An AO^* Based Exact Algorithm for the Canadian Traveler Problem

Abstract

T he Canadian traveler problem (CTP) is a simple, yet challenging, stochastic optimization problem wherein an agent is given a graph where some edges are blocked with certain probabilities and the status of these edges can be disambiguated dynamically upon reaching an incident vertex. The goal is to devise a traversal policy that results in the shortest expected walk length between a given starting vertex and a termination vertex. CTP has been shown to be intractable in many broad settings. In this paper, we introduce an optimal algorithm for the problem based on a Markov decision process formulation, which is a new improvement on AO * search that takes advantage of the special problem structure in CTP. We call our algorithm CAO * , which stands for AO * with caching. CAO * uses a caching mechanism to avoid re-expansion of previously visited states and makes use of admissible upper bounds at a node level for dynamic state-space pruning. CAO * is not polynomial time, but it can dramatically shorten the execution time needed to find an exact solution for moderately sized instances. We present computational experiments on a realistic variant of the problem involving an actual maritime minefield data set.

Any Angle Path Finding in Stochastic Obstacle Scenes

“…In addition to optimal shortest path length, comparison of path finder algorithm execution times is given in Table 4.2. Experiments proved that when number of 3 Experiment was not completed in reasonable time with more than 200 expansions. When disambiguation cost is 0, resulting path is names as zero risk distance and execution time is very close to 0.…”

“…The Canadian traveler problem (CTP) is a simple, but challenging, stochastic optimization problem to describe the very common experience in Canada as the final graph path becomes observable upon the blocked edges are explored. An agent travels on a given graph where some edges are blocked with certain probabilities and these edges update their disambiguation status dynamically when agent reaches an adjacent vertex [3,4]. Suppose that a traveler wants to go from one site to another one by knowing all roads on the unreliable map [5].…”

“…Recently, a new algorithm with the name CAO* is proposed in [6] that can solve the D-SOSP and CTP instances optimally and much faster than the state-of-the-art algorithms. CAO* has its own caching setup to prevent previously visited states to expand again and upper bounds are fair to be used at a node level to prune dynamically state space [3]. It does not complete in polynomial time, but significantly shortens the execution time of finding an exact solution when instances are relatively sized.…”

LAMP: Learning a Motion Policy to Repeatedly Navigate in an Uncertain Environment

“…Optimal policies for the stochastic CTP can be calculated using algorithms such as CAO* [13] or value iteration. However, they must limit the size of the problem or the number of observations the robot is allowed to make to keep the problem tractable.…”

“…Aksakalli et al [13] showed that the stochastic CTP can be modelled as a Markov Decision Process (MDP) and a deterministic Partially Observable Markov Decision Process (POMDP), both of which are formulations frequently used in reinforcement learning. However, generic POMDP solvers cannot be used to find optimal policies for the CTP in practical applications because the state space for the stochastic CTP is exponential.…”