Genetic Algorithms

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23 Οκτ 2013 (πριν από 4 χρόνια και 15 μέρες)

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Genetic Algorithms
:

An Examination of the Traveling Salesman Problem

Troy Cok

Engineering 315

December 3, 2001

Basic Overview

o
Genetic algorithms are attempts to model
evolutionary behavior

o
Survival of the fittest, etc.

o
More than mere
simulations

of life

o
Goal: Exhibit real characteristics of living things

o
GA’s have several uses

o
Problem solvers

o
Basis for competent machine learning

o
Computational models of innovation, creativity, etc.

Classic GA Problem


Traveling Salesman Problem (TSP)


Implications in science, engineering


Control of routing system


Constraints:


Can be in one city at a time


Each city visited once and only once


Problem:


What is the shortest route through N cities?

Mathematical Attempts at TSP


Testing every possibility would require
N! separate additions


For a 15 city tour:


15! = 1.31 x 10
12

separate calculations


Assuming 1 million calculations per second


15.2 days


Increasing complexity…

Solving TSP using GA


Generates a “near
-
perfect” solution in
minutes


Steps:

1.
Create group of random tours


Stored as sequence of numbers (parents)

2.
Choose 2 of the better solutions


Combine and create new sequences (children)


Problems here:


City 1 repeated in Child 1


City 5 repeated in Child 2

Modifications Needed


Algorithm must not allow repeated cities


Also, order must be considered


12345 is same as 32154


Based upon these considerations, a
computer model for N cities can be
created


Gets quite detailed

Some Existing GA Programs

Final Notes


GA’s determine adequate
“solution” to TSP


Much faster than sheer
number
-
crunching


Enables efficient system
control


The better the algorithm,
the better the solution


Ongoing research in this
area