• Korean Management Science Review
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• v.27 no.1
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• pp.75-90
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• 2010

In this paper, we proposed new solution procedure of the air defense missile allocation problem. In order to find the optimal location of missile, we formulated a simple mathematical model maximizing the kill probability of enemy air threat including aircraft and missile. To find the Kill probability, we developed a new procedure using actual experimental data in the mathematical model. Actual experimental data mean real characteristic factor, which was acquired when the missile had been developed through missile fire experiment. The result of this study can offer practical solution for missile allocation and the methodology in this study can be used to the decision making for the optimal military facility allocation.

• IE interfaces
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• v.21 no.3
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• pp.262-273
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• 2008

In Korean peninsular, Air Defense with SAM(Surface-to-Air Missile) is very important, because of threatening by North Korea's theater ballistic missiles installed with nuclear or biochemistry. Effective and successful defense operation largely depends on two factors, SAM's location and the number of SAM for each target based on missile's availability in each SAM's location. However, most previous papers have handled only the former. In this paper, we developed Multi-heuristic algorithm which can handle both factors simultaneously for solving allocation problem of the batteries and missile assignment problem in each battery. To solve allocation problem, genetic algorithm is used to decide location of the batteries. To solve missile assignment problem, a heuristic algorithm is applied to determine the number of SAM for each target. If the proposed model is applied to allocation of SAM, it will improve the effectiveness of missile defense operations.

• Journal of the military operations research society of Korea
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• v.35 no.3
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• pp.47-59
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• 2009

A hybrid Genetic Algorithm is applied to military resource allocation problem. Since military uses many resources in order to maximize its ability, optimization technique has been widely used for analysing resource allocation problem. However, most of the military resource allocation problems are too complicate to solve through the traditional operations research solution tools. Recent innovation in computer technology from the academy makes it possible to apply heuristic approach such as Genetic Algorithm(GA), Simulated Annealing(SA) and Tabu Search(TS) to combinatorial problems which were not addressed by previous operations research tools. In this study, a hybrid Genetic Algorithm which reinforces GA by applying local search algorithm is introduced in order to address military optimization problem. The computational result of hybrid Genetic Algorithm on Missile Interceptor Allocation problem demonstrates its efficiency by comparing its result with that of a simple Genetic Algorithm.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.43-56
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• 2009

In korean peninsular, aircraft defense with SAM (Surface-to-Air Missile) is very important because of short range of combat space in depth. Effective and successful defense operation largely depends on two factors, SAM's location and the number of SAM for each target based on missile's availability in each SAM's location. However, most previous papers have handled only the former. In this paper, we developed Set covering model which can handle both factors simultaneously and Multi-heuristic algorithm for solving allocation problem of the batteries and missile assignment problem in each battery. Genetic algorithm is used to decide optimal location of the batteries. To determine the number of SAM, a heuristic algorithm is applied for solving missile assignment problem. If the proposed model is applied to allocation of SAM, it will improve the effectiveness of air defense operations.

• Journal of the military operations research society of Korea
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• v.26 no.1
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• pp.34-46
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• 2000

The object of this study is to construct a model for an optimal allocation of short surface to air missile defending our targets most efficiently from hostile aircraft´s attack. For the purpose of this, we analyze and establish facility allocation concept of existing models, apply set covering theory appropriate to problem´s properties, present the process of calculating the probability of target being protected, apply Sherali-Kim´s branching variable selection strategy, and then construct the model. As constructed model apply the reducing problem with application, we confirm that we can apply the large scale, real problem.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.1020-1025
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• 2005

The set covering(SC) problem has many practical application of modeling not only real world problems in civilian but also in military. In this paper we study optimal allocation model for maximizing utility of consolidating old fashioned and new air defense weapon system like Patriot missile and develop the new computational algorithm for the SC problem by using simulated annealing(SA) algorithm. This study examines three different methods: 1) simulated annealing(SA); 2) accelerated simulated annealing(ASA); and 3) selection by effectiveness degree(SED) with SA. The SED is adopted as an enhanced SA algorithm that the neighboring solutions could be generated only in possible optimal feasible region at the PERTURB function. Furthermore, we perform various experiments for both a reduced and an extended scale sized situations depending on the number of customers(protective objective), service(air defense), facilities(air defense artillery), threat, candidate locations, and azimuth angles of Patriot missile. Our experiment shows that the SED obtains the best results than others.

• Journal of the Korea Society for Simulation
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• v.15 no.4
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• pp.69-77
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• 2006

In most positioning and allocation practices, many mathematical models are proposed in various fields. The set covering (SC) problem has many practical applications of modeling not only real world problem but also in military. As our air defense weapon systems are getting older and declining the performance, new plans far acquisition of high-tech air defense weapon system are being conducted. In this paper we established simulation model for optimal allocation of KDX which carries new missile defense weapon system by using partial set covering considering both attacker and defender side. By implementating simulation model, we assess the available scenarios and show the optimal pre-positioning of KDX and interceptor's allocation. Furthermore, we provide a variety of experiments and extensive scale sized situations for Korea Indigenous Missile Defense (KIMD) and support decision-making for efficient positioning of unit.

• Journal of the Korea Institute of Military Science and Technology
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• v.18 no.6
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• pp.797-807
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• 2015

The low-altitude PAC-2 Patriot missile system is the backbone of ROK air defense for intercepting enemy aircraft. Currently there is no missile interceptor which can defend against the relatively high velocity ballistic missile from North Korea which may carry nuclear, biological or chemical warheads. For ballistic missile defense, Korea's air defense systems are being evaluated. In attempting to intercept ballistic missiles at high altitude the most effective means is through a multi-layered missile defense system. The missile defense problem has been studied considering a single interception system or any additional capability. In this study, we seek to establish a mathematical model that's available for multi-layered missile defense and minimize total interception fail probability and proposes a solution based on genetic algorithms. We perform computational tests to evaluate the relative speed and solution of our GA algorithm in comparison with the commercial optimization tool GAMS.

• Korean Management Science Review
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• v.32 no.4
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• pp.109-133
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• 2015

This paper considers the allocation and engagement scheduling of air defense missiles by using MIP (mixed integer programming). Specifically, it focuses on developing a realistic MIP model for a real battle situation where multiple enemy missiles are headed toward valuable defended assets and there exist multiple air defense missiles to counteract the threats. In addition to the conventional objective such as the minimization of surviving target value, the maximization of total intercept altitude is introduced as a new objective. The intercept altitude of incoming missiles is important in order to minimize damages from debris of the intercepted missiles and moreover it can be critical if the enemy warhead contains an atomic or chemical bomb. The concept of so called the time window is used to model the engagement situation and a continuous time is assumed for flying times of the both missiles. Lastly, the model is extended to simulate the situation where the guidance radar, which guides a defense missile to its target, has the maximum guidance capacity. The initial mathematical model developed contains several non-linear constraints and a non-linear objective function. Hence, the linearization of those terms is performed before it is solved by a commercially available software. Then to thoroughly examine the MIP model, the model is empirically evaluated with several test problems. Specifically, the models with different objective functions are compared and several battle scenarios are generated to evaluate performance of the models including the extended one. The results indicate that the new model consistently presents better and more realistic results than the compared models.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.39 no.2
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• pp.88-102
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• 2016

This paper considers the allocation and engagement scheduling problem of interceptor missiles, and the problem was formulated by using MIP (mixed integer programming) in the previous research. The objective of the model is the maximization of total intercept altitude instead of the more conventional objective such as the minimization of surviving target value. The concept of the time window was used to model the engagement situation and a continuous time is assumed for flying times of the both missiles. The MIP formulation of the problem is very complex due to the complexity of the real problem itself. Hence, the finding of an efficient optimal solution procedure seems to be difficult. In this paper, an efficient genetic algorithm is developed by improving a general genetic algorithm. The improvement is achieved by carefully analyzing the structure of the formulation. Specifically, the new algorithm includes an enhanced repair process and a crossover operation which utilizes the idea of the PSO (particle swarm optimization). Then, the algorithm is throughly tested on 50 randomly generated engagement scenarios, and its performance is compared with that of a commercial package and a more general genetic algorithm, respectively. The results indicate that the new algorithm consistently performs better than a general genetic algorithm. Also, the new algorithm generates much better results than those by the commercial package on several test cases when the execution time of the commercial package is limited to 8,000 seconds, which is about two hours and 13 minutes. Moreover, it obtains a solution within 0.13~33.34 seconds depending on the size of scenarios.