Weapon Target Assignment Research Articles

A Solution to Dynamic Weapon Assignment Problem Based on Game Theory for Naval Platforms

Weapon target assignment is a critical challenge in military contexts. Traditionally, commanding officers manually decide weapon assignments, but the problem’s complexity has grown over time. To address this, automated systems have been introduced. These systems fall into two categories, which are static (time-independent) and dynamic (considering changes over time). Static systems solve the problem for a single time step without considering temporal changes. Dynamic systems incorporate time as a variable, adapting to evolving scenarios. Two main approaches exist, which are asset-based and target-based. Asset-based approach maximizes the survival probability of assets, which is our focus in this study. We propose a solution using game theory that spans the entire area and all time frames. We employ game theory, treating continuous functions of time as utility functions for vessels. Continuous probability-to-kill values for weapons are defined across the area. Threat trajectories yield continuous kill probabilities for the weapons, translating to vessel utility. To avoid inefficiencies, we align individual vessel utility with global utility. The Nash Equilibrium provides the optimal weapon assignment strategy. Our study uses a naval environment for analysis. In summary, our research leverages game theory to dynamically assign weapons to naval vessels, aiming to maximize asset survival.

Efficient Adaptive Large Neighborhood Search for Sensor–Weapon–Target Assignment

Efficient Adaptive Large Neighborhood Search for Sensor–Weapon–Target Assignment

Dynamic soft-kill weapon-target assignment in naval environments

One of the most significant threats faced by ships is anti-ship missiles. Nowadays, these missiles, equipped with diverse guidance systems, can locate their trajectory and attack the ship. Consequently, ships need to utilize their weapons to attempt to neutralize these threats. This article aims to develop dynamic assignment algorithms to assign a ship’s defensive soft-kill weapons to a set of incoming missiles, to minimize the average damage inflicted on the ship. To this end, initially, a binary linear programming model is developed to solve the static weapon-target assignment problem. Subsequently, a simulation–optimization algorithm and a reinforcement learning-based approach, grounded in the value iteration algorithm, are developed to solve the dynamic weapon-target assignment problem. To compare and evaluate the performance of the developed solution methods, we employ a set of randomly generated test instances. Computational results indicate that the reinforcement learning approach, due to its inherent foresight, outperforms the simulation–optimization approach in reducing the inflicted damages. However, in terms of CPU run time, the simulation–optimization approach is more efficient.

Static Weapon Target Assignment Based on Battle Probabilities and Time Discounted Reward

Target-based weapon-target assignment (WTA) aims to minimize the total value of enemies. It means that maximizing the total reduced value of the enemies is the objective of the target-based WTA. The reward of an assignment is typically set as the reduction in the enemy’s value when an ally and an enemy have combat, and the value is calculated by multiplying the current value of the enemy by the probability of the enemy’s survival after the combat. However, allies may be assigned to enemies who are far away if the reward is calculated similarly. Additionally, a method of calculating battle probability that reflects the characteristics and deployment of enemies and allies is needed in order to apply it in the defense industry. In this paper, we propose a target-based static weapon-target assignment to solve these problems. First, we propose a method to calculate battle probabilities for one-to-one, one-to-many, many-to-one, and many-to-many combat. The probabilities are composed of 4 cases; ally-survival-enemy-survival, ally-survival-enemy-destroyed, ally-destroyed-enemy-survival, and ally-destroyed-enemy-destroyed. Then a time-discounted reward for assignment based on the battle probabilities is calculated to consider the time it takes to have combat. Finally, the tank combat simulation results are discussed. The performance of the proposed WTA algorithm is highlighted through an analysis of assignment results and a comparison of outcomes based on the application of time-discounted rewards.

Target assignment for multiple stages of weapons systems using a deep Q-learning network and a modified artificial bee colony method

Multistage Weapon Target Assignment (MWTA) in defense systems is a critical process that focuses on minimizing deviations and inaccuracies during target assignment across stages like initialization, tracking, and counterattack. The research problem lies in efficiently assigning targets to weapon systems while accounting for distractions and tracking accuracy constraints. Existing approaches often face challenges related to computational complexity, real-time engagement limitations, and scalability issues, leading to inaccuracies in various stages within the system's perceived radius. This paper proposes a novel State-based Modified Artificial Bee Colony Method (SMABCM) that integrates Q-learning to generate adaptive target assignment decisions. SMABCM aims to maximize assignment accuracy by prioritizing low deviation rewards, enabling precise one-to-one target tracking and reducing the population of the artificial bee colony. The Q-learning network dynamically defines generation and reduction states based on deviations to minimize distracting targets and enhance tracking precision. Experimental results demonstrate SMABCM's superior performance over existing approaches in target precision comparison, hit probability, increase in distracting target detection, reduced deviation factor, and computation time. As the speed increases, the proposed SMABCM improves target accuracy by 9.54 %, hit probability by 9.17 %, distracting target detection by 12.35 %, while reducing deviation by 7.39 % and computation time by 10.11 %. This approach addresses complexities in multistage weapon systems through dynamic strategies, contributing to proactive defense against evolving security threats.

A performance comparison of utility functions for game theory based weapon-target assignment

The weapon-target assignment problem has been considered as an essential issue for military applications to provide a protection for defended assets. The goal of a typical weapon-target assignment problem is to maximize the expected survivability of the valuable assets. In this study, defense of naval vessels that encounter aerial targets is considered. The vessels are assumed to have different types of weapons having various firepower and cost as well as the incoming targets may have different attack capabilities. In a typical scenario, in addition to protecting assets, it is also desirable to minimize the cost of weapons. Therefore, an asset-based static weapon-target assignment problem is considered in order to both maximize the expected survivability of the assets and minimize the weapon budget. Thus, a co-operative game theory based solution is proposed which relates the utilities of the individuals to the global utility and reach the Nash equilibrium.

Dynamic Gaussian mutation beetle swarm optimization method for large-scale weapon target assignment problems

The weapon target assignment is a crucial issue for firepower resources optimization in modern warfare. Such a problem is complicated, multi-constrained, strongly nonlinear, NP-complete and the existing studies did not consider the suitability between different weapons and targets. In this paper, a novel weapon target assignment model is established that involves the weapon-target suitability and is closer to the real combat scenarios. Then, in view of that the conventional weapon target assignment methods are difficult to be applied in the large-scale problems efficiently, this work proposes a dynamic Gaussian mutation beetle swarm optimization algorithm with rule-based chaotic initialization. With the assistance of the dynamic parameter adjustment strategies and Gaussian mutation, the improved algorithm has fast convergence speed and high convergence accuracy, and it can solve the weapon target assignment problems with excellent optimization capabilities. Besides, the rule-based chaotic initialization strategy is embedded in this algorithm to generate high-quality population with better diversity. Finally, two comparative simulation cases of different initialization methods and algorithms for solving the large-scale weapon target assignment problems are designed. The results demonstrate that the proposed approach can provide more superior assignment schemes than its competitors with enhanced efficiency.

A hybrid multi-objective evolutionary algorithm with high solving efficiency for UAV defense programming

Emerging Unmanned Aerial Vehicle (UAV) application patterns, including the Loyal Wingman and Unmanned Swarms, have significantly challenged the administration and defense against illegal or trespassing UAVs. The weapon-target assignment (WTA) problem, a famous combinatorial optimization problem in military operations research, is decisive for the success of UAV defense programming. Related investigations face two main challenges: 1) Constructing a multi-objective optimization model reflecting the complexities of new UAV application patterns, and 2) solving the time-consuming WTA problem with high-dimension decision variables as it is NP-complete. This paper introduces a modified differential evolution based on a new mapping method called Pareto-Optimal-Matching that solves multi-objective binary optimization problems and constructs a 3 objective Sensor-Weapon-Target Assignment model. The proposed algorithm overcomes the inherent limitation of traditional differential evolution, which only performs well in continuous problems. Promising results were obtained based on different simulation metrics under various problems (proposed model, MOKP, and ZDT5), validating the superior performance of the proposed algorithm.

A Study on the Weapon–Target Assignment Problem Considering Heading Error

The focus of this study is to investigate the assignment of weapons to multiple targets in a scenario, specifically when an air defense system is confronted with numerous targets, such as low-altitude rockets or groups of drones. The accuracy of weapons in destroying these targets depends heavily on the correct alignment of the launchers with the targets, which can be affected by errors in launcher orientation. Therefore, in solving weapon–target assignment (WTA) problems, it is crucial to account for the heading errors caused by the launcher’s orientation angle. To address this issue, the use of a rotation strategy to align the orientation angle with the target’s approach direction can significantly improve the probability of kill (PK) against the target. However, its unitary implementation has limitations, which may result in missed engagements if there is insufficient time to rotate to the desired orientation angle. Thus, as a remedy, we propose a new WTA method that combines rotation and rotation fix strategy, improving the weakness of losing the opportunity of engagement due to rotation time and heading errors. The efficacy of this approach is evaluated through numerical simulations.

Efficacy analysis of NSGAII and multi-objective particle swarm optimization (MOPSO) in agent based weapon target assignment (WTA) model

Efficacy analysis of NSGAII and multi-objective particle swarm optimization (MOPSO) in agent based weapon target assignment (WTA) model

MOEA with adaptive operator based on reinforcement learning for weapon target assignment

<abstract><p>Weapon target assignment (WTA) is a typical problem in the command and control of modern warfare. Despite the significance of the problem, traditional algorithms still have shortcomings in terms of efficiency, solution quality, and generalization. This paper presents a novel multi-objective evolutionary optimization algorithm (MOEA) that integrates a deep Q-network (DQN)-based adaptive mutation operator and a greedy-based crossover operator, designed to enhance the solution quality for the multi-objective WTA (MO-WTA). Our approach (NSGA-DRL) evolves NSGA-II by embedding these operators to strike a balance between exploration and exploitation. The DQN-based adaptive mutation operator is developed for predicting high-quality solutions, thereby improving the exploration process and maintaining diversity within the population. In parallel, the greedy-based crossover operator employs domain knowledge to minimize ineffective searches, focusing on exploitation and expediting convergence. Ablation studies revealed that our proposed operators significantly boost the algorithm performance. In particular, the DQN mutation operator shows its predictive effectiveness in identifying candidate solutions. The proposed NSGA-DRL outperforms state-and-art MOEAs in solving MO-WTA problems by generating high-quality solutions.</p></abstract>

War game problem considering the mobility of weapons and targets

War-Gaming is recognized as a valuable tool for commanders, leaders, and managers. Well-executed War-Games have delivered significant competitive advantages in numerous conflicts. The war-game confirmed the commanders’ knowledge of weapon systems and performance, as well as the time and space necessary to carry out battlefield maneuvers. One of the primary missions of each army on the battlefield is weapon target assignment. The weapon target assignment (WTA) is a critical problem to command to be solved in battlefield decisions. In a WTA problem, we should assign available weapons to determined targets appropriately to optimize the performance criteria. This study discusses a problem in relation to allocating and scheduling in WTA considering the mobility weapons and mobility targets. Bi-level linear programming problem is defined so that each level independently optimizes its own objective functions but is influenced by actions taken by another unit. To solve the under studied problem, three famous meta-heuristic algorithms including simulated annealing (SA), genetic algorithm (GA) and grey wolf optimizer (GWO) methods are proposed. Since the performance of meta-heuristic algorithms depends on setting the parameters, the Taguchi method has been used statistically for set parameters of the developed Algorithms. Performance evaluation of the presented algorithms is conducted through numerical experiments involving randomly generated test problems. To compare the results of proposed meta-heuristic algorithms, ANOVA and Tukey tests were used. The Computational results have shown that proposed GWO algorithm worked better than the SA and GA algorithms.

Solving multi-objective weapon-target assignment considering reliability by improved MOEA/D-AM2M

The weapon-target assignment problem is a challenging optimization issue, but reliability is seldom considered in the majority of existing literature. To address the high-reliability weapon-target assignment problem, this paper integrates weapon reliability and mission reliability into a multi-objective optimization model (MOD) and presents an improved algorithm termed MOEA/D-iAM2M to the problem. This algorithm effectively combines the strengths of adaptive search space decomposition-based MOEA (MOEA/D-AM2M) and two-stage hybrid learning-based MOEA (HLMEA), resulting in a faster convergence rate and a more extensive distribution of the Pareto solution set. Furthermore, a reference point is incorporated into MOEA/D-iAM2M to facilitate the adaptive weight adjustment. Numerical experiments are carried out to confirm the effectiveness of the proposed MOEA/D-iAM2M. This research is significant in the field of optimization and has practical value in the defense industry.

Elite-centered artificial bee colony algorithm with extended solution boundary

To improve the performance of Artificial Bee Colony (ABC) algorithm, we propose a novel approach (named ESOABC-EC&ACS). First, the existence of solutions outside the constrained region (ESO) is designed to explore the possibility of the search helped by these solutions, which facilitates exploring the boundary of the constrained region and obtaining optimal solutions faster. Then, an elite-centered search equation is proposed to balance exploration and exploitation. Finally, adaptive bee colony scaling is constructed to help convergence. Our approach is the combination of these three techniques. The experimental results demonstrate that ESOABC-EC&ACS outperforms other ABC variants and some non-ABC meta-heuristic algorithms on most of the test functions in terms of solution quality. And the proposed heuristic factor for the dynamic weapon target assignment problem can improve the optimization performance. The ESO is the first universal strategy proposed for the survival of solutions outside the constraint region (out-of-bounds) generated when solving various problems directly, which causes extended solution boundary and affects the exploration of the constrained region boundary.

A Hybrid BA - VNS Algorithm for Solving the Weapon Target Assignment Considering Mobility of Resources

A Hybrid BA - VNS Algorithm for Solving the Weapon Target Assignment Considering Mobility of Resources

Shuffled Frog Leaping Algorithm with Non-Dominated Sorting for Dynamic Weapon-Target Assignment

Shuffled Frog Leaping Algorithm with Non-Dominated Sorting for Dynamic Weapon-Target Assignment

A quantum algorithm for solving weapon target assignment problem

Quantum computers, known to have the potential for exponential speedup in solving some problems due to their superposition property, are expected to facilitate the solution of NP-hard optimisation problems. This study proposes a quantum algorithm to solve the weapon target assignment problem (WTAP), one of the NP-hard optimisation problems. The proposed quantum algorithm is a gate-based approach, and scenario examples are executed on Qiskit quantum computing platform and IBM Lima quantum computer with Falcon r4T processor type. The results manifest that the proposed quantum algorithm has low space and time complexity, demonstrating its memory and computational resources efficiency.

Adaptive large neighborhood search algorithm for multi-stage weapon target assignment problem

Weapon target assignment (WTA) is a critical operational research topic that can be applied to plentiful military fields. A new variant of WTA, the multi-stage WTA problem, is investigated, which is to assign limited weapons to all targets in multiple attacking phases. The attacking flexibility for targets in different stages is considered, and a binary nonlinear integer programming model is developed to formulate the problem. An improved adaptive large-scale neighborhood search (ALNS) algorithm is proposed. First, a priority-based encoding strategy is designed to facilitate the feasible solution generating and solution space exploring. Then, six specific neighborhood structures are designed to generate 15 operators through their combination. The simulated annealing mechanism is integrated to avoid getting trapped in local optima. Moreover, an adaptive learning strategy is employed to improve the exploration capability. Both exact methods and metaheuristics are compared with the ALNS algorithm by instances with different scales. Experimental results show that, for most situations, the ALNS algorithm can obtain higher-quality solutions in a shorter time.

Weapon target assignment strategy for shipboard power system considering high power pulse loads integration

In the current naval combat environment, the instantaneous high-energy nonlinear high-power pulse load is gradually developed into a core equipment and facilities for military ships, and the nonlinear and transient impact characteristics of high-power pulse load are obvious. In this paper, the weapon–target assignment (WTA) modeling and solving problem are studied considering the pulse loads integration. Firstly, the multi-objective optimization method is used in this paper, and the optimization objective function is defined as maximizing the attack ability of high power pulse load in a short time and minimizing the total survival probability of incoming targets. The WTA model under multiple constraints is established. Then, genetic algorithm (GA) is used to solve the problem, taking into account the characteristics of impulsive load and WTA problem. Finally, simulation cases are constructed for experimental analysis. The simulation results show that the proposed model and algorithm can obtain an effective solution to the WTA problem with impulsive load, which has certain significance of reference.

Weapon–Target Assignment Using a Whale Optimization Algorithm

The weapon-target assignment (WTA) is a well-known task distribution issue in complicated combinational optimization, which is essential to management and decision-making in marine coordinated combat. This paper proposes a whale optimization algorithm (WOA) to address the WTA and the purpose was to maximize the combat effectiveness and determine the greatest decision matrix while equitably distributing the weapon unit resources of the weapon systems to the threat targets. The WOA is based on the whales’ bubble-net assaulting behavior that mimics encompassing contraction strategy, bubble-net assaulting strategy and random hunting strategy to successfully resolve the optimization issue. The WOA not only has excellent stability and robustness to determine a quicker convergence speed and greater calculation accuracy but also utilizes exploration or exploitation to avoid search stagnation and accomplish the most effective solution. Four sets of experiments are utilized to confirm the superiority and productivity of the WOA, the results are compared with those of AOA, BA, GWO, MVO, SCA, SOA, SSA and TSA by maximizing the fitness value. The experimental results demonstrate that WOA has a greater convergence precision and stronger optimization efficiency, which is a practical and feasible method to satisfy the fundamental requirements of real-time decision-making.