A dynamic programming algorithm for the traveling salesman problem

1993 ◽  
Vol 23 (4) ◽  
pp. 1-3 ◽  
Author(s):  
Moshe Sniedovich
Keyword(s):  
Dynamic Programming ◽  
Traveling Salesman Problem ◽  
Dynamic Programming Algorithm ◽  
Traveling Salesman ◽  
Programming Algorithm ◽  
The Traveling Salesman Problem

scholarly journals Dynamic programming approaches for the traveling salesman problem with drone

Networks ◽  
2018 ◽  
Vol 72 (4) ◽  
pp. 528-542 ◽  
Author(s):  
Paul Bouman ◽  
Niels Agatz ◽  
Marie Schmidt
Keyword(s):  
Dynamic Programming ◽  
Traveling Salesman Problem ◽  
Traveling Salesman ◽  
The Traveling Salesman Problem

scholarly journals Exact Methods for the Traveling Salesman Problem with Drone

2021 ◽  
Vol 55 (2) ◽  
pp. 315-335
Author(s):  
Roberto Roberti ◽  
Mario Ruthmair
Keyword(s):  
Dynamic Programming ◽  
Traveling Salesman Problem ◽  
State Of The Art ◽  
The State ◽  
Set Partitioning ◽  
Traveling Salesman ◽  
Mixed Integer ◽  
Branch And Price ◽  
Last Mile ◽  
The Traveling Salesman Problem

Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution methods to plan last-mile deliveries with drones are available. We study exact solution approaches for some variants of the traveling salesman problem with drone (TSP-D) in which a truck and a drone are teamed up to serve a set of customers. This combination of truck and drone can exploit the benefits of both vehicle types: the truck has a large capacity but usually low travel speed in urban areas; the drone is faster and not restricted to street networks, but its range and carrying capacity are limited. We propose a compact mixed-integer linear program (MILP) for several TSP-D variants that is based on timely synchronizing truck and drone flows; such an MILP is easy to implement but nevertheless leads to competitive results compared with the state-of-the-art MILPs. Furthermore, we introduce dynamic programming recursions to model several TSP-D variants. We show how these dynamic programming recursions can be exploited in an exact branch-and-price approach based on a set partitioning formulation using ng-route relaxation and a three-level hierarchical branching. The proposed branch-and-price can solve instances with up to 39 customers to optimality outperforming the state-of-the-art by more than doubling the manageable instance size. Finally, we analyze different scenarios and show that even a single drone can significantly reduce a route’s completion time when the drone is sufficiently fast.

scholarly journals A Polynomial-Time Dynamic Programming Algorithm for Phrase-Based Decoding with a Fixed Distortion Limit

2017 ◽  
Vol 5 ◽  
pp. 59-71
Author(s):  
Yin-Wen Chang ◽  
Michael Collins
Keyword(s):  
Dynamic Programming ◽  
Dynamic Programming Algorithm ◽  
Sentence Length ◽  
Target Language ◽  
Programming Algorithm ◽  
Time Dynamic ◽  
Np Complete ◽  
New Perspective ◽  
The Traveling Salesman Problem ◽  
The Impact

Decoding of phrase-based translation models in the general case is known to be NP-complete, by a reduction from the traveling salesman problem (Knight, 1999). In practice, phrase-based systems often impose a hard distortion limit that limits the movement of phrases during translation. However, the impact on complexity after imposing such a constraint is not well studied. In this paper, we describe a dynamic programming algorithm for phrase-based decoding with a fixed distortion limit. The runtime of the algorithm is O( nd! lh d+1) where n is the sentence length, d is the distortion limit, l is a bound on the number of phrases starting at any position in the sentence, and h is related to the maximum number of target language translations for any source word. The algorithm makes use of a novel representation that gives a new perspective on decoding of phrase-based models.

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