologies and data analytic methods to automate and enhance tactical decisions and support warfighters in highly complex combat environments. Novel automated techniques offer opportunities to support the tactical warfighter through enhanced situational awareness, automated reasoning and problem-solving, and faster decision timelines. This study will investigate how game theory and prescriptive analytics methods can be used to develop real-time wargaming capabilities to support warfighters in their ability to explore and evaluate the possible consequences of different tactical COAs to improve tactical missions. This study will develop a conceptual design of a real-time tactical wargaming capability. This study will explore data analytic methods including game theory, prescriptive analytics, and artificial intelligence (AI) to evaluate their potential to support real-time wargaming.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.

Modeling short-range ballistic missile defense and Israel's Iron Dome system

This paper develops a model of short-range ballistic missile defense and uses it to study the performance of Israel’s Iron Dome system. The deterministic base model allows for inaccurate missiles, unsuccessful interceptions, and civil defense. Model enhancements consider the trade-offs in attacking the interception system, the difficulties faced by militants in assembling large salvos, and the effects of imperfect missile classification by the defender. A stochastic model is also developed. Analysis shows that system performance can be highly sensitive to the missile salvo size, and that systems with higher interception rates are more “fragile” when overloaded. The model is calibrated using publically available data about Iron Dome’s use during Operation Pillar of Defense in November 2012. If the systems performed as claimed, they saved Israel an estimated 1778 casualties and $80 million in property damage, and thereby made preemptive strikes on Gaza about 8 times less valuable to Israel. Gaza militants could have inflicted far more damage by grouping their rockets into large salvos, but this may have been difficult given Israel’s suppression efforts. Counter-battery fire by the militants is unlikely to be worthwhile unless they can obtain much more accurate missiles.Fulbright Canada, Norwich Universit

A Methodology to Enhance Quantitative Technology Evaluation Through Exploration of Employment Concepts in Engagement Analysis

The process of designing a new system has often been treated as a purely technological problem, where the infusion or synthesis of new technologies forms the basis of progress. However, recent trends in design and analysis methodologies have tried to shift away from the narrow scope of technology-centric approaches. One such trend is the increase in analysis scope from the level of an isolated system to that of multiple interacting systems. Analysis under this broader scope allows for the exploration of non-materiel solutions to existing or future problems. Solutions of this type can reduce the cost of closing capability gaps by mitigating the need to procure new systems to achieve desired levels of performance. In particular, innovations in the employment concepts can enhance existing, evolutionary, or revolutionary materiel solutions. The task of experimenting with non-materiel solutions often falls to operators after the system has been designed and produced. This begs the question as to whether the chosen design adequately accounted for the possibility of innovative employment concepts which operators might discover. Attempts can be made to bring the empirical knowledge possessed by skilled operators upstream in the design process. However, care must be taken to ensure such attempts do not introduce unwanted bias, and there can be significant difficulty in translating human intuition into an appropriate modeling paradigm for analysis. Furthermore, the capacity for human operators to capitalize on the potential benefits of a given technology may be limited or otherwise infeasible in design space explorations where the number of alternatives becomes very large. This is especially relevant to revolutionary concepts to which prior knowledge may not be applicable. Each of these complicating factors is exacerbated by interactions between systems, where changes in the decision-making processes of individual entities can greatly influence outcomes. This necessitates exploration and analysis of employment concepts for all relevant entities, not only that or those to which the technology applies. This research sought to address the issues of exploring employment concepts in the early phases of the system design process. A characterization of the problem identified several gaps in existing methodologies, particularly with respect to the representation, generation, and evaluation of alternative employment concepts. Relevant theories, including behavioral psychology, control theory, and game theory were identified to facilitate closure of these gaps. However, these theories also introduced technical challenges which had to be overcome. These challenges stemmed from systematic problems such as the curse of dimensionality, temporal credit assignment, and the complexities of entity interactions. A candidate approach was identified through thorough review of available literature: Multi-agent reinforcement learning. Experiments show the proposed approach can be used to generate highly effective models of behavior which could out-perform existing models on a representative problem. It was further shown that models produced by this new method can achieve consistently high levels of performance in competitive scenarios. Additional experimentation demonstrated how incorporation of design variables into the state space allowed models to learn policies which were effective across a continuous design space and outperformed their respective baselines. All of these results were obtained without reliance on prior knowledge, mitigating risks in and enhancing the capabilities of the analysis process. Lastly, the completed methodology was applied to the design of a fighter aircraft for one-on-one, gun-only air combat engagements to demonstrate its efficacy on and applicability to more complex problems.Ph.D