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A Genetic Solution to the Travelling Salesman Problem

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A Genetic Solution to the Travelling Salesman Problem. Ryan Honig ... is the Travelling Salesman Problem? Traveling Salesman Problem (TSP) Definition: Given ... – PowerPoint PPT presentation

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Title: A Genetic Solution to the Travelling Salesman Problem


1
A Genetic Solution to the Travelling Salesman
Problem
Ryan Honig
2
What is the Travelling Salesman Problem?
Traveling Salesman Problem (TSP) Definition
Given a set of points, find the shortest path
that visits each point exactly once and returns
to the starting point.
3
My Goal
  • Main Things I want to do
  • Create an algorithm that can find near-optimal
    solutions for symmetric TSPs.
  • Create a way of heuristically generating a pool
  • Build off of the first algorithm to allow it to
    find near-optimal solutions for asymmetric TSPs.

4
What is the Travelling Salesman Problem? (Cont.)?
Two Types of Problems Symmetric Asymmetric
5
What is the Travelling Salesman Problem? (Cont.)?
Symmetric
A
B
Distance 100
Distance 100
6
Genetic Algorithm
Genetic algorithm an algorithm that has a pool
of solutions, and will at random pick two
solutions and combine them to create a child
solution, then a fitness function is used to rank
the solutions
7
Genetic Algorithm (Cont)?
Parent A
Parent B
A
A
B
B
C
E
E
C
D
D
8
Genetic Algorithm (Cont)?
Combined Path
B
A
B
A
A
B
A
B
E
B
C
A
A
B
D
9
Genetic Algorithm (Cont)?
Child
B
A
B
A
B
E
C
A
B
D
10
Mutations
  • Chance of 1 in 50 to introduce a mutation to the
    next generation (the child if it replaces a
    parent, or the first parent)?

R1
R2
E
B
F
D
G
A
C
E
A
G
D
F
B
C
11
Pool Creating Heuristic
A
A
B
A
E
A
B
A
B
A
A
B
C
E
E
D
D
12
Pool Creating Heuristic (Cont)?
After testing the two different versions of my
program, I found that while the heuristic program
was still slightly better than the random-pool
program, the time it took to run still did not
justify its improvement.
13
Pool Creating Heuristic (Testing)?
A280 2579
2780.54
2729.37
1.75 sec
5.11 sec
12017.46
7.32 sec
ATT48 10628
12104.32
2.31 sec
1.33 sec
BAYG29 1610
1750.92
1693.84
4.32 sec
2385.34
2327.77
1.86 sec
5.76 sec
BAYS29 2020
CH130 6110
6487.37
6.43 sec
6493.65
2.76 sec
14
What is the Travelling Salesman Problem? (Cont.)?
Asymmetric Travelling Salesman Problem
A
B
Distance 100
Distance 200
15
Asymmetric Travelling Salesman
  • After testing my two versions of the symmetric
    program, I began work on converting the
    random-pool program so that it could solve
    asymmetric travelling salesman problems.
  • Working with a data set that only contains 17
    points, data is read in as a text file that
    contains a grid of distances between points
    rather than the coordinates of points
  • I can successfully read the data into a matrix,
    but I am having a hard time converting the actual
    genetic algorithm

16
Asymmetric Travelling Salesman (cont)?
  • I attempted to use the data to create two sets of
    absolute coordinates depending on whether you
    were moving in the clockwise or counter clockwise
    direction, rather than just having the matrix of
    relative distances
  • While this was slightly easier to work with than
    the relative coordinates, I was still not able to
    get an algorithm that can find solutions to the
    asymmetric problem sets in the end

17
The Future of my Program
  • If anyone wants to continue this project, they
    can
  • Finish making the genetic algorithm compatible
    with asymmetric TSPs
  • Make a GUI

18
THE END
Any Questions?
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