Travelling Salesman Problem

Institution

Name

Introduction

A salesman is required to visit all the cities with a known distance between every two cities keeping in mind that the cities have to be visited once. The problem facing the salesman is to determine the shortest possible route the salesman has to use to visit the towns just once and goes back to the original city.

The Travelling Salesman Problem first statement was made by a Viennese mathematician Karl Menger. It brought a connection and relation with the definition of the curve length proposed by Menger that stated that the stretch of a curves’ distance can be defined as the lower limit upper bound of the groups of all numbers that can be contained by taking each group of points of the curve and producing the shortest length of the polygonal graph. This problem is called the messenger problem.

The Travelling Salesman Problem can be stated as where a network has n cities or nodes, and one of the nodes (node 1) is the origin and the cost of travelling which include the
*…show more content…*

No one has come up with the efficient way of coming up with the solution to large size problems as the NP-complete problems are much intractable.

The exact methods provide an exact optimal solution to the problem. One of the ways of solving the Travelling Salesman Problem is simply taking all the available and feasible solutions and evaluating their function values and selecting the best out of the solutions. The process might be inefficient, impractical and time-consuming due to a large number of a possible solution that applies to the problem. Travelling Salesman Problem focuses on getting the heuristically good solution to the problem within a short period.

The solution to the problem can be obtained by carrying numerous trials in the given cities less than their

Related

- Decent Essays
## Acct505 Case1 Essays

- 600 Words
- 3 Pages

2 and 3. Compute # of passengers and train cars using computation approaches employed in some of the above problems.

- 600 Words
- 3 Pages

Decent Essays - Decent Essays
## Case 36 Essay

- 631 Words
- 3 Pages

Our optimal solution (total shipping cost) to meet all ten constraints is $513,000. Origin Muncie will not ship to hub Louisville but will ship 3 rail cars of grain to hub Cincinnati. Origin Brazil will ship 6 rail cars of grain to hub Louisville but will not ship hub Cincinnati. Origin Xenia will not ship to hub Louisville but will ship 5 rail cars to hub Cincinnati. Origin Dummy will ship 1 rail car to hub Louisville but will not ship to hub Cincinnati. Hub Louisville will ship 2 rail cars to customer Macon, 5 rail cars to Greenwood, 0 to Concord, and 0 to customer Chatham. Hub Cincinnati will ship 0 rail cars to customer Macon, 0 rail cars to Greenwood, 3 rail cars to Concord, and 5 rail cars to customer Chatham.

- 631 Words
- 3 Pages

Decent Essays - Decent Essays
## Physical Journeys

- 753 Words
- 4 Pages

Physical journeys can impact upon the traveler in many ways. They can be faced with obstacles which can impact on the traveler and will need to overcome. Physical journeys can impact upon the traveler in various ways. This is shown in Dawes poem “last seen at 12.10am” where a mother is on a journey to find her missing daughter. This is also evident in Michael James Rowland 2007 film “Lucky Miles”, where a group of men’s inner journey of friendship despite differences goes through obstacles which they overcome. Another impact upon a traveler is also shown in Bruce Dawe poem “Drifters” which a frustrated mother’s journey of disappointment, which has impacted her when suddenly faced with picking up her belongings and being, forced to move. A

- 753 Words
- 4 Pages

Decent Essays - Better Essays
## Advertising and New Customers

- 2095 Words
- 9 Pages

And a transportation model is used to minimize the cost of shipping from the production plants to the distribution centers.

- 2095 Words
- 9 Pages

Better Essays - Decent Essays
## Financial Stability In African American Life Essay

- 422 Words
- 2 Pages

It hasn’t been solved because people don’t necessarily realize that this problem is very important. It is important because if people realize and understand

- 422 Words
- 2 Pages

Decent Essays - Good Essays
## The Pros And Cons Of Gun Control

- 1225 Words
- 5 Pages

There exist many different possible solutions to this problem, all depending on what extent we want to take to solve this problem, i.e.

- 1225 Words
- 5 Pages

Good Essays - Decent Essays
## Death Of A Salesman Analysis

- 1351 Words
- 6 Pages

In Arthur Miller’s, Death of a Salesman, Biff Loman confesses the following to his brother, Happy: “I don’t know—what I’m supposed to want” (22). Biff is expressing his internal struggle between wanting to live up to his father’s expectations and his desire to pursue what he really wants-- to be outdoors. Biff is conflicted and views himself as a failure for not achieving his father’s image of success. At the end of the play, Biff realizes that in order for him to be truly successful he has to stop chasing after his father’s unrealistic expectations and start focusing on himself. Biff is finally able to break free of the mental burden of trying to fit Willy’s definition of success, resolving his internal conflict. In addition to Biff,

- 1351 Words
- 6 Pages

Decent Essays - Decent Essays
## Walmart Supply Chain Essay

- 1510 Words
- 7 Pages

Transit time is an important element as well. Any reduction in transit time therefore reduces the overall cost of the delivered goods. Transit times can be improved by

- 1510 Words
- 7 Pages

Decent Essays - Decent Essays
## Misrepresentation Of Adult Men And Women

- 731 Words
- 3 Pages

problem gathered from the results of this and other research. 15 The authors admit there is a need

- 731 Words
- 3 Pages

Decent Essays - Decent Essays
## Real Vacation Research Paper

- 540 Words
- 3 Pages

When finding the distance between each point the first step is finding the points on the coordinate plane. After finding the x and y numbers you plug the numbers in for the distance formula. The formula is(y2-y1)2+(x2-x1)2. After finding the answer to the equation, I multiplied the answer by 65 which would give the answer to the realistic distance between each city. The total of the distances is 10,109.45 miles.Each of these steps are done to find the distance between points orin this case the distance between each city.

- 540 Words
- 3 Pages

Decent Essays - Satisfactory Essays
## Voyaging Sales Representative Problem

- 175 Words
- 1 Pages

Voyaging sales representative issue is an issue that has constantly looked for the best arrangement without fail, on the grounds that the issue businessperson issue yet finished, there are two essential variable that must be met to accomplish a settlement of voyaging sales representative issue, in particular the issue ideal level of separation and the ideal time, any calculation that serves to tackle this issue for the most part experienced issues at an ideal level of separation, while the best calculations for the ideal separations have ideal levels of awful time when it achieves the quantity of focuses that a considerable measure. This paper will talk about a proposed new calculation to take care of voyaging salesperson issue, the objective

- 175 Words
- 1 Pages

Satisfactory Essays - Good Essays
## Solutions Plus Case Problem Essay

- 1005 Words
- 5 Pages

The shipping cost and/or unavailability of transportation between the plants and some locomotive locations will eliminate some of the routes due to cost inefficiency. These routes are the unacceptable routes and will not be considered for distribution from the specified plant. By removing unacceptable routes, Solutions Plus is able to build a linear programming solution to determine which plant/locomotive location combinations are optimal. Based on the shipping cost provided, the routes that are eliminated are as follows:

- 1005 Words
- 5 Pages

Good Essays - Best Essays
## The Problem of Drug Use Among Teenagers

- 2562 Words
- 10 Pages

The main aim of this research proposal is to explore the extensive situation of the problem of

- 2562 Words
- 10 Pages

Best Essays - Decent Essays
## Exact Optimization And Optimization Algorithm

- 780 Words
- 4 Pages

Exact optimisation method is the optimisation method that can guarantee to find all optimal solutions. In principle, the optimality of generated solution can be proofed mathematically. Therefore, exact optimisation is also termed as mathematical optimisation. However, exact optimisation approach is impractical usually. The effort of solving an optimisation problem by exact optimisation grows polynomially with the problem size. For example, to solve a problem by brute force approach, the execution time increases exponentially respect to the dimensions of the problem.

- 780 Words
- 4 Pages

Decent Essays - Satisfactory Essays
## Transport Systems And Transportation Systems

- 1831 Words
- 8 Pages

As quoted by Rodrigue, J-P (2013), “the most important transport problems are often related to urban areas and take place where transport systems fails to satisfy the various requirements of urban mobility because of several reasons. Productivity of any urban area is highly dependent on its transport system and also its efficiency to regulate goods, workers and consumers between multiple origins and destinations”.

- 1831 Words
- 8 Pages

Satisfactory Essays