Weapon Target Assignment Problem Research Articles

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.

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.

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 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.

Solving Weapon-Target Assignment Problem with Salp Swarm Algorithm

Solving Weapon-Target Assignment Problem with Salp Swarm Algorithm

Weapon Target Assignment Model for Small Unit Ground Combat Using Mixed Integer Nonlinear Program and Lagrangian Relaxation

The importance of the weapon target assignment problem is increasing as weapon systems are expected to become intelligent and unmanned on the future battlefield. This study discusses the weapon-target assignment in small-scale ground force combat, which has not been addressed much in other studies. In ground combat, target assignment means the start of an engagement, so assignment should be made taking into account not only the probability of killing an enemy but also the probability of surviving friendly forces. We introduce the WTAG (WTA ground) model that reflects these characteristics and describes methodologies for solving the problem including mixed integer nonlinear problems and Lagrangian relaxation approaches. Our finding is that the algorithm presented can efficiently provide the bounds of the problem in a practical size.

An Algorithm for Exchanging Target Asset Pairs using the Kidney Exchange Model

Since chemical, biological, radiological, nuclear, and high yield explosive (CBRNE) attacks can cause catastrophic damage, it is important to detect and eliminate the means of attack at the origin. In surveillance operations, efficient allocation of friendly intelligence assets and enemy targets is critical for continuous and reliablemonitoring. In this research, we investigate a mathematical model for exchanging target–asset pairs when there are sudden changes in various operational environments. For this task, we refer to the kidney exchange model as a benchmark. In particular, the methods for constructing and solving the target–asset exchange problem in near realtime are presented. Additionally, we introduce the methodology and results for obtaining a feasible solution of the weapon target assignment problem using the exchange model. Our method can facilitate decisions in reconnaissance operations, especially when countless targets and assets are intricately intertwined in future battlefield scenarios.

Decentralized Weapon–Target Assignment Under Asynchronous Communications

The weapon–target assignment problem is a classic task assignment problem in combinatorial optimization, and its goal is to assign some number of workers (the weapons) to some number of tasks (the targets). Classical approaches for this problem typically use a centralized planner leading to a single point of failure and often preventing real-time replanning as conditions change. This paper introduces a new approach for distributed, autonomous assignment planning executed by the weapons where each weapon is responsible for optimizing over distinct subsets of the decision variables. A continuous, convex relaxation of the associated cost function and constraints is introduced, and a distributed primal-dual optimization algorithm is developed that will be shown to have guaranteed bounds on its convergence rate, even with asynchronous computations and communications. This approach has several advantages in practice due to its robustness to asynchrony and resilience to time-varying scenarios, and these advantages are exhibited in experiments with simulated and physical commercial off-the-shelf ground robots as weapon surrogates that are shown to successfully compute their assignments under intermittent communications and unexpected attrition (loss) of weapons.

Learning-Based Policy Optimization for Adversarial Missile-Target Assignment

The missile-target assignment (MTA) is a typical weapon-target assignment problem in Command and Control of modern warfare. Despite the significance of the problem, traditional algorithms still lack efficiency, solution quality, and practicability in the adversarial environment. In this article, we propose a data-driven policy optimization with deep reinforcement learning (PODRL) for the adversarial MTA. We design a comprehensive reward function to motivate the optimization of assignment policy. As such, the learned policy can implicitly model the penetration of missiles under an adversarial environment in a data-driven way. We also present a fair sample strategy to improve the sample efficiency and accelerate the policy optimization. Experimental results show that PODRL can adaptively generate satisfactory solutions in both small-scale and large-scale instances. Furthermore, we evaluate the effectiveness of PODRL in a multiobjective scenario. The result demonstrates that a well-optimized policy can achieve high-quality allocation and demand forecast of the missile resources simultaneously.

Target Assignment Algorithm for Joint Air Defense Operation Based on Spatial Crowdsourcing Mode

Spatial crowdsourcing is a mode that uses distributed artificial computing power to solve specific function sets through Internet outsourcing. It has broad application value in the networked command and control of current joint air defense operations. In this paper, we introduce the spatial crowdsourcing theory into the field of target allocation for joint air defense operations and establish a weapon-target assignment model based on spatial crowdsourcing mode, which is more appropriate to the real situation and highlights the system cooperation capability of joint air defense operations. To solve the model, we propose a heuristic variable weight nonlinear learning factor particle swarm optimization (VWNF-PSO). This algorithm can significantly improve the efficiency and adaptability to weapon-target assignment problems under large-scale extreme conditions. Finally, we establish two kinds of joint air defense operation scenarios to verify the proposed model, then compare the proposed algorithm with variable weight PSO (VWPSO) and adaptive learning factor PSO (AFPSO), to validate the effectiveness and efficiency of the VWNF-PSO algorithm proposed in this paper.

A hybrid multi-objective bi-level interactive fuzzy programming method for solving ECM-DWTA problem

Electronic countermeasure (ECM) has become one of the most significant factors in modern warfare, in the course of combat, the electronic jamming allocation tasks need to be flexibly adjusted with the change of combat stage, which puts forward higher requirements for the modeling and solution method of this kind of problems. To solve the ECM dynamic weapon target assignment (ECM-DWTA) problem, a hybrid multi-target bi-level programming model is established. The upper level takes the sum of the electronic jamming effects in the whole combat stage as an optimization objective, and locally optimizes the ECM weapon (ECM-WP) assignment scheme in each stage. The lower level takes the importance expectation value of the target subjected to interference and combat consumption as double optimization objectives to globally optimize the ECM-WP assignment scheme. Focus on solving this complex model, a hybrid multi-objective bi-level interactive fuzzy programming algorithm (HMOBIF) is proposed, in this method, exponential membership function is used to describe the satisfaction degree of each level. When solving the multi-objective optimization problem composed of membership functions in the upper and lower levels, we use the MOEA/D algorithm to obtain the Pareto Front (PF) solution set, and then each solution in PF is evaluated and selected by the TOPSIS multi-criteria evaluation method. This local and global interactive optimization process of bi-level model is actually the process of executing observation-orientation-decision-action loop in practical combat. According to the current example, we conduct numerical simulation on the parameters in the model and obtain the parameter values suitable for the model solution. The computational experiments on different scale ECM-DWTA problems show that HMOBIF method is superior to four bi-level programming algorithms in terms of performance index, and can better solve ECM-DWTA problems.

Weapon-target assignment problem: exact and approximate solution algorithms

The Weapon-Target Assignment (WTA) problem aims to assign a set of weapons to a number of assets (targets), such that the expected value of survived targets is minimized. The WTA problem is a nonlinear combinatorial optimization problem known to be NP-hard. This paper applies several existing techniques to linearize the WTA problem. One linearization technique (Camm et al. in Oper Res 50(6):946–955, 2002) approximates the nonlinear terms of the WTA problem via convex piecewise linear functions and provides heuristic solutions to the WTA problem. Such approximation problems are, though, relatively easy to solve from the computational point of view even for large-scale problem instances. Another approach proposed by O’Hanley et al. (Eur J Oper Res 230(1):63–75, 2013) linearizes the WTA problem exactly at the expense of incorporating a significant number of additional variables and constraints, which makes many large-scale problem instances intractable. Motivated by the results of computational experiments with these existing solution approaches, a specialized new exact solution approach is developed, which is called branch-and-adjust. The proposed solution approach involves the compact piecewise linear convex under-approximation of the WTA objective function and solves the WTA problem exactly. The algorithm builds on top of any existing branch-and-cut or branch-and-bound algorithm and can be implemented using the tools provided by state-of-the-art mixed integer linear programming solvers. Numerical experiments demonstrate that the proposed specialized algorithm is capable of handling very large scale problem instances with up to 1500 weapons and 1000 targets, obtaining solutions with optimality gaps of up to \(2.0\%\) within 2 h of computational runtime.

New Weapon Target Assignment Algorithms for Multiple Targets Using a Rotational Strategy and Clustering Approach

This paper proposes practical weapon target assignment (WTA) algorithms for a defense system to counter multiple targets concentrated within a narrow area, such as low-altitude rocket threats or drone swarms. Since the probability of kill (PK) is greatly affected by heading errors between launchers and targets in this type of engagement, WTA problems must first be formulated, considering heading error, to reflect more realistic engagement situations. Two WTA algorithms—a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rotation-fixed strategy</i> and a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rotation strategy—</i> are proposed based on this formulation. Moreover, we propose a method for determining launchers’ initial orientation angles, based on a clustering approach, to further improve the engagement performance of the two algorithms. Numerical simulations were performed to demonstrate the effectiveness of the proposed methods.