Traveling Salesman Problem: an Overview of Applications, Formulations, and Solution Approaches

Matai, Rajesh; Singh, Surya Prakash; Mittal, Murari Lal

doi:10.5772/12909

Cited by 197 publications

(125 citation statements)

References 99 publications

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“…Countless literatures had tried this formulation but among which the easiest to appreciate is in [8] where the writers illustrated TSP as follows:…”

Section: Travelling Salesman Problemmentioning

confidence: 99%

A Preliminary Study on Minimum Spanning Tree Algorithm Approach for Travelling Salesman Problem

Baidoo¹

2016

CAE

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Much attention has be drawn by the Travelling salesman problem lately as it is one of the problem in mathematics and computer science which although is easy to understand but very difficult to solve.In this paper, a preliminary study is undertaken to construct a minimum spanning tree algorithm to approximately solve the TSP. An implementation of the travelling salesman problem using a modified pure minimum spanning tree algorithm is also presented. The propose algorithm provides an evaluation of the cost of a round trip and it executes in practical time. The algorithm verifies from a constructed tour and presents a shortcut path to all destinations. The proposed approach performance is benchmark with a case study.

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“…Countless literatures had tried this formulation but among which the easiest to appreciate is in [8] where the writers illustrated TSP as follows:…”

Section: Travelling Salesman Problemmentioning

confidence: 99%

A Preliminary Study on Minimum Spanning Tree Algorithm Approach for Travelling Salesman Problem

Baidoo¹

2016

CAE

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“…The problem is classified as symmetric if = , ∀ , , or asymmetric if ̸ = , ∀ , [20]. This problem is known to be NP-hard [21]; thus, in order to get the optimal solution, a significant computational effort is required and demands the use of efficient algorithms.…”

Section: Considered Problem and Metaheuristics: Overviewmentioning

confidence: 99%

“…Essentially, they involve finding an extreme value (maximum or minimum) called optimal, from a function with numerous local extremes, called objective function. Some of those problems are classical in Operations Research area, such as the traveling salesman problem, and involve a significant number of publications in the specialized literature [17][18][19][20]. The traveling salesman problem (TSP) is a classical optimization problem, whose idea is to find the shortest route between a set of given cities, starting and ending at the same city, such that each city is visited exactly once.…”

Section: Considered Problem and Metaheuristics: Overviewmentioning

confidence: 99%

Improving the Fine-Tuning of Metaheuristics: An Approach Combining Design of Experiments and Racing Algorithms

Barbosa

Senne

2017

Journal of Optimization

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Usually, metaheuristic algorithms are adapted to a large set of problems by applying few modifications on parameters for each specific case. However, this flexibility demands a huge effort to correctly tune such parameters. Therefore, the tuning of metaheuristics arises as one of the most important challenges in the context of research of these algorithms. Thus, this paper aims to present a methodology combining Statistical and Artificial Intelligence methods in the fine-tuning of metaheuristics. The key idea is a heuristic method, called Heuristic Oriented Racing Algorithm (HORA), which explores a search space of parameters looking for candidate configurations close to a promising alternative. To confirm the validity of this approach, we present a case study for finetuning two distinct metaheuristics: Simulated Annealing (SA) and Genetic Algorithm (GA), in order to solve the classical traveling salesman problem. The results are compared considering the same metaheuristics tuned through a racing method. Broadly, the proposed approach proved to be effective in terms of the overall time of the tuning process. Our results reveal that metaheuristics tuned by means of HORA achieve, with much less computational effort, similar results compared to the case when they are tuned by the other fine-tuning approach.

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“…The Traveling Salesman Problem (TSP) [73]- [75] is one of the most widely studied problems in the arena of discrete combinatorial optimization problems. The basic concept of the TSP is to find a closed tour of a given number of cities, visiting each city exactly once and returning to the starting city, by minimizing the length of the tour.…”

Section: Summary Of Natural Computing Algorithmsmentioning

confidence: 99%

Investigating Performance of Various Natural Computing Algorithms

Chawda¹,

Patel²

2017

IJISA

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Abstract-Nature is there since millenniums. Natural elements have withstood harsh complexities since years and have proved their efficiency in tackling them. This aspect has inspired many researchers to design algorithms based on phenomena in the natural world since the last couple of decades. Such algorithms are known as natural computing algorithms or nature inspired algorithms. These algorithms have established their ability to solve a large number of real-world complex problems by providing optimal solutions within the reasonable time duration. This paper presents an investigation by assessing the performance of some of the well-known natural computing algorithms with their variations. These algorithms include Genetic Algorithms, Ant Colony Optimization, River Formation Dynamics, Firefly Algorithm and Cuckoo Search. The Traveling Salesman Problem is used here as a test bed problem for performance evaluation of these algorithms. It is a kind of combinatorial optimization problem and known as one the most famous NP-Hard problems. It is simple and easy to understand, but at the same time, very difficult to find the optimal solution in a reasonable time -particularly with the increase in a number of cities. The source code for the above natural computing algorithms is developed in MATLAB R2015b and applied on several TSP instances given in TSPLIB library. Results obtained are analyzed based on various criteria such as tour length, required iterations, convergence time and quality of solutions. Conclusions derived from this analysis help to establish the superiority of Firefly Algorithms over the other algorithms in comparative terms.

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Traveling Salesman Problem: an Overview of Applications, Formulations, and Solution Approaches

Cited by 197 publications

References 99 publications

A Preliminary Study on Minimum Spanning Tree Algorithm Approach for Travelling Salesman Problem

A Preliminary Study on Minimum Spanning Tree Algorithm Approach for Travelling Salesman Problem

Improving the Fine-Tuning of Metaheuristics: An Approach Combining Design of Experiments and Racing Algorithms

Investigating Performance of Various Natural Computing Algorithms

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