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Part I. GENETIC ALGORITHMS
Chapter 1.
Chapter 2.
Chapter 3.
Chapter 4.
GAs: What Are They?
GAs: How Do They Work?
GAs: Why Do They Work?
GAs: Selected Topics
Chapter 1
GAs: What Are They?
Simple Genetic Algorithm
(SGA)
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Darwin’s theory of evolution states that the strongest
species survive, and thus reproduce themselves,
creating more outstanding offspring.
GA is a parallel, global search and optimal technique
based on natural or artificial genetic operations, which
include the operators of reproduction(selection),
crossover(one point), and mutation(bit reverse).
GA can effectively solve complex, confliction,
mathematically difficult and constrained multiple
objective problem.
The Evolutionary Cycle
Selection
Parents
Recombination
Population
Mutation
Replacement
Offspring
Flow Chart
Algorithm
Procedure EVOLUTION_PROGRAM
Begin
t0
Initialize P(t)
Evaluate P(t)
While (not termination-condition) do
Begin
tt+1
Select P(t) from P(t-1)
Alter P(t)
Evaluate P(t)
End
End
Example
(one variable optimization problem)
max f ( x )  x  sin( 10  x )  1
x   1..2
Results
Components of GA
1.
2.
3.
4.
5.
6.
A genetic representation
Genetic operators
Values for various parameters
An evaluation function
A way to create an initial population
GA algorithm
Hillclimbing, Simulated
Annealing, and Genetic
Algorithms
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Example:
max f (v)  11 one(v) 150
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Comparison:
Example
max f (v)  11 one(v)  150
v1  (110110101110101111111011011011)
v 2  (111000100100110111001010100011)
v3  (000010000011001000000010001000)
f (v1 )  11  22  150  92
f (v2 )  11 15  150  15
f (v3 )  11  6  150  84
global max :
v g  (111111111111111111111111111111)
f (v g )  11  30  150  180
local max :
v g  (000000000000000000000000000000)
f (v g )  11  0  150  150
Hillclimbing
Procedure Iterated Hillclimber
begin
t0
repeat
local  FALSE
select a current string vc at random
evaluate vc
repeat
select 30 new strings in the neighborhood of vc
by flipping single bits of vc
select the string vn from the set of new strings
with the largest value of objective function f
if f (vn) < f (vn) then vc  vn
else local  TRUE
until local
tt+1
until t = max
end
Simulated Annealing
Procedure Simulated Annealing
begin
t0
Initialize temperature T
select a current string vc at random
evaluate vc
repeat
repeat
select a new string vn
in the neighborhood of vc
by flipping single bits of vc
if f (vc) < f (vn)
then vc  vn
else
if random[0..1) < exp{(f (vn) - f (vc))/T}
then vc  vn
tt+1
until (termination-condition)
T  g(T,t)
tt+1
until (stop-criterion)
end
Genetic Algorithm
Procedure Genetic Algorithm
Begin
t0
Initialize P(t)
Evaluate P(t)
While (not termination-condition) do
Begin
tt+1
Select P(t+1) from P(t)
Alter P(t)
Evaluate P(t)
End
End
Hillclimbing & Simulated annealing
Procedure Iterated Hillclimber
begin
t0
repeat
local  FALSE
select a current string vc at random
evaluate vc
repeat
select 30 new strings in the neighborhood
of vc by flipping single bits of vc
select the string vn from the set of new
strings with the largest value of
objective function f
if f (vn) < f (vn) then vc  vn
else local  TRUE
until local
tt+1
until t = max
end
Procedure Simulated Annealing
begin
t0
Initialize temperature T
select a current string vc at random
evaluate vc
repeat
repeat
select a new string vn
in the neighborhood of vc
by flipping single bits of vc
if f (vc) < f (vn)
then vc  vn
else
if random[0..1) < exp{(f (vn) - f
(vc))/T}
then vc  vn
until (termination-condition)
T  g(T,t)
tt+1
until (stop-criterion)
end
Hillclimbing, Simulated
Annealing, and Genetic
Algorithms

Comparison:
GA vs. Conventional
Optimization
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a coding of solution set --- solutions themselves
multi-direction --- one direction
a population of solutions --- a single solution
fitness function --- derivatives or other auxiliary
knowledge
probabilistic transition rules --- deterministic rules