The dynamic weapon-target assignment problem

Caption title. "To appear in Proc. 1989 Symposium on C2 research, Washington, D.C.Includes bibliographical references.Research supported by the Joint Directors of Laboratories (JDL), Basic Research Group on C3 Systems, under contract with the Office of Naval Research. ONR/N00014-85-K-0782 ONR/N00014-84-K-0519Patrick Hosein, Michael Athans

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

The problem of targeting and engaging individual missiles (targets) with an arsenal of interceptors (weapons) is known as the weapon target assignment problem. This problem has been well-researched since the seminal work in 1958. There are two distinct categories of the weapon target assignment problem: static and dynamic. The static weapon target assignment problem considers a single instance in which a known number of incoming missiles is to be engaged with a finite number of interceptors. By contrast, the dynamic weapon target assignment problem considers either follow on engagement(s) should the first engagement(s) fail, a subsequent salvo of incoming missiles, or both. This research seeks to define and solve a realistic dynamic model. First, assignment heuristics and metaheuristics are developed to provide rapid near-optimal solutions to the static weapon target assignment. Next, a technique capable of determining how many of each interceptor type to reserve for a second salvo by means of approximate dynamic programming is developed. Lastly, a model that realistically considers erratic flight paths of incoming missiles and determines assignments and firing sequences of interceptors within a simulation to minimize the number of hits to a protected asset is developed. Additionally, the first contemporary survey of the weapon target assignment problem since 1985 is presented. Collectively, this work extends the research of missile defense into practical application more so than currently is found within the literature

Exact and Heuristic Methods for the Weapon Target Assignment Problem

The Weapon Target Assignment (WTA) problem is a fundamental problem arising in defense-related applications of operations research. This problem consists of optimally assigning n weapons to m targets so that the total expected survival value of the targets after all the engagements is minimum. The WTA problem can be formulated as a nonlinear integer programming problem and is known to be NP-complete. There do not exist any exact methods for the WTA problem which can solve even small size problems (for example, with 20 weapons and 20 targets). Though several heuristic methods have been proposed to solve the WTA problem, due to the absence of exact methods, no estimates are available on the quality of solutions produced by such heuristics. In this paper, we suggest linear programming, integer programming, and network flow based lower bounding methods using which we obtain several branch and bound algorithms for the WTA problem. We also propose a network flow based construction heuristic and a very large-scale neighborhood (VLSN) search algorithm. We present computational results of our algorithms which indicate that we can solve moderately large size instances (up to 80 weapons and 80 targets) of the WTA problem optimally and obtain almost optimal solutions of fairly large instances (up to 200 weapons and 200 targets) within a few second

Real-Time Heuristic Algorithms for the Static Weapon-Target Assignment Problem

The problem of targeting and engaging individual missiles (targets) with an arsenal of interceptors (weapons) is known as the weapon target assignment problem. As many solution techniques are based upon a transformation of the objective function, their final solutions rarely produce optimal solutions. We propose a nonlinear branch and bound algorithm to provide the first optimization approach to the untransformed problem found in the literature. Further, we propose a new heuristic based upon the branch and bound algorithm which dominates other heuristics explored in optimality gap. We also propose a heuristic based upon the optimal solution to the quiz problem which finds solutions within 6% of optimal for small problems and provides statistically similar results as one of the best heuristics found in the literature for larger problems while solving these problems in ten thousandths of the time

Game Theoretic Target Assignment Strategies in Competitive Multi-Team Systems

The task of optimally assigning military ordinance to enemy targets, often termed the Weapon Target Assignment (WTA) problem, has become a major focus of modern military thought. Current formulations of this problem consider the enemy targets as either passive or entirely defensive. As a result, the assignment problem is solved purely as a one sided team optimization problem. In practice, however, especially in environments characterized by the presence of an intelligent adversary, this one sided optimization approach has very limited use. The presence of an adversary often necessitates incorporating its intended actions in the process of solving the weapons assignment problem. In this dissertation, we formulate the weapon target assignment problem in the presence of an intelligent adversary within the framework of game theory. We consider two teams of opposing units simultaneously targeting each other and examine several possible game theoretic solutions of this problem. An issue that arises when searching for any solution is the dimensionality of the search space which quickly becomes overwhelming even for simple problems with a small number of units on each side. To solve this scalability issue, we present a novel algorithm called Unit Level Team Resource Allocation (ULTRA), which is capable of generating approximate solutions by searching within appropriate subspaces of the search space. We evaluate the performance of this algorithm on several realistic simulation scenarios. We also show that this algorithm can be effectively implemented in real-time as an automatic target assigning controller in a dynamic multi-stage problem involving two teams with large number of units in conflict

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

Human-Machine Collaborative Optimization via Apprenticeship Scheduling

Coordinating agents to complete a set of tasks with intercoupled temporal and resource constraints is computationally challenging, yet human domain experts can solve these difficult scheduling problems using paradigms learned through years of apprenticeship. A process for manually codifying this domain knowledge within a computational framework is necessary to scale beyond the ``single-expert, single-trainee" apprenticeship model. However, human domain experts often have difficulty describing their decision-making processes, causing the codification of this knowledge to become laborious. We propose a new approach for capturing domain-expert heuristics through a pairwise ranking formulation. Our approach is model-free and does not require enumerating or iterating through a large state space. We empirically demonstrate that this approach accurately learns multifaceted heuristics on a synthetic data set incorporating job-shop scheduling and vehicle routing problems, as well as on two real-world data sets consisting of demonstrations of experts solving a weapon-to-target assignment problem and a hospital resource allocation problem. We also demonstrate that policies learned from human scheduling demonstration via apprenticeship learning can substantially improve the efficiency of a branch-and-bound search for an optimal schedule. We employ this human-machine collaborative optimization technique on a variant of the weapon-to-target assignment problem. We demonstrate that this technique generates solutions substantially superior to those produced by human domain experts at a rate up to 9.5 times faster than an optimization approach and can be applied to optimally solve problems twice as complex as those solved by a human demonstrator.Comment: Portions of this paper were published in the Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI) in 2016 and in the Proceedings of Robotics: Science and Systems (RSS) in 2016. The paper consists of 50 pages with 11 figures and 4 table

Essays on Integer Programming in Military and Power Management Applications

This dissertation presents three essays on important problems motivated by military and power management applications. The array antenna design problem deals with optimal arrangements of substructures called subarrays. The considered class of the stochastic assignment problem addresses uncertainty of assignment weights over time. The well-studied deterministic counterpart of the problem has many applications including some classes of the weapon-target assignment. The speed scaling problem is of minimizing energy consumption of parallel processors in a data warehouse environment. We study each problem to discover its underlying structure and formulate tailored mathematical models. Exact, approximate, and heuristic solution approaches employing advanced optimization techniques are proposed. They are validated through simulations and their superiority is demonstrated through extensive computational experiments. Novelty of the developed methods and their methodological contribution to the field of Operations Research is discussed through out the dissertation

Maximisation of Expected Target Damage Value

The weabon assignment problem has been modelled as a nonlinear integer programming problem'. The problem is to assign weapons to the targets to maximise the optimum-target damagevalue. There are constsainfs on various types of weapons available and on minimum number of weapons by types to be assigned to various targets. The objective function is nonlinear, theconstraints are linear in nature, and the,decision variables are restricted to be integers.The results obtained by Bracken and McCormick' should not be applied to solve t h e problem ofweapon assignment to target to maximise the optimum target damage value, because firstly, the results violate the constraints, and secondly, instead of using the integer programming techniques, the crude method of rounding off has been used,to obtain the sglution.-In this study, the I-GRST algorithm developed by ~ c eapnd Pant2.'h as been used to solve the weapon 3ssignnient problem. The results obtained are better than the results ohrn~nedb y Bracken ;~ndM cCormick'nnd also do not violate any constraints