# Analysis Of The Travelling Salesman Problem

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The Travelling Salesman Problem (TSP) is well known in the field of combinatorial optimization. It is a NP-complete problem and there is no efficient method to solve this problem and give best result. Many algorithms are used to solve travelling salesman problem. Some algorithms give optimal solution but some other algorithms gives nearest optimal solution. The genetic algorithm is a heuristic method which is used to improve the solution space for genetic algorithm. The genetic algorithm results in nearest optimal solution within a reasonable time. This paper mainly focuses on various stages of genetic algorithm and comparative study on various methods used for genetic algorithm. The paper also proposes a method to solve the travelling salesman problem and hence improve the solution space.

Keywords

Travelling Salesman Problem, Genetic Algorithm, Selection, Sequential Constructive Crossover, Mutation

I. INTRODUCTION
Optimization is the process of making something better. An optimization problem is the problem of finding the best solution from all available solution spaces. The terminology “best” solution implies that there is more than one solution. Travelling salesman problem also results in more than one solution but the aim is to find the best solution in a reduced time and the performance is also increased. So the heuristic genetic algorithm is used.

1. Travelling Salesman Problem
The Travelling Salesman Problem (TSP) [1] is an optimization problem used to find the