Constraint Programming for Path Planning with Uncertainty - Solving the Optimal Search Path Problem

The optimal search path (OSP) problem is a single-sided detection search problem where the location and the detectability of a moving object are uncertain. A solution to this $\mathcal{NP}$-hard problem is a path on a graph that maximizes the probability of finding an object that moves according to a known motion model. We developed constraint programming models to solve this probabilistic path planning problem for a single indivisible searcher. These models include a simple but powerful branching heuristic as well as strong filtering constraints. We present our experimentation and compare our results with existing results in the literature. The OSP problem is particularly interesting in that it generalizes to various probabilistic search problems such as intruder detection, malicious code identification, search and rescue, and surveillance.