Path Planning Problem under non-probabilistic Uncertainty

Abstract: This paper considers theoretical solutions for path planning problems under non-probabilistic uncertainty used in the travel salesman problems under uncertainty. The uncertainty is on the paths between the cities as nodes in a travelling salesman problem. There is at least one path between two nodes/stations where the travelling time between the nodes is not precisely known. This could be due to environmental effects like crowdedness (rush period) in the path, the state of the charge of batteries, weather conditions, or considering the safety of the route while travelling. In this work, we consider two different advanced uncertainty models (i) probabilistic-precise uncertain model: Probability distributions and (ii) non-probabilistic--imprecise uncertain model: Intervals. We investigate what theoretical results can be obtained for two different optimality criteria: maximinity and maximality in the travelling salesman problem.