An exact method for a class of robust shortest path problems with scenarios

Abstract

In this variant of the robust shortest path problem, the cost of traversing an arc is given by a discrete set of scenarios. The problem is then to find a (robust) path that takes into account the information arising from the multiple cost realizations of the possible scenarios. To account for a robust path, we adopt the bw‐robustness criterion, which ameliorates the dramatic role played by worst‐case approaches. Under this criterion, the parameter b represents a desirable upper bound for the cost that the decision maker wants for most of the scenarios; while parameter w strictly bounds the cost and represents a value that the decision maker is not willing to exceed in any scenario. To solve the problem, we extend the pulse algorithm, a general‐purpose solution strategy that has been used on shortest path problems with side constraints. The proposed algorithm compares favorably against an integer programming approach both in terms of speed and scalability on networks with up to 39 377 nodes and 192 094 arcs.

On the shortest $$\alpha$$-reliable path problem

“…In addition to being one of the state-of-the-art algorithms for the CSP, efficiently solving real-road networks with up to 6 million nodes and 15 million arcs in Cabrera et al (2020), the pulse algorithm has been successfully extended to solve other hard shortest path variants. The same principles have been applied to solve the elementary shortest path problem with resource constraints (Lozano et al 2016;Li and Han 2019), the biobjective shortest path problem (Duque et al 2015), the weight constrained shortest path problem with replenishment (Bolívar et al 2014), the orienteering problem with time windows (Duque et al 2014), and the scenario-based robust shortest path problem (Duque and Medaglia 2019), among other shortest path variants.…”

An exact bidirectional pulse algorithm for the constrained shortest path

“…The PA has been successfully extended for the elementary shortest path problem with resource constraints [19], the biobjective shortest path problem [12], the weight CSP with replenishment [4], the orienteering problem with time windows [11], and more recently, the robust shortest path problem [13]. Beyond the domain of shortest path problems, several authors have used the PA as a component to solve other hard combinatorial problems.…”