scholarly journals Computational Experience in Methods for Finding Tight Lower Bounds for the Sparse Travelling Salesman Problem

10.5772/7824 ◽  
2010 ◽  
Author(s):  
Fredrick Mtenzi
Keyword(s):  
Lower Bounds ◽  
Travelling Salesman Problem ◽  
Computational Experience ◽  
Travelling Salesman

New lower bounds for the Symmetric Travelling Salesman Problem

1989 ◽  
Vol 45 (1-3) ◽  
pp. 233-254 ◽  
Author(s):  
G. Carpaneto ◽  
M. Fischetti ◽  
P. Toth
Keyword(s):  
Lower Bounds ◽  
Travelling Salesman Problem ◽  
Travelling Salesman

The Travelling Salesman Problem in symmetric circulant matrices with two stripes

2008 ◽  
Vol 18 (1) ◽  
pp. 165-175 ◽  
Author(s):  
IVAN GERACE ◽  
FEDERICO GRECO
Keyword(s):  
Computational Complexity ◽  
Lower Bound ◽  
Lower Bounds ◽  
Travelling Salesman Problem ◽  
Minimum Cost ◽  
Circulant Matrix ◽  
Upper And Lower Bounds ◽  
Circulant Matrices ◽  
Travelling Salesman ◽  
New Construction

The Symmetric Circulant Travelling Salesman Problem asks for the minimum cost tour in a symmetric circulant matrix. The computational complexity of this problem is not known – only upper and lower bounds have been determined. This paper provides a characterisation of the two-stripe case. Instances where the minimum cost of a tour is equal to either the upper or lower bound are recognised. A new construction providing a tour is proposed for the remaining instances, and this leads to a new upper bound that is closer than the previous one.

scholarly journals Weighted amplifiers and inapproximability results for Travelling Salesman problem

2020 ◽  
Author(s):  
Miroslav Chlebík ◽  
Janka Chlebíková
Keyword(s):  
Lower Bounds ◽  
Constraint Satisfaction ◽  
Steiner Tree ◽  
Travelling Salesman Problem ◽  
Main Tool ◽  
Fine Tuning ◽  
Slight Improvement ◽  
Expander Graph ◽  
Travelling Salesman ◽  
Improve Approximation

Abstract The expander graph constructions and their variants are the main tool used in gap preserving reductions to prove approximation lower bounds of combinatorial optimisation problems. In this paper we introduce the weighted amplifiers and weighted low occurrence of Constraint Satisfaction problems as intermediate steps in the NP-hard gap reductions. Allowing the weights in intermediate problems is rather natural for the edge-weighted problems as Travelling Salesman or Steiner Tree. We demonstrate the technique for Travelling Salesman and use the parametrised weighted amplifiers in the gap reductions to allow more flexibility in fine-tuning their expanding parameters. The purpose of this paper is to point out effectiveness of these ideas, rather than to optimise the expander’s parameters. Nevertheless, we show that already slight improvement of known expander values modestly improve the current best approximation hardness value for TSP from $$\frac{123}{122}$$ 123 122 (Karpinski et al. in J Comput Syst Sci 81(8):1665–1677, 2015) to $$\frac{117}{116}$$ 117 116 . This provides a new motivation for study of expanding properties of random graphs in order to improve approximation lower bounds of TSP and other edge-weighted optimisation problems.

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
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