Heuristics for the Canadian traveler problem with neutralizations

Abstract

Canadian Traveler Problem with Neutralizations (CTPN) is a recently introduced challenging graph-theoretic path-planning problem. In CTPN, traversability status of some edges in the underlying graph is dependent on an a priori probability distribution. A traveling agent has two capabilities called disambiguation and neutralization. In the disambiguation case, the true status of an ambiguous edge (traversable or untraversable) is revealed when the agent is at either end of such edges. If the neutralization capability is exploited, the edge immediately becomes traversable. These capabilities are limited and may add a cost of increased path length. The goal of the agent is to find the shortest expected path length by devising an optimal policy that dictates when and where to disambiguate or neutralize. CTPN has important and practical applications within the context of expert and intelligent systems. These include autonomous robot navigation, adaptive transportation systems, naval and land minefield countermeasures, and navigation inside disaster areas for emergency relief operations. There is a recently proposed state-of-the-art exact algorithm that solves CTPN to optimality, called CAON* (AO* with Caching and Neutralizations). CAON* is based on an extension of the well-known AO* (AND-OR search) algorithm. Even though CAON* has significant improvements compared to its predecessors, it still has exponential run time and space complexity and it has been shown to solve only small instances of CTPN in practice. In this study, we introduce new heuristics for CTPN based on novel strategies that can be used to solve much larger and realistic problem instances. We provide computational experiments on Delaunay graphs to assess and compare the performance of these heuristics and CAON*, in terms of both run time and solution quality. Our computational experiments indicate that the proposed heuristics run extremely fast (well under a second in all cases) and they result in up to 58% improvement over existing heuristics with respect to expected path lengths with an overall improvement of 32% across our computational experiments.