Abstract We introduce a probabilistically complete algorithm for solving a visibility-based pursuit-evasion problem in two-dimensional polygonal environments with multiple pursuers. The input for our algorithm is an environment and the initial positions of the pursuers. The output is a joint strategy for the pursuers that guarantees that the evader has been captured. We create a Sample-Generated Pursuit-Evasion Graph (SG-PEG) that utilizes an abstract sample generator to search the pursuers' Joint Configuration Space for a pursuer solution strategy that captures the evaders, or reports that no such strategy exists under the current constraints. We ran our algorithm in simulation and provide results.