On the Forward Shortest Path Tour Problem

Carrabs, Francesco; Cerulli, Raffaele; Festa, Paola; Laureana, Federica

doi:10.1007/978-3-319-67308-0_53

Cited by 6 publications

(2 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Therefore, the lower bound we used to evaluate the quality of the solutions of the GRASP metaheuristic, is the optimal solution of the FSPTP on the set of Large instances. To solve the FSPTP we used the polynomial time algorithm proposed by Carrabs et al [7].…”

Section: Computational Resultsmentioning

confidence: 99%

See 1 more Smart Citation

The constrained forward shortest path tour problem: Mathematical modeling and GRASP approximate solutions

et al. 2020

Self Cite

View full text Add to dashboard Cite

This paper deals with the Constrained Forward Shortest Path Tour Problem, an NP‐complete variant of the Forward Shortest Path Tour Problem. Given a directed weighted graph G = (V, A), where the set of nodes V is partitioned into clusters T1, …, TN, the aim is determining a shortest path between two given nodes, s and d, with the properties that clusters must be visited according to a given order, and each arc can be crossed at most once. We introduce a mathematical formulation of the problem, and a reduction procedure to reduce the number of variables involved in the model. Furthermore, we propose a Greedy Randomized Adaptive Search Procedure (GRASP) algorithm to solve large instances of the problem. Computational tests show that the reduction procedure is very effective and its application significantly speeds up the resolution of the model. Moreover, the computational results certify the effectiveness of GRASP that often finds the optimal solution and, in general, provides quickly high‐quality sub‐optimal solutions.

show abstract

Section: Computational Resultsmentioning

confidence: 99%

“…Carrabs et al [7] defined the Forward Shortest Path Tour Problem, a simpler version of the CFSPTP, where a feasible path can cross repeated arcs. The word forward in the name of the problem means that a node of a given cluster can be visited if and only if at least one node for each preceding cluster has been already visited.…”

Section: Introductionmentioning

confidence: 99%