Hybrid Evolution of Heterogeneous Neural Networks

Transcription

Hybrid Evolution of
Heterogeneous Neural Networks
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Zdeněk Buk
[email protected]
Miroslav Šnorek
[email protected]
http://cig.felk.cvut.cz
Computational Intelligence Group
Department of Computer Science and Engineering
Faculty of Electrical Engineering
Czech Technical University in Prague
ICANN 2008
Outline
●
Continual Evolution Algorithm (CEA) description
●
Data structures – encoding of the individuals
●
Evolution process
●
Control functions
●
Testing, experiments
●
Population behavior
●
Conclusion
18th International Conference on Artificial Neural Networks
3-6 September 2008, Diplomat Hotel, Prague, Czech Republic
Zdeněk Buk, [email protected], http://cig.felk.cvut.cz
Continual Evolution Algorithm
●
Hybrid genetic algorithm
–
●
combination of genetic and gradient-based methods
Separate evolution of structure and parameters
of individuals (models, neural networks)
●
Variable population size
●
Sequential replacement of individuals
–
evolution in continual time dimension
–
age parameter of each individual
Individuals encoding
xi =a i , pi , si , bi 
●
Separate evolution of structure and parameters
of individuals (models, neural networks)
xi =a i , pi , si , bi 
age of the individual
xi =a i , pi , si , bi 
structural vector
xi =a i , pi , si , bi 
structural vector
topology of the network
xi =a i , pi , si , bi 
structural vector
topology of the network
activation functions
xi =a i , pi , si , bi 
parametric vector
behavioral vector
xi =a i , pi , si , bi 
parametric vector
behavioral vector
weights
xi =a i , pi , si , bi 
Evolution process
●
Hybrid genetic algorithm
–
●
combination of genetic and gradient-based methods
2 Dimensional evolution
Evolution process
Crossover and mutation
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
Individual 2
Individual 1
p1
s1
b1
p2
s2
b2
Random mutation
Offspring
Individual 2
Individual 1
p1
s1
b1
p2
s2
b2
Random mutation
Offspring
Individual 2
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
Individual 2
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
Individual 2
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
Individual 2
Random mutation
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
Copy
Individual 2
Individual 1
p1
s1
b1
p2
s2
b2
Offspring
pi
si
bi
Individual 2
Time dimension
●
Training the behavioral vector during time
using gradient algorithm.
Age=0
pi
si
bi
Time
Time dimension
●
Age=0
Age=1
pi
si
bi
Time
Time dimension
●
Age=0
Age=1
Age=2
pi
si
bi
Time
Probability control
●
Probability functions
●
RP – reproduction probability,
●
DP – death probability, elimination of bad solutions
in population.
●
Balancing functions
●
to keep the population size in some reasonable
limits.
Reproduction probability
●
Raw reproduction probability function
*
*
RP  xi = RP a i , F  xi 
Fitness
RP*
Age
Fitness
Age
Death probability
●
Raw death probability function
*
*
DP  xi = DP a i , F  xi 
Fitness
DP*
Age
Fitness
Age
Balancing functions
●
Computation of final probabilities.
●
Depend on raw probabilities and population size.
●
Big population grows slower,
●
small population grows faster.
*
RP  xi = BAL RP  N , RP  xi 
*
DP  xi = BAL DP  N , DP  xi 
Evolution control
Evolution control
Evolution control
Evolution control
Evolution control
Evolution control
Evolution control
●
●
●
●
Construction of the neural networks.
Universal topology based on fully recurrent
network.
Structure
–
topology → adjacency matrix
–
activation functions → parametrized Λ-functions
Behavior
–
weight matrix
●
●
Neural networks based on fully recurrent
topology construction using CEA
Activation function optimization
●
Benchmark tasks
●
Learn to oscillate experiment
Population behavior
Population behavior
Fitness
Population behavior
Iterations
Conclusion
●
●
Reduction of the number of fitness function
evaluations.
Using the probability and balancing functions it
is possible to change the CEA to behave more
–
–
–
like random search,
standard genetic algorithm,
or gradient algorithm.
Conclusion
●
CEA → universal optimization algorithm
●
mainly for problems with separate description
–
of structure
–
and behavior
→ typically neural networks.
●
Automatic control of the size of the population
–
exploitation ↔ exploration

Hybrid Evolution of Heterogeneous Neural Networks

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