A Genetic Solution to the Travelling Salesman Problem

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A Genetic Solution to the Travelling Salesman
Problem
Ryan Honig
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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.
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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.

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What is the Travelling Salesman Problem? (Cont.)?
Two Types of Problems Symmetric Asymmetric
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What is the Travelling Salesman Problem? (Cont.)?
Symmetric
A
B
Distance 100
Distance 100
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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
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Genetic Algorithm (Cont)?
Parent A
Parent B
A
A
B
B
C
E
E
C
D
D
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Genetic Algorithm (Cont)?
Combined Path
B
A
B
A
A
B
A
B
E
B
C
A
A
B
D
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Genetic Algorithm (Cont)?
Child
B
A
B
A
B
E
C
A
B
D
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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
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Pool Creating Heuristic
A
A
B
A
E
A
B
A
B
A
A
B
C
E
E
D
D
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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.
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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
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What is the Travelling Salesman Problem? (Cont.)?
Asymmetric Travelling Salesman Problem
A
B
Distance 100
Distance 200
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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

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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

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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

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THE END
Any Questions?