  This paper considers an M-pursuer N-evader scenario involving virtual
targets. The virtual targets serve as an intermediary target for the pursuers,
allowing the pursuers to delay their final assignment to the evaders. However,
upon reaching the virtual target, the pursuers must decide which evader to
capture. It is assumed that there are more pursuers than evaders and that the
pursuers are faster than the evaders. The objective is two-part: first, assign
each pursuer to a virtual target and evader such that the pursuer team's energy
is minimized, and second, choose the virtual targets' locations for this
minimization problem. The approach taken is to consider the Apollonius geometry
between each pursuer's virtual target location and each evader. Using the
constructed Apollonius circles, the pursuer's travel distance and maneuver at a
virtual target are obtained. These metrics serve as a gauge for the total
energy required to capture a particular evader and are used to solve the joint
virtual target selection and pursuer-evader assignment problem. This paper
provides a mathematical definition of this problem, the solution approach
taken, and an example.
