A Lagrange Relaxation Method for Solving Weapon‐Target Assignment Problem

Abstract

We study the weapon-target assignment WTA problem which has wide applications in the area of defense-related operations research. This problem calls for finding a proper assignment of weapons to targets such that the total expected damaged value of the targets to be maximized. The WTA problem can be formulated as a nonlinear integer programming problem which is known to be NP-complete. There does not exist any exact method for the WTA problem even small size problems, although several heuristic methods have been proposed. In this paper, Lagrange relaxation method is proposed for the WTA problem. The method is an iterative approach which is to decompose the Lagrange relaxation into two subproblems, and each subproblem can be easy to solve to optimality based on its specific features. Then, we use the optimal solutions of the two subproblems to update Lagrange multipliers and solve the Lagrange relaxation problem iteratively. Our computational efforts signify that the proposed method is very effective and can find high quality solutions for the WTA problem in reasonable amount of time.

MOQPSO‐D/S for Air and Missile Defense WTA Problem under Uncertainty

“…Select guider particles gbest 1 and gbest 2 with application of two-stage method. If > max /2, the guider particle gbest 2 would not be selected. Update the position of every particle according to (10).…”

“…Given the importance, WTA has been studied with application of Lagrange relaxation algorithm [2], ant colony algorithm [3], genetic algorithm [4], clone selection algorithm [5], and particle swarm optimization algorithm [6]. Most of these researches construct WTA model based on single objective optimization with the objective function of maximizing the kill probability to enemy.…”

An optimal assignment of multi-type weapons to single-target

“…Now Based on these data, the commander center has to make a proper assignment to allocate the missiles to fire the enemy's platform. We solve the linear integer problem (15)(16)(17)(18)(19) with the input data given in Table I via CPLEX, and get the following solution…”

“…Besides, Julstrom [18] proposed effective string and permutation-coded genetic algorithms ____________________________________ 978-1-47 --/1/$31.00 ©201 IEEE which can be seeded with greedy heuristic's solutions. Ni et al [19] proposed a Lagrange relaxation method for solving weapon-target assignment problem, see also in [20] for a feasible descent approximation algorithm. Darryl and Carl [21] presented an approximate dynamic programming techniques to solve the two-stage WTA problem.…”

An efficient algorithm for the weapon target assignment problem

“…In our previous works [8] and [9], we have studied Lagrange relaxation and linear integer programming methods for the WTA problem. This paper can be viewed as a further extension of our previous works.…”