Genetic Algorithms - My presentation from 6111

AI and Robotics

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

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Genetic Algorithms

Przemyslaw Pawluk

CSE 6111

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