Dynamic 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.

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 Modified RL-IGWO Algorithm for Dynamic Weapon-Target Assignment in Frigate Defensing UAV Swarms

Unmanned aerial vehicle (UAV) swarms have significant advantages in terms of cost, number, and intelligence, constituting a serious threat to traditional frigate air defense systems. Ship-borne short-range anti-air weapons undertake terminal defense tasks against UAV swarms. In traditional air defense fire control systems, a dynamic weapon-target assignment (DWTA) is disassembled into several static weapon target assignments (SWTAs), but the relationship between DWTAs and SWTAs is not supported by effective analytical proof. Based on the combat scenario between a frigate and UAV swarms, a model-based reinforcement learning framework was established, and a DWAT problem was disassembled into several static combination optimization (SCO) problems by means of the dynamic programming method. In addition, several variable neighborhood search (VNS) operators and an opposition-based learning (OBL) operator were designed to enhance the global search ability of the original Grey Wolf Optimizer (GWO), thereby solving SCO problems. An improved grey wolf algorithm based on reinforcement learning (RL-IGWO) was established for solving DWTA problems in the defense of frigates against UAV swarms. The experimental results show that RL-IGWO had obvious advantages in both the decision making time and solution quality.

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.

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.

Research on Dynamic Weapon Target Assignment Based on Cross-Entropy

The weapon target assignment (WTA) is a classical problem of defense-related applications which is proved to be a NP-complete problem. In this paper, a practical and available dynamic weapon target assignment (DWTA) formulation is given which incorporates two meaningful and conflicting objectives, that is, minimizing weapon costs and maximizing combat benefits. As we know, heuristic methods have some shortcomings such as slow convergence speed and local optimum in solving the nonlinear integer optimization problem. To this end, a novel DWTA algorithm based on cross-entropy (CE) method is introduced, where the resources requirement condition for targets is taken into consideration. The CE method associates an estimation problem with the DWTA optimization problem, and then, the estimation problem is transformed into a convex optimization problem. The Karush–Kuhn–Tucker conditions are applied to solve the convex optimization problem, and the iteration formulas to find the optimal solution are deducted. Furthermore, in order to verify the performance of CE method in dealing with the DWTA problem, several simulations in different combat scenarios are implemented. The results reveal that, compared with the benchmark heuristic and Monte-Carlo (MC) methods, there are some notable advantages in solving the DWTA problem based on CE method with regard to the solution quality and time consumption.

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

Simplified swarm optimization with initialization scheme for dynamic weapon–target​ assignment problem

The dynamic weapon–target assignment (DWTA) problem is a critical issue in the field of military operations research. The problem is highly constrained; thus, the use of an evolutionary method to solve the DWTA problem often encounters a population of infeasible solutions resulting in prohibitive computational burden. Aiming at accelerating the solution process and improving the solution quality, this work proposes an improved simplified swarm optimization called SSODT with two novel schemes: the deterministic initialization scheme, and the target exchange scheme. The deterministic initialization scheme is used in population initialization and utilizes problem-specific knowledge of DWTA to speed up the convergence of SSODT by generating a promising feasible solution which has a greater potential for evolving globally. The target exchange scheme is a local search updating feasible solutions in a manner that exchanges their variables without violating the engagement feasibility to enhance the exploitation capability of SSODT. The proposed method is empirically verified on thirty-six artificial problems and compared with widely popular evolutionary methods. The results demonstrate that the proposed SSODT is better than its competitors in terms of both solution quality and efficiency.

Solving the dynamic weapon target assignment problem by an improved artificial bee colony algorithm with heuristic factor initialization

Dynamic weapon target assignment (DWTA) is an effective method for solving the problem of battlefield firepower optimization in multiple stages and multiple rounds. The resolving time of the DWTA affects current allocation results and assignment results in the next round. Aiming at the slow convergence rate and the low search efficiency in solving DWTA, this paper proposes an improved artificial bee colony (ABC) algorithm with a new initialization method utilizing rule-based heuristic factors. The traditional ABC algorithm converges slowly and easily falls into local extremum. Therefore, in the study, we firstly put forward an improved ABC algorithm based on ranking selection and elite guidance to improve the search efficiency. Secondly, aiming at the low quality of the initial solution generated randomly, we put forward 4 kinds of rule-based heuristic factors: heuristic factor based on weapon-choice-priority, heuristic factor based on target-choice-priority, heuristic factor based on target-choice-priority with a random sequence, and heuristic factor based on target-choice-priority with a random sequence and Cannikin Law. The heuristic factors are used in population initialization to improve the quality of initial solutions. Finally, the heuristic factor initialization method is combined with the improved ABC algorithm to solve the DWTA problem with the integer encoding according to the characteristics of DWTA. A comparative experiment of different algorithms for solving the DWTA problem with different scales was carried out. The experimental results showed that the improved ABC algorithm combined with heuristic factor initialization could get the high-quality initial solution, accelerate the solution process, and improve the accuracy in solving DWTA.

A Hybrid Multiobjective Discrete Particle Swarm Optimization Algorithm for Cooperative Air Combat DWTA

A hybrid multiobjective discrete particle swarm optimization (HMODPSO) algorithm is proposed to solve cooperative air combat dynamic weapon target assignment (DWTA). First, based on the threshold of damage probability and time window constraints, a new cooperative air combat DWTA multiobjective optimization model is presented, which employs the maximum of the target damage efficiency and minimum of ammunition consumption as two competitive objective functions. Second, in order to tackle the DWTA problem, a mixed MODPSO and neighborhood search algorithm is proposed. Furthermore, the repairing operator is introduced into the mixed algorithm, which not only can repair infeasible solutions but also can improve the quality of feasible solutions. Besides, the Cauchy mutation is adopted to keep the diversity of the Pareto optimal solutions. Finally, a typical two-stage DWTA scenario is performed by HMODPSO and compared with three other state-of-the-art algorithms. Simulation results verify the effectiveness of the new model and the superiority of the proposed algorithm.

Optimal multi-stage allocation of weapons to targets using adaptive dynamic programming

We consider the optimal allocation of resources (weapons) to a collection of tasks (targets) with the objective of maximizing the reward for completing tasks (destroying targets). Tasks arrive in two stages, where the first stage tasks are known and the second stage task arrivals follow a random distribution. Given the distribution of these second stage task arrivals, simulation and mathematical programming are used within a dynamic programming framework to determine optimal allocation strategies. The special structure of the assignment problem is exploited to recursively update functional approximations representing future rewards using subgradient information. Through several theorems, optimality of the algorithm is proven for a two-stage Dynamic Weapon-Target Assignment Problem.

Novel Evolutionary Game Based Multi-Objective Optimisation for Dynamic Weapon Target Assignment

This paper develops a novel multi-objective optimisation method based on the Evolutionary Game Theory to solve Weapon Target Assignment problems in real-time. The main research question of this study was how to consider multi-objective functions all together and choose a best solution among many possible non-dominant optimal solutions. The key idea is the best solution can be considered as a solution which best survives in other solution spaces. Therefore, the proposed method first obtains individual solutions for each objective function. Then, Evolutionary Game Theory considers each solution as a player and evaluates them in the solution spaces of other players to check how they can survive in those spaces. The main innovation is that, unlike other multi-objective optimisation approaches, the proposed approach not only considers a set of optimal solutions regarding multi-objective functions, but also finds the best optimal solution in terms of the survivability. The stability and the real-time computation of the proposed algorithm is tested on an adapted and constrained Dynamic Weapon Target Assignment problem matching a real military requirement. The performance of the proposed approach is evaluated via numerical simulations.

An Efficient Rule-Based Constructive Heuristic to Solve Dynamic Weapon-Target Assignment Problem

In this paper, we propose an efficient rule-based heuristic to solve asset-based dynamic weapon-target assignment (DWTA) problems. The main idea of the proposed heuristic is to utilize the domain knowledge of DWTA problems to directly achieve weapon assignment, without large number of function evaluations. We update the saturation states of constraints in the assignment process to guarantee the feasibility of generated solutions. For the purpose of testing the performance of the proposed heuristic, we build a general Monte Carlo simulation-based DWTA framework. For comparison, we also employ a Monte Carlo method (MCM) to make DWTA decisions in different defense scenarios. From simulations with DWTA instances under different scales, the heuristic has obvious advantages over the MCM with regard to solution quality and computation time. The proposed method can solve large-scale DWTA problems (e.g., those including 100 weapons, 100 targets, and four defense stages) within only a few seconds.

Efficient Decision Makings for Dynamic Weapon-Target Assignment by Virtual Permutation and Tabu Search Heuristics

The dynamic weapon-target assignment (DWTA) problem is a typical constrained combinatorial optimization problem with the objective of maximizing the total value of surviving assets threatened by hostile targets through all defense stages. A generic asset-based DWTA model is established, especially for the warfare scenario of force coordination, to formulate this problem. Four categories of constraints, involving capability constraints, strategy constraints, resource constraints (i.e., ammunition constraints), and engagement feasibility constraints, are taken into account in the DWTA model. The concept of virtual permutation (VP) is proposed to facilitate the generation of feasible decisions. A construction procedure (CP) converts VPs into feasible DWTA decisions. With constraint satisfaction guaranteed by the synergy of VPs and the CP, an elaborate local search (LS) operator, namely move-to-head operator, is constructed to avoid repeatedly generating the same decisions. The operator is integrated into two tabu search (TS) algorithms to solve DWTA problems. Comparative experiments involving a random sampling method, an LS method, a hybrid genetic algorithm, a hybrid ant-colony optimization algorithm, and our TS algorithms show that the proposed TS heuristics for DWTA outperform their competitors in most test cases and they are competent for high-quality real-time DWTA decision makings.

Evolutionary decision-makings for the dynamic weapon-target assignment problem

The dynamic weapon-target assignment (DWTA) problem is an important issue in the field of military command and control. An asset-based DWTA optimization model was proposed with four kinds of constraints considered, including capability constraints, strategy constraints, resource constraints and engagement feasibility constraints. A general “virtual” representation of decisions was presented to facilitate the generation of feasible decisions. The representation is in essence the permutation of all assignment pairs. A construction procedure converts the permutations into real feasible decisions. In order to solve this problem, three evolutionary decision-making algorithms, including a genetic algorithm and two memetic algorithms, were developed. Experimental results show that the memetic algorithm based on greedy local search can generate obviously better DWTA decisions, especially for large-scale problems, than the genetic algorithm and the memetic algorithm based on steepest local search.

Survey of the research on dynamic weapon-target assignment problem

The basic concepts and models of weapon-target assignment (WTA) are introduced and the mathematical nature of the WTA models is also analyzed. A systematic survey of research on WTA problem is provided. The present research on WTA is focused on models and algorithms. In the research on models of WTA, the static WTA models are mainly studied and the dynamic WTA models are not fully studied in deed. In the research on algorithms of WTA, the intelligent algorithms are often used to solve the WTA problem. The small scale of static WTA problems has been solved very well, however, the large scale of dynamic WTA problems has not been solved effectively so far. Finally, the characteristics of dynamic WTA are analyzed and directions for the future research on dynamic WTA are discussed.