A model-based algorithm for the Probabilistic Orienteering Problem

The Orienteering Problem is a routing problem aiming at selecting a subset of a given set of customers to be visited within a given time budget, so that a total revenue is maximized. Multiple variants of the problem have been studied. The Probabilistic Orienteering Problem is one of these variants, where customers will require a visit according to a certain given probability. Stochasticity makes the model more practical, but concurrently more difficult to solve. Effective approaches to solve the problem potentially lead to higher quality planning in real-life logistics, thanks to the exploitation of the probabilistic informations that can normally be derived from historical data. In this paper we present an iterative model-based algorithm that solves a sequence of deterministic problems and is able to retrieve and certify optimal solutions if run for sufficient time. Experimental results show that the new approach is performing well when compared against both the exact (proven optimality) and heuristic (high quality solutions) algorithms available in the literature. • A stochastic version of the orienteering problem is considered. • Model-based approach to derive heuristic or exact solutions. • Probabilistic problem solved as a finite sequence of deterministic problems. • Current state-of-the-art results for the problem under consideration.