A branch‐and‐price algorithm for a targeting problem

Hankuk University of Foreign Studies, Sŏul, Seoul, South Korea
Naval Research Logistics (Impact Factor: 0.72). 10/2007; 54(7):732 - 741. DOI: 10.1002/nav.20247


In this paper, we consider a new weapon-target allocation problem with the objective of minimizing the overall firing cost. The problem is formulated as a nonlinear integer programming model, but it can be transformed into a linear integer programming model. We present a branch-and-price algorithm for the problem employing the disaggregated formulation, which has exponentially many columns denoting the feasible allocations of weapon systems to each target. A greedy-style heuristic is used to get some initial columns to start the column generation. A branching strategy compatible with the pricing problem is also proposed. Computational results using randomly generated data show this approach is promising for the targeting problem. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007

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    • "They have been found to be effective and efficient in solving many NPhard combinatorial optimization problems. For the individual application of Lagrangian relaxation or column generation , please see [15] [16] [17] or [18] [19] [20]. For recent developments in the combination of the two methods, please refer to [21] [22] [23] [24]. "
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    ABSTRACT: This article considers the order batching problem in steelmaking and continuous-casting production. The problem is to jointly specify the slabs needed to satisfy each customer order and group all the slabs of different customer orders into production batches. A novel mixed integer programming model is formulated for the problem. Through relaxing the order assignment con-straints, a Lagrangian relaxation model is then obtained. By exploiting the relationship between Lagrangian relaxation and column generation, we develop a combined algorithm that contains nested double loops. At the inner loop, the subgradient method is applied for approximating the Lagrangian dual problem and pricing out columns of the master problem corresponding to the linear dual form of the Lagrangian dual problem. At the outer loop, column generation is employed to solve the master problem exactly and adjust Lagrangian multipliers. Computational experiments are carried out using real data collected from a large steel company, as well as on large-scaled problem instances randomly generated. The results demonstrate that the combined algorithm can obtain tighter lower bound and higher quality solution within an acceptable computation time as compared to the conventional Lagrangian relaxation algorithm.
    Naval Research Logistics 06/2011; 58(4):370-388. DOI:10.1002/nav.20452 · 0.72 Impact Factor
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    • "Besides, some WTA models also take into account the cost of weapons. For examples, Kwon et al. [19] employed the overall firing cost as the objective function for optimization. Interested readers can find a more complicated model which considers the function of special assets in the work of Hosein et al. [20]. "
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    ABSTRACT: 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.
    IEEE Transactions on Systems Man and Cybernetics - Part A Systems and Humans 06/2011; 41(3-41):598 - 606. DOI:10.1109/TSMCA.2010.2089511 · 2.18 Impact Factor
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    • "Besides, the cost of weapons is also taken into account in some models, like that in the research of Kwon et al. [22]. A more complicated model that considers the function of special assets can be found in [23]. "
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    ABSTRACT: 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.
    IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews) 12/2010; 40(6-40):649 - 662. DOI:10.1109/TSMCC.2010.2049261 · 2.17 Impact Factor
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