An Approximate Algorithm For A Weapon Target Assignment Stochastic Program

Abstract

The Weapon Target Assignment (WTA) problem considers optimally assigning M weapons to N targets so that the total expected damage to the targets is maximized. If at some time t the numbers and locations of weapons and targets are known with certainty, then a single assignment may be made at time t such that all of the weapons are committed. This formulation is denoted static WTA. In its most general form, static WTA is known to be NP-complete. A more difficult problem results when the numbers and locations of targets are not known a priori. Typically, constraints on the weapons maneuverability and range will require a sequence of partial assignments at times t ₁, t ₂,..., t _k , where at each t _i , a subset of the n targets are known with certainty and the remainder are either not known or known only stochastically. This dynamic WTA formulation may be modeled as a stochastic program (SP). In general, stochastic programs may be solved by decomposing the SP into a sequence of deterministic problems. However, for dynamic WTA, the integrality and non-linearity of the problem makes it difficult to obtain a solution by decomposition. This paper studies an algorithm that finds an optimal solution for a similar problem which is close to optimal for the original problem but is amenable to on-line execution.