# 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.

## Keywords

Weapon target assignment Stochastic programming.## Preview

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