Computing a Heuristic Solution to the Watchman Route Problem by Means of Photon Mapping Within a 3D Virtual Environment Testbed

We present an algorithm providing a heuristic solution to the NP-hard optimization problem known as the watchman route problem (WRP) within a 3D virtual environment testbed populated by simulated unmanned vehicles (UVs). The contribution made by our algorithm is three-fold. First, we utilize photon mapping as our means of representing the information sensed by a UV. Second, we use the photon map to generate an online solution to the closely-related NP-hard art gallery problem (AGP). Third, we use a 3D Chan-Vese segmentation algorithm initialized by our AGP-solver to produce a candidate set of path-planning waypoints. The use of photon mapping with our online AGP solver allows us to adapt UV operation to accommodate variable, less-than-ideal environmental circumstances. The use of our 3D Chan-Vese segmentation algorithm creates a set of candidate waypoints that yield greater visibility coverage when computing the WRP than would be obtainable otherwise. Our algorithm provides for quick learning among the unmanned vehicles operating within the testbed’s virtual environment by generating easily-transferrable WRP-solving waypoints.