Parallel Programming to solve Traveling Salesman Problem. Team Parallax Jaydeep Untwal Sushil Mohite Harsh Sadhvani parallax.hpearth.

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1 Parallel Programming to solve Traveling Salesman Problem Team Parallax Jaydeep Untwal Sushil Mohite Harsh Sadhvani parallax.hpearth.com

2 What is the traveling salesman problem? Given a list of cities and distances Find shortest path to visit each and every city and return to the original city

3 Example Watertown Buffalo Jamestown Rochester Syracuse Ithaca Binghamton Albany New York City

4 Why to have a parallel approach? Is a NP problem and takes exponential time to find the solution Finds various solutions simultaneously Speedup is considerably high when parallel approach is used

5 Our Approaches 2-Opt Technique Nearest Neighbor

6 Input/Output Input: 2D symmetric distance matrix Output: Tour configuration and total distance Ex:

7 2-Opt Technique Sequential Parallel 1. Start with a random initial tour configuration 2. Keep swapping crossing edges until no better results can be obtained 3. Repeat Steps 1 and 2 for k iterations 4. Return best of k iterations 1. Perform sequential algorithm parallely with different starting initial tour 2. Return best of all parallel executions

8 Nearest Neighbor Sequential Parallel 1. Start with a random city (c) 2. Add an unselected city (m) nearest to selected city (c) 3. Repeat Step 2 with city (m) as starting point and continue Steps 2 & 3 till all cities are added 4. Connect the last and the first city 5. Repeat Algorithm for k' iterations and return the best result 1. Perform sequential algorithm parallely with different starting city 2. Return best of all parallel executions

9 Comparison 2-Opt Technique - O(kT E^2) k - number of iterations T - number of times swapping is repeated E - number of edges - n(n-1)/2 Pros Heuristic Search Variable running time Cons Optimal Solution is not guaranteed Positional information required for searching crossing edges Overhead of structuring input

10 Comparisons Nearest Neighbor - O(n^3) N - number of cities Pros Cons Optimal Solution Easy to implement No overhead to structure input Expensive for sequential approach Fixed running time

11 Research Paper 1 Title: Approximate Travelling Salesman Algorithms Authors: B. Golden, L. Bodin, T. Doyle and W. Stewart Jr. Journal: Operations Research Volume 28 Issue 3 Date: 05/01/1980 Page Number: 694 URL: View Paper

12 Research Paper 1 In this paper, the authors discuss about the various possible approaches like convex hull, nearest neighbor etc. Discuss and analyze the computational time and quality of solution generated by each algorithm. Discuss about algorithms which can be used for a specific problem.

13 Research Paper 2 Title: New parallel randomized algorithms for the travelling salesman problem Authors: L. Shi, S. Olafsson and N. Sun Journal: Computers & Operations Research Volume 26 Issue 4 Date: 04/09/1999 Page Numbers: URL: View Paper

14 Research Paper 2 Introduces a new method called Nested Partitions for solving the Travelling Salesman Problem Basic idea is to partition the problem into feasible regions and compute a solution for each region Keep repeating this until we get an optimal solution for that region and cannot find a better solution after further partitioning Merge these small solutions into one single solution The authors believe that using different methods of partitioning can affect the efficiency of the method Discuss and analyze different partitioning methods

15 Research Paper 3 Title: Parallel Genetic Algorithms Applied to the Traveling Salesman Problem Authors: Prasanna Jog, Jung S., D. Van Gucht Journal: SIAM Journal on Optimization, Vol 1, No 4 Date: 11/01/1991 Page Numbers: URL: View Paper

16 Research Paper 3 This paper discusses about genetic algorithms (GA) that can be used to solve the traveling salesman problem Discusses how natural selection in genetic algorithms can be used in the Travelling Salesman Problem

17 THANK YOU

Massively Parallel Approximation Algorithms for the Traveling Salesman Problem

Massively Parallel Approximation Algorithms for the Traveling Salesman Problem Vaibhav Gandhi May 14, 2015 Abstract This paper introduces the reader to massively parallel approximation algorithms which