The weapon target assignment problem (WTA) is a class of combinatorial optimization problems present in the fields of optimization and operations research.
It consists of finding an optimal assignment of a set of weapons of various types to a set of targets in order to maximize the total expected damage done to the opponent.
Thus, we see that the WTA allows one to formulate optimal assignment problems wherein tasks require cooperation among agents.
Both static and dynamic versions of WTA can be considered.
In the static case, the weapons are assigned to targets once.
While the majority of work has been done on the static WTA problem, recently the dynamic WTA problem has received more attention.
The main one is to search for a lost object or person by heterogeneous assets such as dogs, aircraft, walkers, etc.
The "value" of each element of the partition is the probability that the object is located there.
The weapon target assignment problem is often formulated as the following nonlinear integer programming problem: subject to the constraints Where the variable
An exact solution can be found using branch and bound techniques which utilize relaxation (approximation).
[1] Many heuristic algorithms have been proposed which provide near-optimal solutions in polynomial time.
[2] A commander has 5 tanks, 2 aircraft, and 1 sea vessel and is told to engage 3 targets with values 5, 10, and 20.
Each weapon type has the following success probabilities against each target: One feasible solution is to assign the sea vessel and one aircraft to the highest valued target (3).
One could then assign the remaining aircraft and 2 tanks to target #2, resulting in expected survival value of
Finally, the remaining 3 tanks are assigned to target #1 which has an expected survival value of