Weapon Target Assignment Problem Research Articles

Research on the weapon target assignment problem in the combined air defense missile system for training simulation

In modern warfare, when the weapon system and the targets are constantly being improved and upgraded, ensuring the distribution of firepower to optimally destroy the target will help the commander to make quick and accurate decisions, thereby improving combat effectiveness. This paper proposes a method to build a command-control automatic system based on solving the weapon target assignment (WTA) problem in a combination of short and medium-range air defense missile systems so that the total damage of targets is maximum and the damage of protected area is minimum. Based on combinatorial optimization algorithms, the probability of kill, linear programming method using Hungarian algorithm, the paper presents a mathematical model of WTA and its optimal solution for short- and medium-range air defense missile systems serving the training simulation problem, thereby giving the results of evaluating the effectiveness of the algorithm.

Self-Adaptive Multi-Task Differential Evolution Optimization: With Case Studies in Weapon–Target Assignment Problem

Multi-task optimization (MTO) is related to the problem of simultaneous optimization of multiple optimization problems, for the purpose of solving these problems better in terms of optimization accuracy or time cost. To handle MTO problems, there emerges many evolutionary MTO (EMTO) algorithms, which possess distinguished strategies or frameworks in the aspect of handling the knowledge transfer between different optimization problems (tasks). In this paper, we explore the possibility of developing a more efficient EMTO solver based on differential evolution by introducing the strategies of a self-adaptive multi-task particle swarm optimization (SaMTPSO) algorithm, and by developing a new knowledge incorporation strategy. Then, we try to apply the proposed algorithm to solve the weapon–target assignment problem, which has never been explored in the field of EMTO before. Experiments were conducted on a popular MTO test benchmark and a WTA-MTO test set. Experimental results show that knowledge transfer in the proposed algorithm is effective and efficient, and EMTO is promising in solving WTA problems.

The Weapon Target Assignment Problem: Rational Inference of Adversary Target Utility Valuations from Observed Solutions

Identifying an adversary’s strategic goals and values requires deliberate and unbiased analysis. This research is motivated by the premise that, if one observes an adversary’s actions or planned actions, it is possible to draw reasonable inferences about their values, thereby reducing misperceptions and informing better decisions. Within the context of the static weapon target assignment problem, this research develops and empirically compares alternative methods to rationalize an adversary’s value hierarchy over targets that informs their observed decisions. Such methods either identify the extreme points of a polytope within a unit simplex of relative target values that encompasses all possible relative target values based on a weak dominance criterion or a subset of points within the polytope. This research characterizes the solution methods’ practical tractability for use on larger-sized problems and their generalizability to other problems. Even for the superlative technique examined, testing illustrates the computationally challenging nature of identifying the defining polytope of relative target values, and the work concludes with suggestions for metaheuristic technique development.

Solving the Dynamic Weapon Target Assignment Problem by an Improved Multiobjective Particle Swarm Optimization Algorithm

Dynamic weapon target assignment (DWTA) is an effective method to solve the multi-stage battlefield fire optimization problem, which can reflect the actual combat scenario better than static weapon target assignment (SWTA). In this paper, a meaningful and effective DWTA model is established, which contains two practical and conflicting objectives, namely, maximizing combat benefits and minimizing weapon costs. Moreover, the model contains limited resource constraints, feasibility constraints and fire transfer constraints. The existence of multi-objective and multi-constraint makes DWTA more complicated. To solve this problem, an improved multiobjective particle swarm optimization algorithm (IMOPSO) is proposed in this paper. Various learning strategies are adopted for the dominated and non-dominated solutions of the algorithm, so that the algorithm can learn and evolve in a targeted manner. In order to solve the problem that the algorithm is easy to fall into local optimum, this paper proposes a search strategy based on simulated binary crossover (SBX) and polynomial mutation (PM), which enables elitist information to be shared among external archive and enhances the exploratory capabilities of IMOPSO. In addition, a dynamic archive maintenance strategy is applied to improve the diversity of non-dominated solutions. Finally, this algorithm is compared with three state-of-the-art multiobjective optimization algorithms, including solving benchmark functions and DWTA model in this article. Experimental results show that IMOPSO has better convergence and distribution than the other three multiobjective optimization algorithms. IMOPSO has obvious advantages in solving multiobjective DWTA problems.

Weapon-Target Assignment Problem Using Modified Water Wave Optimization Algorithm

The weapon-target assignment (WTA) is a classic problem. The WTA mathematical model is that warship formations are reasonably equipped with weapons resources for each weapon system to attack the air threaten targets. The purpose of targets optimization is to maximize combat effectiveness, that is to say, the mathematical expectation is maximum. We adopt the greedy strategy and improved propagation operation is to strengthen the water wave optimization (WWO) search performance. This article elaborates a modified water wave optimization (MWWO) to solve the WTA problem, which can detect optimized allocation decision matrix and search for the maximum mathematical expectation. Based on parameter optimization, the overall performance of the MWWO is more stable, the search speed is accelerated and the accuracy is improved. The experiment results indicate that the MWWO are verified and avoids local optimum, and can be more convenient for solving the WTA and obtain better performance.

Two-stage hybrid heuristic search algorithm for novel weapon target assignment problems

The objective of the weapon target assignment (WTA) problem is to maximize the total damage of targets or minimize the total consumption of weapons. However, the existing studies of the WTA problem did not consider the uncertainty of weapon adequacy in practical battlefield scenarios. In this paper, we study a novel WTA problem, called the WTA problem with uncertainty (WTAU), and the uncertainty refers to the uncertainty of weapon adequacy. The objective of the WTAU is to find a WTA scheme to maximize the total value of destroyed targets by using as few weapons as possible in situations where the adequacy of weapons is uncertain. To address the uncertainty of weapons adequacy, we formulate the WTAU problem as a nonlinear integer programming model. To improve the computing efficiency, we design a two-stage hybrid heuristic search (TSHHS) algorithm based on prior WTAU knowledge. In the first stage of the TSHHS algorithm, a logarithmic transformation method is employed to obtain the optimal target destruction (TD) scheme and an initial WTA scheme. In the second stage, a constructive heuristic method based on the maximum marginal return (MMRBH) and a simple optimization (SimpleO) method are developed to obtain a promising WTA scheme. Moreover, we perform extensive experiments to analyze the performance of the proposed method. The results of numerical experiments show that the proposed method can provide a high-quality WTA scheme with a short computing time in scenarios involving adequate or inadequate weapons.

A multi-objective sparse evolutionary framework for large-scale weapon target assignment based on a reward strategy

The asset-based weapon target assignment (ABWTA) problem is one of the important branches of the weapon target assignment (WTA) problem. Due to the current large-scale battlefield environment, the ABWTA problem is a multi-objective optimization problem (MOP) with strong constraints, large-scale and sparse properties. The novel model of the ABWTA problem with the operation error parameter is established. An evolutionary algorithm for large-scale sparse problems (SparseEA) is introduced as the main framework for solving large-scale sparse ABWTA problem. The proposed framework (SparseEA-ABWTA) mainly addresses the issue that problem-specific initialization method and genetic operators with a reward strategy can generate solutions efficiently considering the sparsity of variables and an improved non-dominated solution selection method is presented to handle the constraints. Under the premise of constructing large-scale cases by the specific case generator, two numerical experiments on four outstanding multi-objective evolutionary algorithms (MOEAs) show Runtime of SparseEA-ABWTA is faster nearly 50% than others under the same convergence and the gap between MOEAs improved by the mechanism of SparseEA-ABWTA and SparseEA-ABWTA is reduced to nearly 20% in the convergence and distribution.

Bi-objective dynamic weapon-target assignment problem with stability measure

In this paper, we develop a new bi-objective model for dynamic weapon-target assignment problem. We consider that the initial weapon assignment plan of defense is disrupted during engagement because of a destroyed air target, breakdown of a weapon system or a new incoming air target. The objective functions are defined as the maximization of probability of no-leaker and the maximization of stability in engagement order of weapon systems. Stability is defined as assigning same air target in sequence in engagement order of a weapon system so that reacquisition and re-tracking of air target are not required by sensors. We propose a new solution procedure to generate updated assignment plans by maximizing efficiency of defense while maximizing stability through swapping weapon engagement orders. The proposed solution procedure generates non-dominated solutions from which defense can quickly choose the most-favored course of action. We solve a set of representative problems with different sizes and present computational results to evaluate effectiveness of the proposed approach.

A Novel Elitism Co-Evolutionary Algorithm for Antagonistic Weapon-Target Assignment

The Antagonistic Weapon-Target Assignment (AGWTA) problem is a crucial decision issue in Command & Control (C2). Since this is a minimax problem, co-evolutionary algorithms can be used to solve it effectively. However, the co-evolutionary algorithm is originally designed for continuous minimax problems which loses its efficiency to discrete contexts. In this paper, a novel elitism co-evolutionary algorithm is proposed to solve the AGWTA. Firstly, an improved AGWTA model for air combat based on the attack and evasion strategies is proposed. Secondly, an elite cooperative genetic algorithm based on the framework of the co-evolutionary algorithm is put forward. In this proposed algorithm, a problem-specific coding method and evolution operator are designed. Meanwhile, an elite individual update mechanism is presented. Finally, based on the analysis of the relationship between the feasible solutions under the air combat environment, an evaluation index is proposed. Experiments show that the proposed algorithm has higher accuracy than traditional co-evolutionary algorithms for solving AGWTA problems.

A Modified MOEA/D Algorithm for Solving Bi-Objective Multi-Stage Weapon-Target Assignment Problem

In command of modern intelligent operations, in addition to solving the problem of multi-unit coordinated task assignment, it is also necessary to obtain a suitable plan according to the needs of decision makers. Based on these requirements, we established a multi-stage bi-objective weapon-target assignment model, and designed a new algorithm with niche and region self-adaptive aggregation (named MOEA/ D-NRSA) based on the decomposition-based multi-objective evolutionary algorithm (MOEA/D) to obtain richer solutions that meet the preferences of different decision makers. Compared with MOEA/D, MOEA/ D-NRSA has advantages in improving the convergence and maintaining the distribution of the solution. On the one hand, it contains a population evolution method based on niche technology to obtain better offspring; on the other hand, it has a new neighborhood selection and update strategy. This strategy first clusters the individuals in the objective space to divide into different regions, in which the subproblems can independently select the appropriate aggregation mode according to the clustering density of the region and update its neighborhood. This strategy can improve the uneven distribution of individuals and maintain the diversity and distribution of the population. Numerical experiments selected state-of-the-art algorithms for comparison, which proved the superiority of MOEA/D-NRSA.

A dynamic weapon target assignment based on receding horizon strategy by heuristic algorithm

Weapon-target assignment problem is the crucial decision support in Command & Control system. As a typical operational scenario, asset defense has less research on the issue of asset-based dynamic weapon target assignment, and the major models of A-DWTA are challenging in practical application. In this paper, an A-DWTA model is first established by receding horizon decomposition strategy, which closely reflects the operational requirement. Then a heuristic algorithm based on statistical marginal return is proposed to solve the A-DWTA model. Experimental results show that the proposed algorithm for solving the A-DWTA model has advantages of real-time and robustness. The obtained decision plan can complete the operational mission in fewer stages and be adjusted adaptively by model and algorithm parameters.

Efficient Decision Approaches for Asset-Based Dynamic Weapon Target Assignment by a Receding Horizon and Marginal Return Heuristic

The weapon-target assignment problem is a crucial decision support in a Command and Control system. As a typical operational scenario, the major asset-based dynamic weapon target assignment (A-DWTA) models and solving algorithms are challenging to reflect the actual requirement of decision maker. Deriving from the “shoot–look–shoot” principle, an “observe–orient–decide–act” loop model for A-DWTA (OODA/A-DWTA) is established. Focus on the decide phase of the OODA/A-DWTA loop, a novel A-DWTA model, which is based on the receding horizon decomposition strategy (A-DWTA/RH), is established. To solve the A-DWTA/RH efficiently, a heuristic algorithm based on statistical marginal return (HA-SMR) is designed, which proposes a reverse hierarchical idea of “asset value-target selected-weapon decision.” Experimental results show that HA-SMR solving A-DWTA/RH has advantages of real-time and robustness. The obtained decision plan can fulfill the operational mission in the fewer stages and the “radical-conservative” degree can be adjusted adaptively by parameters.

Development of an accelerating hungarian method for assignment problems

The Hungarian method is a well-known method for solving the assignment problem. This method was developed and published in 1955. It was named the Hungarian method because two theorems from two Hungarian mathematicians were used. In 1957, it was noticed that this algorithm is strongly polynomial and has a complexity of order O(n 4 ) This is the reason why the Hungarian method is also known as the Kuhn-Munkres algorithm. Later on, in 1971 the complexity of the method was improved to order O(n 3 ) A smallest uncovered element is selected to create a single zero at every iteration. This is a weakness and is alleviated by selecting more than one smallest uncovered element thus creating more than one zero at every iteration to come up with what we now call the Accelerating Hungarian (AH) method. From the numerical illustration of the Hungarian method given in this paper, we require 6 iterations to reach optimality. It can also be shown that selecting a single smallest uncovered element (e s ) makes the Hungarian method inefficient when creating zeros. From the same numerical illustration of the proposed algorithm (AH) also given in this paper, it can be noted that only one iteration is required to reach optimality and that a total of six zeros are created in one iteration. Assignment model and the Hungarian method have application in addressing the Weapon Target Assignment (WTA) problem. This is the problem of assigning weapons to targets while considering the maximum probability of kill. The assignment problem is also used in the scheduling problem of physicians and medical staff in the outpatient department of large hospitals with multi-branches. The mathematical modelling of this assignment problem results in complex problems. A hybrid meta-heuristic algorithm SCA–VNS combining a Sine Cosine Algorithm (SCA) and Variable Neighbourhood Search (VNS) based on the Iterated Hungarian algorithm is normally used.

A heuristic and metaheuristic approach to the static weapon target assignment problem

The weapon target assignment (WTA) problem, which has received much attention in the literature and is of continuing relevance, seeks within an air defense context to assign interceptors (weapons) to incoming missiles (targets) to maximize the probability of destroying the missiles. Kline et al. (J Heuristics 25:1–21, 2018) developed a heuristic algorithm based upon the solution to the Quiz Problem to solve the WTA. This heuristic found solutions within 6% of optimal, on average, for smaller problem instances and, when compared to a leading WTA heuristic from the literature, identified superlative solutions for larger instances within hundredths of a second, in lieu of minutes or hours of computational effort. Herein, we propose and test an improvement to the aforementioned heuristic, wherein a modified implementation iteratively blocks exiting assignments to an initial feasible solution, allowing superior solutions that would otherwise be prevented via a greedy selection process to be found. We compare these results to the optimal solutions as reported by a leading global optimization solver (i.e., BARON) and find solutions that are, at worst, within 2% of optimality and, at best, up to 64% better than the solutions reported to be optimal by BARON. To wit, the developed metaheuristic outperformed BARON in 25% of all instances tested, as BARON reported a suboptimal solution as being optimal for 21.1% of the instances, and it could not identify an optimal solution for the remaining 6.67% of the instances within 2 h of CPU time, a liberally imposed time limit that far exceeds practical usage considerations for this application.

A modified crow search algorithm for the weapon-target assignment problem

The Weapon-Target Assignment (WTA) problem is one of the most important optimization problems in military operation research. In the WTA problem, assets of defense aim the best assignment of each weapon to target for decreasing expected damage directed by the offense. In this paper, Modified Crow Search Algorithm (MCSA) is proposed to solve the WTA problem. In MCSA, a trial mechanism is used to improve the quality of solutions using parameter LIMIT. If the solution is not improved after a predetermined number of iterations, then MCSA starts with a new position in the search space. Experimental results on the different sizes of the WTA problem instances show that MCSA outperforms CSA in all problem instances. Also, MCSA achieved better results for 11 out of 12 problem instances compared with four state-of-the-art algorithms. The source codes of MCSA for the WTA are publicly available at http://www.3mrullah.com/MCSA.html.

Swarm Intelligence Algorithms for Weapon-Target Assignment in a Multilayer Defense Scenario: A Comparative Study

Weapon-target assignment (WTA) is a kind of NP-complete problem in military operations research. To solve the multilayer defense WTA problems when the information about enemy’s attacking plan is symmetric to the defender, we propose four heuristic algorithms based on swarm intelligence with customizations and improvements, including ant colony optimization (ACO), binary particle swarm optimization (BPSO), integer particle swarm optimization (IPSO) and sine cosine algorithm (SCA). Our objective is to assess and compare the performance of different algorithms to determine the best algorithm for practical large-scale WTA problems. The effectiveness and performance of various algorithms are evaluated and compared by means of a benchmark problem with a small scale, the theoretical optimal solution of which is known. The four algorithms can obtain satisfactory solutions to the benchmark problem with high quality and high robustness, while IPSO is superior to BPSO, ACO and SCA with respect to the solution quality, algorithmic robustness and computational efficiency. Then, IPSO is applied to a large-scale WTA problem, and its effectiveness and performance are further assessed. We demonstrate that IPSO is capable of solving large-scale WTA problems with high efficiency, high quality and high robustness, thus meeting the critical requirements of real-time decision-making in modern warfare.

Developing Optimal Policies to Fight Pandemics and COVID-19 Combat in the United States

The world has faced many outbreaks and pandemics with hundreds of millions of deaths throughout its history. Those epidemics are global health concerns and as well as serious economic issues. There is certain need to allocate scarce sources efficiently to fight such epidemics in both personal and global dimensions. Here we develop and propose two optimization models to maximize the total protection from any epidemic, pandemic or bioterror attacks; the first one is personal protection model or protocol and the other one is mass protection model that is inspired by the well-known weapon-target assignment problem of operations research. These efforts are optimal allocation of scarce medical and economic resources to save millions of lives- gift of life. We implement our general mathematical programming models with real-world data to fight the coronavirus pandemic for a person and the United States. Our personal protection protocol provides 99.99% protection from COVID-19 for an American through personal strategies when the mass protection model supplies 96.961% protection on average from coronavirus pandemic for the United States through across country policies. The mass protection model which recommends general policy frame for health care policy makers could be applied for any epidemic at any level from county to city, to state and country as well as in global scale. The mathematical relation between the personal protection protocol and the mass protection model also highlights the fact of unus pro omnibus, omnes pro uno (one for all, all for one) for fighting epidemics- particularly the moving enemy, novel coronavirus which is double invisible due to its viral nature and the availability of the high level of asymptomatic cases. Recognize the enemy, as protecting yourself means protecting people, love life, follow the rules and stay at home. That is the greatest ever social impact.Published on 28 April 2020.

An approximate dynamic programming approach for comparing firing policies in a networked air defense environment

An objective for effective air defense is to identify the firing policy for interceptor allocation to incoming missiles that minimizes the expected total damage to defended assets over a sequence of engagements. We formulate this dynamic weapon target assignment problem as a Markov decision process and utilize a simulation-based, approximate dynamic programming (ADP) approach to solve problem instances based on a representative scenario. Least squares policy evaluation and least squares temporal differences algorithms are developed to determine approximate solutions. A designed experiment investigates problem features such as conflict duration, attacker and defender weapon sophistication, and defended asset values. An empirical comparison of the ADP policies and two baseline policies (i.e., firing either one or two interceptors at each incoming theater ballistic missile (TBM)) yields several insights: the ADP policies outperform both baseline polices when conflict duration is short and attacker weapons are sophisticated; firing one interceptor at each TBM (regardless of inventory status) outperforms the tested ADP policies when conflict duration is long and attacker weapons are less sophisticated; and firing two interceptors at each TBM (regardless of inventory status), which is the United States Army’s currently implemented policy, is never the superlative policy for the test instances investigated.

동적 무장할당 문제에서의 GRASP 알고리즘 연구

동적 무장할당 문제에서의 GRASP 알고리즘 연구

An Efficient Marginal-Return-Based Constructive Heuristic to Solve the Sensor–Weapon–Target Assignment Problem

In network-centric warfare, the interconnections among various combat resources enable an advanced operational pattern of cooperative engagement. The operational effectiveness and outcome strongly depends on the reasonable utilization of available sensors and weapons. In this paper, a mathematical model for the coallocation of sensors and weapons is built, taking into account the interdependencies between weapons and sensors, the resource constraints, the capability constraints, as well as the strategy constraints. A marginal-return-based constructive heuristic (MRBCH) is proposed to solve the formulated sensor–weapon–target assignment (S-WTA) problem. MRBCH exploits the marginal return of each sensor–weapon–target triplet and dynamically updates the threat value of all targets. It relies only on simple lookup operations to choose each assignment triplet, thus resulting in very low computational complexity. For performance evaluation, we build a general Monte Carlo simulation-based S-WTA framework. Furthermore, we employ a random sampling method and an extension of the state-of-the-art algorithm Swt_opt as competitors. The computational results show that MRBCH consistently performs very well in solving S-WTA instances of different scales, and it can generate assignment schemes much more efficiently than its competitors.