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A Genetic Solution to the Travelling Salesman

Problem

Ryan Honig

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.

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.

What is the Travelling Salesman Problem? (Cont.)?

Two Types of Problems Symmetric Asymmetric

What is the Travelling Salesman Problem? (Cont.)?

Symmetric

A

B

Distance 100

Distance 100

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

Genetic Algorithm (Cont)?

Parent A

Parent B

A

A

B

B

C

E

E

C

D

D

Genetic Algorithm (Cont)?

Combined Path

B

A

B

A

A

B

A

B

E

B

C

A

A

B

D

Genetic Algorithm (Cont)?

Child

B

A

B

A

B

E

C

A

B

D

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

Pool Creating Heuristic

A

A

B

A

E

A

B

A

B

A

A

B

C

E

E

D

D

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.

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

What is the Travelling Salesman Problem? (Cont.)?

Asymmetric Travelling Salesman Problem

A

B

Distance 100

Distance 200

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

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

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

THE END

Any Questions?

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