Shortest Path Tour Problem

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Shortest path tour problem with time windows - ScienceDirect

https://www.sciencedirect.com/science/article/pii/S0377221719307222

Apr 01, 2020 · The Shortest Path Tour Problem (SPTP) has been firstly introduced by Bajaj (1971) as a constrained version of the Shortest Path Problem (SPP). The problem is formulated on a graph and the nodes are clustered in several ordering sets. A cost is associated with each arc of the graph. The aim is to find a path with minimum cost, such that the sets ...Author: Luigi Di Puglia Pugliese, Daniele Ferone, Paola Festa, Francesca Guerriero

Solving the shortest path tour problem - ScienceDirect

https://www.sciencedirect.com/science/article/pii/S0377221713003433

Nov 01, 2013 · The shortest path tour problem (SPTP) is a variant of the shortest path problem (SPP) and appeared for the first time in the scientific literature in Bertsekas’s dynamic programming and optimal control book . The SPTP has been recently studied by Festa in . The paper of Festa is the first systematic contribution for solving the SPTP.Cited by: 14

A Dynamic Programming algorithm for Shortest Path Tour problem

https://stackoverflow.com/questions/59442298/a-dynamic-programming-algorithm-for-shortest-path-tour-problem

The shortest path tour problem (SPTP) consists of finding a shortest path from a given origin node s to a given destination node t in a directed graph with non-negative arc lengths with the constraint that the optimal path P should successively pass through at least one node from given node subsets T1, T2, . . .

Shortest path tour problem with time windows - ScienceDirect

https://www.sciencedirect.com/science/article/abs/pii/S0377221719307222

This paper aims at studying a new variant of the shortest path tour problem, where time window constraints are taken into account. This is the first work dealing with the shortest path tour problem with time windows. The problem is formally described and its theoretical properties are analyzed.Author: Luigi Di Puglia Pugliese, Daniele Ferone, Paola Festa, Francesca Guerriero

[PDF] The shortest path tour problem : problem definition ...

https://www.semanticscholar.org/paper/The-shortest-path-tour-problem-%3A-problem-definition-Festa/d2f639c285fe6f1f549b403aa52f9c22ecc5e37e

The shortest path tour problem (SPTP) consists of finding a shortest path from a given origin node s to a given destination node d in a directed graph with nonnegative arc lengths with the constraint that the optimal path P should successively pass through at least one node from given node subsets T1, T2, . . . , TN , where ⋂N k=1 Tk = ∅.

An efficient exact approach for the constrained shortest ...

https://www.tandfonline.com/doi/abs/10.1080/10556788.2018.1548015

Given a directed graph with non-negative arc lengths, the Constrained Shortest Path Tour Problem (C S P T P) is aimed at finding a shortest path from a single-origin to a single-destination, such that a sequence of disjoint and possibly different-sized node subsets are crossed in a given fixed order. Moreover, the optimal path must not include ...Cited by: 4

The constrained shortest path tour problem - ScienceDirect

https://www.sciencedirect.com/science/article/pii/S0305054816300715

Oct 01, 2016 · 1. Introduction. The constrained shortest path tour problem (CSPTP) consists in finding a single-origin single-destination shortest path in a directed graph such that a given set of constraints is satisfied.In particular, in addition to the restrictions imposed in the original version of the problem (see , , ), requiring that the path needs to cross a sequence of node subsets that are given in ...Cited by: 11

The shortest path tour problem: problem deflnition ...

http://groups.di.unipi.it/optimize/Events/proceedings/T/B/1/TB1-1.pdf

The shortest path tour problem and the idea behind it were given in 2005 as Exercise 2.9 in Bertsekas’s Dynamic Programming and Optimal Control book [3], 1. 3 5 6 s=1 7=d 1 4 2 4 1 1 4 1 3 3 5 2 2 Classical Shortest Path 1,3,7 Shortest Path Tour 1,3,2,3,7 Figure 1: …

Chess Knight Problem Find Shortest path from source to ...

https://www.techiedelight.com/chess-knight-problem-find-shortest-path-source-destination/

Given a chess board, find the shortest distance (minimum number of steps) taken by a Knight to reach given destination from given source. The idea is to use Breadth First Search (BFS) as it is a Shortest Path problem. Below is the complete algorithm.

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