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Слайды и текст к этой презентации:
№2 слайд
Содержание слайда: Developed: Germany in the 1970’s
Developed: Germany in the 1970’s
Early names: I. Rechenberg, H.-P. Schwefel
Typically applied to:
numerical optimisation
Attributed features:
fast
good optimizer for real-valued optimisation
relatively much theory
Special:
self-adaptation of (mutation) parameters standard
№6 слайд
Содержание слайда: z values drawn from normal distribution N(,)
z values drawn from normal distribution N(,)
mean is set to 0
variation is called mutation step size
is varied on the fly by the “1/5 success rule”:
This rule resets after every k iterations by
= / c if ps > 1/5
= • c if ps < 1/5
= if ps = 1/5
where ps is the % of successful mutations, 0.8 c 1
№10 слайд
Содержание слайда: Chromosomes consist of three parts:
Chromosomes consist of three parts:
Object variables: x1,…,xn
Strategy parameters:
Mutation step sizes: 1,…,n
Rotation angles: 1,…, n
Not every component is always present
Full size: x1,…,xn, 1,…,n ,1,…, k
where k = n(n-1)/2 (no. of i,j pairs)
№11 слайд
Содержание слайда: Main mechanism: changing value by adding random noise drawn from normal distribution
Main mechanism: changing value by adding random noise drawn from normal distribution
x’i = xi + N(0,)
Key idea:
is part of the chromosome x1,…,xn,
is also mutated into ’ (see later how)
Thus: mutation step size is coevolving with the solution x
№12 слайд
Содержание слайда: Net mutation effect: x, x’, ’
Net mutation effect: x, x’, ’
Order is important:
first ’ (see later how)
then x x’ = x + N(0,’)
Rationale: new x’ ,’ is evaluated twice
Primary: x’ is good if f(x’) is good
Secondary: ’ is good if the x’ it created is good
Step-size only survives through “hitch-hiking”
Reversing mutation order this would not work
№15 слайд
Содержание слайда: Chromosomes: x1,…,xn, 1,…, n
Chromosomes: x1,…,xn, 1,…, n
’i = i • exp(’ • N(0,1) + • Ni (0,1))
x’i = xi + ’i • Ni (0,1)
Two learning rate parameters:
’ overall learning rate
coordinate wise learning rate
1/(2 n)½ and 1/(2 n½) ½
Boundary rule: i’ < 0 i’ = 0
№17 слайд
Содержание слайда: Chromosomes: x1,…,xn, 1,…, n ,1,…, k
Chromosomes: x1,…,xn, 1,…, n ,1,…, k
where k = n • (n-1)/2
Covariance matrix C is defined as:
cii = i2
cij = 0 if i and j are not correlated
cij = ½ • ( i2 - j2 ) • tan(2 ij) if i and j are correlated
Note the numbering / indices of the ‘s
№18 слайд
Содержание слайда: The mutation mechanism is then:
The mutation mechanism is then:
’i = i • exp(’ • N(0,1) + • Ni (0,1))
’j = j + • N (0,1)
x ’ = x + N(0,C’)
x stands for the vector x1,…,xn
C’ is the covariance matrix C after mutation of the values
1/(2 n)½ and 1/(2 n½) ½ and 5°
i’ < 0 i’ = 0 and
| ’j | > ’j = ’j - 2 sign(’j)
NB Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is probably the best EA for numerical optimisation, cf. CEC-2005 competition
№22 слайд
Содержание слайда: Parents are selected by uniform random distribution whenever an operator needs one/some
Parents are selected by uniform random distribution whenever an operator needs one/some
Thus: ES parent selection is unbiased - every individual has the same probability to be selected
Note that in ES “parent” means a population member (in GA’s: a population member selected to undergo variation)
№23 слайд
Содержание слайда: Applied after creating children from the parents by mutation and recombination
Applied after creating children from the parents by mutation and recombination
Deterministically chops off the “bad stuff”
Two major variants, distinguished by the basis of selection:
(,)-selection based on the set of children only
(+)-selection based on the set of parents and children:
№24 слайд
Содержание слайда: (+)-selection is an elitist strategy
(+)-selection is an elitist strategy
(,)-selection can “forget”
Often (,)-selection is preferred for:
Better in leaving local optima
Better in following moving optima
Using the + strategy bad values can survive in x, too long if their host x is very fit
Selective pressure in ES is high compared with GAs,
7 • is a traditionally good setting (decreasing over the last couple of years, 3 • seems more popular lately)
№25 слайд
Содержание слайда: Given a dynamically changing fitness landscape (optimum location shifted every 200 generations)
Given a dynamically changing fitness landscape (optimum location shifted every 200 generations)
Self-adaptive ES is able to
follow the optimum and
adjust the mutation step size after every shift !
№28 слайд
Содержание слайда: Task: to create a colour mix yielding a target colour (that of a well known cherry brandy)
Task: to create a colour mix yielding a target colour (that of a well known cherry brandy)
Ingredients: water + red, yellow, blue dye
Representation: w, r, y ,b no self-adaptation!
Values scaled to give a predefined total volume (30 ml)
Mutation: lo / med / hi values used with equal chance
Selection: (1,8) strategy
№29 слайд
Содержание слайда: Fitness: students effectively making the mix and comparing it with target colour
Fitness: students effectively making the mix and comparing it with target colour
Termination criterion: student satisfied with mixed colour
Solution is found mostly within 20 generations
Accuracy is very good
№30 слайд
Содержание слайда: The Ackley function (here used with n =30):
The Ackley function (here used with n =30):
Evolution strategy:
Representation:
-30 < xi < 30 (coincidence of 30’s!)
30 step sizes
(30,200) selection
Termination : after 200000 fitness evaluations
Results: average best solution is 7.48 • 10 –8 (very good)
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