The Travelling Salesman Problem (A Guided Tour of Combinatorial Optimisation

1986 ◽  
Vol 70 (454) ◽  
pp. 327
Author(s):  
Mike Worboys ◽  
E. L. Lawler ◽  
J. K. Lenstra ◽  
A. H. G. Rinnooy Kan ◽  
D. B. Shmoys
Keyword(s):  
Travelling Salesman Problem ◽  
Combinatorial Optimisation ◽  
Travelling Salesman ◽  
Guided Tour

Evolving Combinatorial Problem Instances That Are Difficult to Solve

2006 ◽  
Vol 14 (4) ◽  
pp. 433-462 ◽  
Author(s):  
Jano I. van Hemert
Keyword(s):  
Evolutionary Computation ◽  
Structural Properties ◽  
Constraint Satisfaction ◽  
Travelling Salesman Problem ◽  
Combinatorial Problem ◽  
Boolean Satisfiability ◽  
Combinatorial Optimisation ◽  
Travelling Salesman ◽  
Binary Constraint ◽  
Problem Instances

This paper demonstrates how evolutionary computation can be used to acquire difficult to solve combinatorial problem instances. As a result of this technique, the corresponding algorithms used to solve these instances are stress-tested. The technique is applied in three important domains of combinatorial optimisation, binary constraint satisfaction, Boolean satisfiability, and the travelling salesman problem. The problem instances acquired through this technique are more difficult than the ones found in popular benchmarks. In this paper, these evolved instances are analysed with the aim to explain their difficulty in terms of structural properties, thereby exposing the weaknesses of corresponding algorithms.

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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