Main Article Content
This paper introduces and studies a graph-based variant of the path planning problem arising in hostile environments. We consider a setting where an agent (e.g. a robot) must reach a given destination while avoiding being intercepted by probabilistic entities which exist in the graph with a given probability and move according to a probabilistic motion pattern known a priori. Given a goal vertex and a deadline to reach it, the agent must compute the path to the goal that maximizes its chances of survival. We study the computational complexity of the problem, and present two algorithms for computing high quality solutions in the general case: an exact algorithm based on Mixed-Integer Nonlinear Programming, working well in instances of moderate size, and a pseudo-polynomial time heuristic algorithm allowing to solve large scale problems in reasonable time. We also consider the two limit cases where the agent can survive with probability 0 or 1, and provide specialized algorithms to detect these kinds of situations more efficiently.