# Genetic Algorithms

AI and Robotics

Oct 23, 2013 (4 years and 8 months ago)

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Genetic Algorithms

What is a GA

Terms and definitions

Basic algorithm

2

What is a GA

Searches for good solutions among
possible solutions.

Uses evolutionary mechanisms including
natural selection, reproduction, mutation

The best possible solution may be missed

Useful in problems that are too big or too
difficult to solve with conventional
techniques
.

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Terms and definitions (1)

A
solution

is coded by a

string
,
also called

chromosome
.

The words string and
chromosome are used interchangeably

A strings
fitness
is a measure of how good
a solution it codes. Fitness is calculated by
a
fitness function
.

4

Terms and definitions (2)

Selection:
The procedure to choose parents

Roulette wheel selection

is a way of picking out
a string from among a group of strings (a
population
).

A wedge on a roulette wheel proportional to the
string's fitness.

A 'fit' string is more likely to be chosen than an
'unfit' string.

5

Terms and definitions (3)

Crossover

is the procedure by which two
chromosomes mate to create a new offspring
chromosome

parent 1 is copied of up to a randomly chosen
point, and parent 2 is copied from that point
onwards.

Parent 1

1 0 0

|
1 1 0

Parent 2

0 1 1 | 1 0 0

Offspring1

1 0 0

1 0 0

Offspring2

0 1 1

1 1 0

6

Terms and definitions (4)

Mutation

:

with a certain probability flip a
bit in the offspring

Various ways to implement mutation,
optional.

7

Basic Genetic Algorithm

1.
Start:

Generate random population of
n

chromosomes (suitable solutions for the
problem)

2.
Fitness:

Evaluate the fitness
f(x)
of each
chromosome
x

in the population

3.
New population
:
Create a new population
by repeating following steps until the new
population is complete

4.
Test:
If the end condition is satisfied, stop,
and return the best solution in current
population

8

New population

Selection:

Select two parent chromosomes from a
population according to their fitness (the better
fitness, the bigger chance to be selected)

Crossover:

With a crossover probability cross over
the parents to form a new offspring (children). If no
crossover was performed, offspring is an exact copy
of parents.

Mutation:

With a mutation probability mutate new
offspring at each locus (position in chromosome).

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Termination Criteria

after a pre
-
specified number of
generations

when an individual solution reaches a
pre
-
specified level of fitness

when the variation of individuals from
one generation to the next reaches a
pre
-
specified level of stability, e.g. all
become equal

10

How to represent an individual

How to choose

the fitness function

the selection method

the crossover method

the frequency of mutations

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More on Selection

Roulette Wheel Selection
: proportional to the
fitness

Rank Selection
: rank is assigned based on
fitness, then choose proportional to the rank

-
State Selection
: sort and always choose
the best

Elitism
: copy the best individuals in the next
generation

Tournament selection

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More on Crossover

Random point of split

Fixed point of split

Single point: split in two

Two points: split in three

Uniform: bits are chosen randomly

Arithmetic crossover: the offspring is a result of some
arithmetic operation

Two parents

Three parents

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Applications

Optimization problems

Search in a pool of candidate
solutions

Tutorial:

http://cs.felk.cvut.cz/~xobitko/ga/