Download Genetic Algorithms Initial Population

introduction to
Genetic Algorithms
Yonatan Shichel
Genetic Algorithms
What are Genetic Algorithms?
 Bio-Inspired artificial intelligence class
of probabilistic optimization algorithms
 Well-suited for nonlinear/hard problems
with a large search space
 Developed by John Holland
 Influenced by Darwin’s Origin of species
Evolution
Darwin’s principles
 Variety of species individuals
within the population
 Competition for limited resources
 Overproduction of offspring
generation
 Survival of the fittest
Origin of Species, 1859
Evolution
How does it work?
 Initial population
• Variety of shapes, colors, behaviors
• Each individual fits differently to the
environment
Evolution
How does it work?
 Initial population
 Reproduction
• Offspring combines both parents properties
• Siblings may differ
in properties
• Mutations may occur
Evolution
How does it work?
 Initial population
 Reproduction
 Limited environmental resources
• Only a portion of the
individuals survive
• Survival chances –
according to fitness
measure...
• ... usually.
Evolution
Observations
 Changes in the population content
• “good” properties are kept, “bad” are distinct
• evolutionary pressure
Genetic Algorithms
The computational model
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individuals
select fitter individuals for reproduction
recombine between individuals
mutate individuals
Genetic Algorithms
The computational model
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individuals
select fitter individuals for reproduction
recombine between individuals
mutate individuals
Genetic Algorithms
The computational model
Gn
Gn+1
fitness
55
44
12
31
95
32
87
12
0
65
53
2
91
73
crossover
+
=
mutation
GA in action
The Knapsack problem (NP)
 There are N items:
• Each item i has a weight wi
• Each item i has a value vi
 The knapsack has a limited capacity of
W units.
 The problem description:
v
• Maximize
i
i
• While
w
i
i
W
GA in action
The Knapsack problem (NP)
 For example:
A B C D E F G H I
J
14
26
19
45
5
25
34
18
30
12
20
24
18
70
14
23
50
17
41
21
 Knapsack capacity = 100
GA in action
Before we begin…
1.
Define the genome encoding
2.
Define the fitness function
GA in action
Genome Encoding
Bit array:
0 = don’t take the item
1 = take the item
1 1 0 0 1 0 0 0 0 0
A B - - E - - - - (items taken: A, B, E)
GA in action
Genome Encoding
Bit array:
0 = don’t take the item
1 = take the item
1 1 1 1 1 1 1 0 1 0
A B C D E F G - I (items taken: A, B, C, D, E, F, G, I)
GA in action
Fitness Function



v
:
w

W


  i  i

Fitness  items  items
W   wi : otherwise 

items
A
B
C
D
E
F
G
H
I
J
14
26
19
45
5
25
34
18
30
12
20
24
18
70
14
23
50
17
41
21
wA  wB  wE  45  100
Fitness  v A  vB  vE  58
GA in action
Fitness Function



v
:
w

W


  i  i

Fitness  items  items
W   wi : otherwise 

items
A
B
C
D
E
F
G
H
I
J
14
26
19
45
5
25
34
18
30
12
20
24
18
70
14
23
50
17
41
21
wA  wB  wC  wD  wE  wF  wG  wI  198  100
Fitness  W  wA  wB  wC  wD  wE  wF  wG  wI   98
Genetic Algorithms
Fitness Evaluation
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individuals
select fitter individuals for reproduction
recombine between individuals
mutate individuals
Genetic Algorithms
Fitness Evaluation
For each individual, calculate the fitness value:
Genetic Algorithms
Selection
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individuals
select fitter individuals for reproduction
recombine between individuals
mutate individuals
Genetic Algorithms
Selection
 Fitness-proportionate (roulette wheel)
 Rank Selection (scaling)
 Tournament Selection
 …
Genetic Algorithms
Crossover
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individuals
select fitter individuals for reproduction
recombine between individuals
mutate individuals
Genetic Algorithms
Crossover
Using a crossover probability PC per individual:
 Single point crossover
 Two/multi points crossover
 Uniform / weighted crossover
 …
Genetic Algorithms
Mutation
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individuals
select fitter individuals for reproduction
recombine between individuals
mutate individuals
Genetic Algorithms
Mutation
Using a crossover probability PM per bit:
 Bit flip mutation
 Bit switch mutation
 …
Genetic Algorithms
Crossover & Mutation examples
Genetic Algorithms
Initial Population
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individuals
select fitter individuals for reproduction
recombine between individuals
mutate individuals
Genetic Algorithms
Initial Population
Create a fixed size population using:
 Random generated individuals
 Individuals resulted from previous
evolutionary runs
GA in action
Initial Population
Example of random population:
Genetic Algorithms
Termination Condition
produce an initial population of individuals
while (termination condition not met) do
evaluate the fitness of all individuals
select fitter individuals for reproduction
recombine between individuals
mutate individuals
Genetic Algorithms
Termination Condition
 When an optimal solution is found
 When the results converge to constant value
 After a predetermined number of generations
Genetic Algorithms
Sample Evolutionary Run
 Population size: 100 individuals
 Crossover: Single pt., PC=0.9
 Mutation: Bit flip, PM=0.01
 Selection: tournament, groups of 2
 Termination condition: after 100
generations
Genetic Algorithms
Sample Evolutionary Run
Genetic Algorithms
Conclusions
 GA is nondeterministic – two runs may
end with different results
 There’s no indication whether best
individual is optimal
 Fitness tends to converge during time
Genetic Algorithms
GA variations
 Coevolution
• Cooperative
• Competitive
 Parallel GA
 Hybrid GA