Genetic Algorithms - My presentation from 6111

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23 Οκτ 2013 (πριν από 3 χρόνια και 7 μήνες)

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Genetic Algorithms

Przemyslaw Pawluk


CSE 6111

Advanced Algorithm Design and Analysis

03
-
12
-
2007

03
-
12
-
2007

2

Agenda


The overview of the genetic idea


The structure of genetic algorithms


Where to use?


The genetic algorithm for Traveling
Salesman Problem


Summary

3

The overview


definitions


Genotype (genome)


population of abstract
representations of candidate solutions.


Phenotype


the candidate solution.


Fitness function


particular type of
objective function that quantifies the
optimality of the solution.


4

Generation, Selection, Modification


The genetic algorithm usually starts from
randomly generated population.


In each generation, the fitness of every individual
in the population is evaluated,


Multiple individuals are stochastically selected
from the current population (based on their
fitness), and modified (recombined and possibly
randomly mutated) to form a new population.


The new population is then used in the next
iteration of the algorithm.

5

Algorithm

Choose initial population

Evaluate the fitness of each individual in the population

Repeat until
gen_no
>
max_gen_no

or
best
<=


<loop
-
inv:

gen_no
<
max_gen_no
and we have a

set of

valid solution
s and a best solution

best
that is not
necessarily optimal>

Select best
-
ranking individuals to reproduce

Breed new generation through crossover and mutation
(genetic operations) and give birth to offspring
(
gen_no
++)

Evaluate the individual fitnesses of the offspring (set
best
)

Replace worst ranked part of population with offspring


6

Changes
-

Mutation, Crossover


Mutation


the random change in the
chromosome.




Crossover


two chromosomes change some
portion of information

i.e. Random change
of some bits in the
representation

7

Genotype representation


Usually binary arrays (lists) are used, to
make the crossover operations easy
however other representation are also used.

8

Termination


A solution is found that satisfies minimum criteria.


Fixed number of generations reached.


Allocated budget (computation time/money)
reached.


The highest ranking solution's fitness is reaching
or has reached a plateau such that successive
iterations no longer produce better results.


Manual inspection.


Combinations of the above.


9

Applications of GA


Designing neural networks, both
architecture and weights


Robot trajectory


Evolving LISP programs (genetic
programming)


Strategy planning


Finding shape of protein molecules


TSP and sequence scheduling


Functions for creating images


10

Traveling Salesman Problem


Input


the set of cities (nodes) and the
distances between them.


Output


the permutation of cities.



Goal


to find the minimal Hamiltonian tour.





d
x
i
x
i+
1
is a distance between

x
i

and

x
i+1



(

d
x
i
x
i+
1
+ d
x
n
x
1
)

min

n
-
1

i
=1

11

Traveling Salesman Problem


Permutation encoding used to encode
chromosomes.


Each chromosome is a string of numbers,
which represents number
of town
in a

entry

sequence.



Chromosome A

1

5

3

2

6

4

7

9

8

Chromosome
B


8

5

6

7

2

3

1

4

9

12

TSP


crossover and mutation


Mutation


take 2 arbitrary elements and
swap them


Crossover

Chromosome A

1

5

3

2

6

4



7

9

8


Chromosome
B


8


5

6

7


2

3

1

4

9

Offspring A

1

5

3

2

6

4


8 7 9

Offspring B

5

6

2

3

1

4


7

9

8

13

Traveling Salesman Problem


Traveling salesman problem is NP
-
hard.


The time to find the optimal solution is
exponential.


Application of the GA can reduce the time
to polynomial, but do not guarantee that the
optimal solution will be found.


Example:
Genetic Algorithm for TSP
.


14

Summary


Improvements by crossing over


Random mutation to avoid stucking in

local
min/max


Widely used

15

Questions