Case Study: The Traveling Salesman Problem

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Introduction
Traveling Salesman Problem (TSP) is a well-known NP hard problem and it is a combinatorial optimization problem in research studies. When cities increase in number then its complexity will also produce quickly in exponential degree. To solve this problem in polynomial time its very difficult to find it in shortest possible way and minimum cost.

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The Traveling Salesman Problem
The theme of traveling salesman problem (TSP) [16] is to discover a tour with a given no of city, visit every city just once and then come back to the beginning of a city where from the length of a tour is minimize. Traveling salesman problem have a great importance especially in practical application, i.e. optimal route problem,
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Researcher does well a lot work on this problem to find an optimized solution for this problem but no one able provide accurate solution to solve this problem. Many scientists tried several approaches but everyone got the solution by its own way by using different algorithms one of the approaches was used “ a multilevel graph portioning scheme to solve travel sales man problem”[1] although traveling sales man problem is not a simple problem because it belong to NP-Complete class problem. they tried to solve this problem by using multilevel graph partitioning scheme in which they used vertices and edge to represent the graph but in this problem its several weaknesses one of them is the arbitrary initial portioning of the vertex set that is capable of can affecting the desire result quality. Most popular paradigm is the arbitrary initial partitioning of a vertices, it can a have major affect quality of a solution. Comprehensive methods depend on characteristics of the whole graph and not depend on the arbitrary initial partitioning. The most ordinary instance is spectral partitioning, where a partition is resulting from the range of the adjacency matrix [2wi].Another problem arise when we need parallel processing of the records that required in parallel processing where data sets need to be…show more content…
This is very common and popular approach first chosen by Dorigo [4, 5] who is an Italian scholar in the 1990s. An Ant colony algorithm is a pretended performance it imitates foraging behavior of real ant. On the path when an ant watches the food they release the pheromone. They recognize the pheromone concentration, they select the way according to the pheromone concentration, then all ants chooses the shortest path in search of to reach at final destination. Similarly in this research paper [3] they have applied this ant colony algorithm to the Travel Salesman Problem for optimizing, they have chosen the ant colony algorithm model [7, 9] for this model demonstrate that if we put m ants in n cities, it builds a artificial ant colony scheme, every ant events shall meet the terms with subsequent requirement, firstly a absorption of genetic pheromone choose possibility that ant selects the next city, secondly an ant can’t select the city which have been selected as after that city, thirdly An Ant modify concentration of genetic on the pathway after thronging all of the cities, this technique was used to overcome this problem, but the approach is not satisfactory due to the following reason that all achievements of ant colony algorithm is primarily at experimental level. There are very less assumption which can clarify why adapting an ant colony algorithm can

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