Pursuit-evasion problems comprise a set of pursuers that strive to catch oneor several evaders, often in a constrained environment. This thesis proposesand compares heuristic algorithms for pursuit-evasion problems wherein several double integrator agents pursue a single evader in a bounded subset of theEuclidean plane. Different methods for assigning surrounding target points tothe pursuers are tested numerically. In addition, a method which finds the timeoptimal strategy for pursuing a static target in an unconstrained setting is presented, and is then used to pursue the assigned, dynamic, target. Numericalresults show that the time optimal strategy for pursuing a static target translateswell to the dynamic problem.