Lagrangian relaxation approach to the targeting problem

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. We applied Lagrangian relaxation and a branch-and-bound method to the problem after transforming the nonlinear constraints into linear ones. An efficient primal heuristic is developed to find a feasible solution to the problem to facilitate the procedure. In the branch-and-bound method, three different branching rules are considered and the performances are evaluated. Computational results using randomly generated data are presented.