A Genetic Solution to the Traveling Salesman Problem

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A Genetic Solution to the Traveling Salesman
Problem
Ryan Honig
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What is the Traveling 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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What is the Traveling Salesman Problem? (Cont.)
Two Types of Problems Symmetric Asymmetric
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What is the Traveling Salesman Problem? (Cont.)
Symmetric
A
B
Distance 100
Distance 100
5
What is the Traveling Salesman Problem? (Cont.)
Asymmetric
A
B
Distance 100
Distance 200
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My Goal

• Three Things I want to do
• Create an algorithm that can find near-optimal
  solutions for symmetric TSPs.
• Build off of the first algorithm to allow it to
  find near-optimal solutions for asymmetric TSPs.
• Create a graphic Interface to run the algorithms
  and visualize the set of points.

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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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What Ive done this quarter

• Fixed the bugs in my basic genetic algorithm so
  that it actually ran
• Added in mutations so that the pool doesnt get
  filled with entirely the same path
• Added a heuristic to generate the initial pool
  rather than have it be randomly generated

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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)

• I tested the program with the heuristic to
  initialize the pool against the program that has
  a random pool, and although the results are
  slightly better (errors from best known solution
  around 4-4.5 rather than about 5, it runs a lot
  slower.
• Im not sure if I should try and develop a new
  heuristic to use or just continue using the
  random pool program.

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The Future of my Program

• Try and find a new heuristic to use to initialize
  the pool
• Make the program compatible with asymmetric TSPs
• Make a GUI

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Plans for a GUI

• Allow user to input the name of the file
  containing the set of points
• Display the set of points in a graphical
  representation, along with some the path that the
  algorithm will find for it
• Allow the user to instead of reading a set of
  points from a text file, click to create points
  on the graphical representation to have the
  algorithm run on

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THE END
Any Questions?