A New Formulation for the Travelling Salesman Problem

1984 ◽  
Vol 5 (1) ◽  
pp. 21-25 ◽  
Author(s):  
A. Claus
Keyword(s):  
Travelling Salesman Problem ◽  
Travelling Salesman ◽  
New Formulation

scholarly journals Equivalent cyclic polygon of a euclidean travelling salesman problem tour and modified formulation

2021 ◽  
Author(s):  
A. Herraiz ◽  
M. Gutierrez ◽  
M. Ortega-Mier
Keyword(s):  
Objective Function ◽  
Travelling Salesman Problem ◽  
Geometric Parameters ◽  
Geometric Transformation ◽  
Travelling Salesman ◽  
New Formulation ◽  
Additional Constraints ◽  
Cyclic Polygon ◽  
The Way

AbstractWe define a geometric transformation of Euclidean Travelling Salesman Problem (TSP) tours that leads to a new formulation of the TSP. For every Euclidean TSP n-city tour, it is possible to construct an inscribed n-polygon (Equivalent Cyclic Polygon, ECP) such that the lengths of the edges are equal to the corresponding TSP tour links and follow the same sequence order. The analysis of the ECP elicits the possibility of defining a new objective function in terms of angles instead of distances. This modification opens the way to identify characterizing geometric parameters of the TSP as well as to explore new heuristics based on the inclusion of additional constraints. The experimentation with a set of cases shows promising results compared to the traditional compact formulations. The behavior of the ECP-based TSP formulations is better when the nodes of the TSP are randomly or evenly distributed.

scholarly journals Tourist Route Optimization in the Context of Covid-19 Pandemic

2021 ◽  
Vol 13 (10) ◽  
pp. 5492
Author(s):  
Cristina Maria Păcurar ◽  
Ruxandra-Gabriela Albu ◽  
Victor Dan Păcurar
Keyword(s):  
Travelling Salesman Problem ◽  
Route Planning ◽  
Route Optimization ◽  
Travelling Salesman ◽  
Social Distancing ◽  
Tourist Destinations ◽  
Innovative Method ◽  
The Social ◽  
Immediate Response

The paper presents an innovative method for tourist route planning inside a destination. The necessity of reorganizing the tourist routes within a destination comes as an immediate response to the Covid-19 crisis. The implementation of the method inside tourist destinations can bring an important advantage in transforming a destination into a safer one in times of Covid-19 and post-Covid-19. The existing trend of shortening the tourist stay length has been accelerated while the epidemic became a pandemic. Moreover, the wariness for future pandemics has brought into spotlight the issue of overcrowded attractions inside a destination at certain moments. The method presented in this paper proposes a backtracking algorithm, more precisely an adaptation of the travelling salesman problem. The method presented is aimed to facilitate the navigation inside a destination and to revive certain less-visited sightseeing spots inside a destination while facilitating conformation with the social distancing measures imposed for Covid-19 control.

A column-and-row generation approach for the flying sidekick travelling salesman problem

2021 ◽  
Vol 124 ◽  
pp. 102913
Author(s):  
Maurizio Boccia ◽  
Adriano Masone ◽  
Antonio Sforza ◽  
Claudio Sterle
Keyword(s):  
Travelling Salesman Problem ◽  
Travelling Salesman

scholarly journals Converting MST to TSP Path by Branch Elimination

2020 ◽  
Vol 11 (1) ◽  
pp. 177
Author(s):  
Pasi Fränti ◽  
Teemu Nenonen ◽  
Mingchuan Yuan
Keyword(s):  
Spanning Tree ◽  
Closed Loop ◽  
Minimum Spanning Tree ◽  
Travelling Salesman Problem ◽  
Open Loop ◽  
Travelling Salesman ◽  
Elimination Algorithm ◽  
Number Of Iterations ◽  
Number Of Branches

Travelling salesman problem (TSP) has been widely studied for the classical closed loop variant but less attention has been paid to the open loop variant. Open loop solution has property of being also a spanning tree, although not necessarily the minimum spanning tree (MST). In this paper, we present a simple branch elimination algorithm that removes the branches from MST by cutting one link and then reconnecting the resulting subtrees via selected leaf nodes. The number of iterations equals to the number of branches (b) in the MST. Typically, b << n where n is the number of nodes. With O-Mopsi and Dots datasets, the algorithm reaches gap of 1.69% and 0.61 %, respectively. The algorithm is suitable especially for educational purposes by showing the connection between MST and TSP, but it can also serve as a quick approximation for more complex metaheuristics whose efficiency relies on quality of the initial solution.

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