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Travelling Salesman Problem (TSP)

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Travelling Salesman Problem (TSP)

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Traveling Salesman Problem - PowerPoint PPT Presentation

ppt on travelling salesman problem

Traveling Salesman Problem

Traveling salesman problem by susan ott for 252 overview of presentation brief review of tsp examples of simple heuristics better than brute force algorithm traveling ... – powerpoint ppt presentation.

  • Brief review of TSP
  • Examples of simple Heuristics
  • Better than Brute Force Algorithm
  • Given a complete, weighted graph on n nodes, find the least weight Hamiltonian cycle, a cycle that visits every node once.
  • Though this problem is easy enough to explain, it is very difficult to solve.
  • Finding all the Hamiltonian cycles of a graph takes exponential time. Therefore, TSP is in the class NP.
  • Algorithms that construct feasible solutions, and thus upper bounds for the optimal value., Hoffman and Padberg
  • The verticies given
  • Since all of these branches off of trial one are already more than the bound, we will not pursue them since adding another city will only increase the tour length!
  • Now lets see what happens in trial 2.
  • So from trial 2 we will move on with 2a, 2b, and 2d.
  • First, though, lets check out 3a, 3b, 3c, and 3d.

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Computer Science > Artificial Intelligence

Title: looking ahead to avoid being late: solving hard-constrained traveling salesman problem.

Abstract: Many real-world problems can be formulated as a constrained Traveling Salesman Problem (TSP). However, the constraints are always complex and numerous, making the TSPs challenging to solve. When the number of complicated constraints grows, it is time-consuming for traditional heuristic algorithms to avoid illegitimate outcomes. Learning-based methods provide an alternative to solve TSPs in a soft manner, which also supports GPU acceleration to generate solutions quickly. Nevertheless, the soft manner inevitably results in difficulty solving hard-constrained problems with learning algorithms, and the conflicts between legality and optimality may substantially affect the optimality of the solution. To overcome this problem and to have an effective solution against hard constraints, we proposed a novel learning-based method that uses looking-ahead information as the feature to improve the legality of TSP with Time Windows (TSPTW) solutions. Besides, we constructed TSPTW datasets with hard constraints in order to accurately evaluate and benchmark the statistical performance of various approaches, which can serve the community for future research. With comprehensive experiments on diverse datasets, MUSLA outperforms existing baselines and shows generalizability potential.

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travelling salesman problem

Travelling Salesman Problem

Mar 31, 2019

520 likes | 1.65k Views

Travelling Salesman Problem. an unfinished story. Contents. Description of the problem History Sample Algorithms Performance Comparison TSP with Parallel Computing Conclusion. Description of the Problem.

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  • insertion heuristics
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Presentation Transcript

Travelling Salesman Problem an unfinished story...

Contents • Description of the problem • History • Sample Algorithms • Performance Comparison • TSP with Parallel Computing • Conclusion

Description of the Problem Givena number of cities and the costs of travelling fromany city to anyother city, whatis the least-cost round-trip route thatvisitseach city exactly once and thenreturns to the starting city?

History The origins of the travelling salesman problem are unclear. A handbook for travelling salesmen from 1832 mentions the problem and includes example tours through Germany and Switzerland, but contains no mathematical treatment.

Sample Algorithms • Constructive Heuristics • Nearest Neighbour (Greedy) • Insertion Heuristics • 2-OPT • 3-OPT • Genetic Algoritms • Simulated Annealing • Neural Network

Performance Comparison

Performance Comparison continued...

TSP with Parallel Computing Time (sec.) NP

TSP with Parallel Computing

Conclusion • For small-size TSP (n < 50), improved greedy 2-opt algorithm is recommended. • For medium-size TSP ( 50 < n < 100), improved 2-opt algorithm and neural network are recommended for their optimality and efficiency. • For large-size problem (100 < n < 500), the improved genetic algorithm is recommended. • For any problem-size, if the computational time is not a constraint, the improved neural network is always recommended.

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COMMENTS

  1. PPT

    A Brief History • The problem was first defined in the 1800s by the Irish mathematician W.R. Hamilton and the British mathematician Thomas Kirkman. • It was, however, first formulated as a mathematical problem only in 1930 by Karl Menger. • The name Travelling Salesman Problem was introduced by American HasslerWhiteney.

  2. PPT

    Traveling Salesman Problem. The TSP involves finding the minimum traveling cost for visiting a fixed set of customers. The vehicle must visit each customer exactly once and return to its point of origin also called depot. The objective function is the total cost of the tour. 3. 2. 3. 4. 2.

  3. PDF Networks 3: Traveling salesman problem

    Two TSP tours are called 3-adjacent if one can be obtained from the other by deleting three edges and adding three edges. A TSP tour T is called 3-optimal if there is no 3-adjacent tour to T with lower cost than T. 3-opt heuristic. Look for a 3-adjacent tour with lower cost than the current tour. If one is found, then it replaces the current tour.

  4. PPT

    The Traveling Salesman Problem Rohit Ray ESE 251. Overview The goal of the Traveling Salesman Problem (TSP) is to find the most economical way to tour of a select number of "cities" with the following restrictions: • You must visit each city once and only once • You must return to the original starting point 13,509 U.S. cities with populations of more than 500 people connected ...

  5. Traveling salesman problem

    The traveling salesman problem (TSP) is a widely studied combinatorial optimization problem, which, given a set of cities and a cost to travel from one city to another, seeks to identify the tour that will allow a salesman to visit each city only once, starting and ending in the same city, at the minimum cost. 1.

  6. Traveling Salesman Problem

    Traveling Salesman Problem.ppt - Free download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online. Graph Theory

  7. Travelling Salesman Problem (TSP)

    The name Travelling Salesman Problem was introduced by American Hassler Whiteney. The origin of TSP lies with Hamilton's Icosian Game, which was a recreational puzzle based on finding a Hamiltonian cycle. Richard M. Karp showed in 1972 that the Hamiltonian cycle problem was NP-complete, which implies the NP-hardness of TSP.

  8. Travelling salesman problem

    The generalized travelling salesman problem, also known as the "travelling politician problem", deals with "states" that have (one or more) "cities" and the salesman has to visit exactly one "city" from each "state". One application is encountered in ordering a solution to the cutting stock problem in order to minimize knife changes.

  9. The Euclidean Travelling Salesman Problem

    The Euclidean Travelling Salesman Problem Peter Eades Professor of Software Technology University of Sydney. The problem • A salesman's territory consists of n cities. • He must tour all the cities, and minimise travel time. 4571km 4730km Brisbane Brisbane Byron Bay Byron Bay Sydney Sydney Adelaide Adelaide Melbourne Melbourne • We want an algorithm that gives a minimum tour.

  10. Traveling Salesman Problem (TSP)

    Problem Statement. In TSP, a salesman must visit n cities. The salesman wishes to make a tour or Hamiltonian. cycle. He must visit each city exactly once and finish. at the city he starts from. There is a cost c (i, j) or to travel from. city i to city j. For the symmetric TSP, c (i, j) c (j, i).

  11. Traveling Salesman Problem

    Hamiltons Iconsian game. 5. History of TSP (1) The general form of TSP appeared in 1930s by Karl. Menger in Vienna and Havard. A breakthrough by George Dantzig, Ray Fulkerson, and Selmer Johnson in1954. 49 - 120 550 - 2,392 - 7,397 19,509 cities. From year 1954 to year 2001.

  12. Travelling Salesman Problem Example with Solution PPT

    If salesman starting city is A, then a TSP tour in the graph is-A → B → D → C → A Cost of the tour = 10 + 25 + 30 + 15 = 80 units In this article, we will discuss how to solve travelling salesman problem using branch and bound approach with example. PRACTICE PROBLEM BASED ON TRAVELLING SALESMAN PROBLEM USING BRANCH AND BOUND APPROACH ...

  13. PPT

    The Travelling Salesman Problem Brett D. Estrade [email protected] - Spring 2004. 49 city solved by George Dantzig, Ray Fulkerson, and Selmer Johnson (1954) Overview The goal of the Traveling Salesman Problem (TSP) is to find the "cheapest" tour of a select number of "cities" with the following restrictions: • You must visit each city once and only once • You must return ...

  14. Traveling Salesman Problem

    Title: Traveling Salesman Problem 1 Traveling Salesman Problem By Susan Ott for 252 2 Overview of Presentation. Brief review of TSP ; Examples of simple Heuristics ; Better than Brute Force Algorithm; 3 Traveling Salesman Problem. Given a complete, weighted graph on n nodes, find the least weight Hamiltonian cycle, a cycle that visits every ...

  15. Looking Ahead to Avoid Being Late: Solving Hard-Constrained Traveling

    Many real-world problems can be formulated as a constrained Traveling Salesman Problem (TSP). However, the constraints are always complex and numerous, making the TSPs challenging to solve. When the number of complicated constraints grows, it is time-consuming for traditional heuristic algorithms to avoid illegitimate outcomes. Learning-based methods provide an alternative to solve TSPs in a ...

  16. Travelling Salesman Problem

    The Travelling Salesman Problem (also known as the Travelling Salesperson Problem or TSP) is an NP-hard graph computational problem where the salesman must visit all cities (denoted using vertices in a graph) given in a set just once. The distances (denoted using edges in the graph) between all these cities are known.

  17. PPT

    History The origins of the travelling salesman problem are unclear. A handbook for travelling salesmen from 1832 mentions the problem and includes example tours through Germany and Switzerland, but contains no mathematical treatment. Sample Algorithms • Constructive Heuristics • Nearest Neighbour (Greedy) • Insertion Heuristics • 2-OPT ...