# Genetic Algorithms

AI and Robotics

Oct 23, 2013 (3 years and 12 days ago)

47 views

1

Genetic Algorithms

Contents

1. Basic Concepts

2. Algorithm

3. Practical considerations

2

Basic Concepts

Individuals

(or members of population or chromosomes)

individuals surviving from the previous generation

+

children

generation

Simulated Annealing

Tabu Search

versus

Genetic Algorithms

a single solution is carried

over from one iteration

to the next

population based method

3

Fitness

of an individual (a schedule) is measured by the value of the

associated objective function

Representation

Example

from scheduling problems:

the order of jobs to be processed can be represented as a permutation:

[1, 2, ... ,
n
]

Initialisation

How to choose initial individuals?

High
-
quality solutions obtained from another heuristic technique

can help a genetic algorithm to find better solutions more quickly

than it can from a random start.

4

Reproduction

Crossover
: combine the sequence of operations on one machine

in one parent schedule with a sequence of operations on

another machine in another parent.

Example 1
. Ordinary crossover operator is not useful!

Cut Point 1

Cut Point 2

P1 = [
2
1

3

4

5
6 7]

P2 = [
4

3

1

2

5

7 6]

O1 = [
4

3 1

2

5
6 7]

O2 = [
2

1 3

4

5

7 6]

Cut Point

P1 = [
2 1 3
4 5 6 7
]

P2 = [
4 3 1
2 5 7 6
]

O1 = [
2 1 3
2 5 7 6
]

O2 = [
4 3 1

4 5 6 7
]

Example 2
. Partially Mapped Crossover

3

1

4

2

5

5

5

Example 3
. Preserves the absolute positions of the jobs taken from P1

and the relative positions of those from P2

Cut Point 1

P1 = [
2 1

3 4 5 6 7]

P2 = [
4 3

1 2
5 7 6
]

O1 = [
2 1

4 3 5 7 6
]

O2 = [4 3 2 1 5 6 7]

Example 4
. Similar to Example 3 but with 2 crossover points.

Cut Point 1

Cut Point 2

P1 = [2 1
3 4 5
6 7]

P2 = [4 3
1

2

5
7 6
]

O1 = [
3 4 5
1 2 7 6
]

6

Mutation

enables genetic algorithm to explore the search space

not reachable by the crossover operator.

in the sequence

[1,2, ... ,
n
]

[2,1, ... ,
n
]

Exchange mutation
: the interchange of two randomly chosen elements

of the permutation

Shift mutation
: the movement of a randomly chosen element a

random number of places to the left or right

Scramble sublist mutation
: choose two points on the string in random

and randomly permuting the elements between these two positions.

7

Selection

Roulette wheel
: the size of each slice corresponds to the fitness of

the appropriate individual.

slice for the 1st individual

slice for the 2nd individual

selected individual

.

.

.

Steps for the roulette wheel

1. Sum the fitnesses of all the population members,
TF

2. Generate a random number
m
, between 0 and
TF

3. Return the first population member whose fitness added to the

preceding population members is greater than or equal to
m

8

Tournament selection

1. Randomly choose a group of
T
individuals from the population.

2. Select the best one.

How to guarantee that the best member of a population will survive?

Elitist model
: the best member of the current population is set

to be a member of the next.

9

Algorithm

Step 1
.

k
=1

Select
N

initial schedules
S
1,1
,... ,

S
1,N

using some heuristic

Evaluate each individual of the population

Step 2
.

Create new individuals by mating individuals in the current population

using crossover and mutation

Delete members of the existing population to make place for

the new members

Evaluate the new members and insert them into the population

S
k+1,1
,... ,

S
k+1,N

Step 3
.

k = k
+1

If
stopping condition =
true

then return the best individual as the solution and STOP

else go to Step 2

10

Example

Metric: minimize total tardiness (tardiness of a job is the amount by

Population size: 3

Selection: in each generation the single most fit individual

reproduces using adjacent pairwise interchange chosen at random

there are 4 possible children, each is chosen with probability 1/4

Duplication of children is permitted.

Children can duplicate other members of the population.

Initial population: random permutation sequences

11

Generation 1

Individual

25314

14352

12345

Cost

25

17

16

Selected individual: 12345 with offspring 13245, cost 20

Generation 2

Individual

13245

14352

12345

Cost

20

17

16

Average fitness is improved, diversity is preserved

Selected individual: 12345 with offspring 12354, cost 17

Generation 3

Individual

12354

14352

12345

Cost

17

17

16

Selected individual: 12345 with offspring 12435, cost 11

12

Generation 4

Individual

14352

12345

12435

Cost

17

16

11

Selected individual: 12435

This is an optimal solution.

:

Since only the most fit member is allowed to reproduce

(or be mutated) the same member will continue to reproduce unless

replaced by a superior child.

13

Practical considerations

Population size: small population run the risk of seriously

under
-
covering the solution space, while large populations will

require computational resources.

Empirical results suggest that population sizes around 30

are adequate in many cases, but 50
-
100 are more common.

Mutation is usually employed with a very low probability.