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Real-Time Heuristics and Metaheuristics for Static and Dynamic Weapon Target Assignments

Improved predictability could increase the accuracy of missile defense systems in multiple engagements.

Projectile weapons have been a consistent threat of hostilities throughout history. Military advantage has always been aided by the capacity to inflict damage from a distance. In the 20th century, missile technology advanced to the point that an adversary had the potential to attack a protected asset from great distances. To neutralize this stand-off threat, the concept of air defense evolved. However, as the ability to reduce a missile threat increased, so, too, did the quantity and quality of missiles available, and research into the effective allocation of air defense resources emerged.

Originally introduced into the field of operations research by Manne (1958), the Weapon Target Assignment (WTA) Problem, or Missile Allocation Problem (MAP) as it is sometimes known, seeks to assign available interceptors to incoming missiles so as to minimize the probability of a missile destroying a protected asset. While much of the literature on the WTA focuses on the defensive perspective, some have considered the offensive perspective, wherein the objective is to maximize the probability of destroying enemy protected assets.

There are two distinct categories of the WTA: the Static WTA (SWTA) and the Dynamic WTA (DWTA). Originally modeled by Manne (1958), the SWTA defines a scenario wherein a known number of incoming missiles (targets) are observed and a finite number of interceptors (weapons), with known probabilities of successfully destroying the targets (probabilities of kill), are available for a single exchange. The solution to the SWTA informs the defense on how many of each weapon type to shoot at each target. In the SWTA, no subsequent engagements are considered since time is not a dimension considered in the problem.

By contrast, the DWTA includes time as a dimension. Variants of the DWTA include the two-stage DWTA and the shoot-look-shoot DWTA. The two-stage DWTA replicates the SWTA in its first stage, but includes a second stage wherein a number of targets of various types are known only to a probability distribution. In this variant, the solution to the DWTA informs the defense on how to allocate the weapons in the first stage and how many to reserve for the second stage in order to minimize the probability of destruction. The shoot-look-shoot variant also replicates the SWTA, however it enables the defense to observe which targets may have survived the engagement (leakers) and allows for a subsequent engagement opportunity. The solution to this variant similarly informs the defense on how to allocate the weapons and how many weapons to reserve to reengage any leakers.

The WTA has been solved to optimality with exact algorithms. However, as Lloyd & Witsenhausen (1986) showed that the WTA is NP-Complete, the majority of solution techniques seek to find near optimal solutions in real-time, or “fast enough to provide an engagement solution before the oncoming targets reached their goals”. These real-time solution techniques are products of heuristic algorithms or are solved using exact algorithms applied to transformations of the formulation.

The research report goes on to review the various formulations for both the SWTA and DWTA. The basic formulations of each are examined and the transformations that have been implemented are explored. Novel formulations that have sought to model and solve the problem in unique settings are reviewed, as are the exact algorithms that have been used to solve the SWTA and DWTA.

This work was done by Captain Alexander G. Kline for the Air Force Institute of Technology. AFRL-0273

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Real-Time Heuristics and Metaheuristics for Static and Dynamic Weapon Target Assignments

(reference AFRL-0273) is currently available for download from the TSP library.

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    Aerospace & Defense Technology Magazine

    This article first appeared in the August, 2019 issue of Aerospace & Defense Technology Magazine (Vol. 4 No. 5).

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    Overview

    The document is a doctoral dissertation by Alexander G. Kline, titled "Real-Time Heuristics and Metaheuristics for Static and Dynamic Weapon Target Assignments," completed at the Air Force Institute of Technology between March 2016 and October 2018. The research addresses the complex problem of weapon target assignment, which is crucial for military operations, particularly in scenarios involving missile defense systems.

    The dissertation explores both static and dynamic environments where weapon systems must be assigned to targets efficiently and effectively. Static assignments refer to scenarios where the targets and weapons are fixed, while dynamic assignments involve changing conditions, such as moving targets or evolving threats. The author employs real-time heuristics and metaheuristics—advanced computational techniques that provide approximate solutions to complex optimization problems—to enhance decision-making processes in these contexts.

    Kline's work emphasizes the importance of timely and accurate target assignments to maximize the effectiveness of military resources. The dissertation presents various algorithms and methodologies designed to improve the speed and accuracy of these assignments, thereby contributing to operational readiness and strategic advantage. The research includes a thorough analysis of existing methods, identifies their limitations, and proposes innovative solutions that leverage real-time data and computational power.

    The document also discusses the implications of these findings for military strategy and operations, highlighting how improved target assignment can lead to better resource allocation, reduced response times, and increased mission success rates. The author acknowledges the support of various organizations and individuals throughout the research process, and the work is presented with a clear structure, including an abstract, acknowledgments, and a comprehensive bibliography.

    Overall, Kline's dissertation is a significant contribution to the field of military operations research, providing valuable insights and practical solutions for enhancing weapon target assignment processes. It reflects the author's deep understanding of the challenges faced in modern warfare and the potential of advanced computational techniques to address these challenges effectively. The research is approved for public release, indicating its relevance and importance to broader defense and military communities.

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