Motivated by the increasing popularity of electric vehicles (EV) and a lack of charging stations in the road network, we study the shortest path hitting set (SPHS) problem. Roughly speaking, given an input graph G, the goal is to compute a small-size subset H of vertices of G such that by placing charging stations at vertices in H, every shortest path in G becomes EV-feasible, i.e., an EV can t...

Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge shortest length paths between all and goal destinations. Determining exact in an environment obstacles is NP-hard however. In this paper, we investigate when polynomial-time approximations path search are sufficient to determine optimal assignment goals. particular, propose algorith...

a shortest path problem is a practical issue in networks for real-world situations. this paper addresses the fuzzy shortest path (fsp) problem to obtain the best fuzzy path among fuzzy paths sets. for this purpose, a new efficient algorithm is introduced based on a new definition of ideal fuzzy sets (ifss) in order to determine the fuzzy shortest path. moreover, this algorithm is developed for ...

This article provides an overview of the performance and the theoretical complexity of approximate and exact methods for various versions of the shortest path problem. The proposed study aims to improve the resolution of a more general covering problem within a column generation scheme in which the shortest path problem is the sub-problem.

Recoverable robustness is a concept to avoid over-conservatism in robust optimization by allowing a limited recovery after the full data is revealed. We investigate two settings of recoverable robust shortest path problems. In both settings the costs of the arcs are subject to uncertainty. For the first setting, at most k arcs of the chosen path can be altered in the recovery. In the second set...

Min-max and min-max regret criteria are commonly used to define robust solutions. After motivating the use of these criteria, we present general results. Then, we survey complexity results for the min-max and min-max regret versions of some combinatorial optimization problems: shortest path, spanning tree, assignment, min cut, min s-t cut, knapsack. Since most of these problems are NP -hard, we...