A robust approach to the missile defence location problem

Abstract

This paper proposes a model for determining a robust defence strategy against ballistic missile threat. Our approach takes into account a variety of possible future scenarios and different forms of robustness criteria, including the well-known absolute robustness criterion. We consider two problem variants. In the first, the number of ballistic missile interceptor systems is minimised, such that a predetermined defence level is achieved. In the second variant, the defence level is maximised for a given number of available interceptor systems. The solutions of both variants consist of a subset of all possible locations of the interceptor systems. We applied two solution approaches to this problem: a heuristic and an exact solution method. The heuristic method is based on simulated annealing and produces good results within a short amount of computation time. We also developed an integer programming formulation which can be solved to optimality using a standard solver. The computation time is higher, but because of the nice properties of the proposed IP-formulation, it can still be solved within reasonable amount of computation time. These two solution approaches were tested using a fictive, but realistic dataset. The results illustrate the effects of the predetermined defence levels and the availability of interceptor systems, as well as the robustness of the solutions produced. Finally, we used our dataset to illustrate the differences between both variants and their use in practice.