Hybrid Evolution of Heterogeneous Neural Networks

Transcription

1 Hybrid Evolution of Heterogeneous Neural Networks Zdeněk Buk Miroslav Šnorek Computational Intelligence Group Department of Computer Science and Engineering Faculty of Electrical Engineering Czech Technical University in Prague ICANN 2008

2 Outline Continual Evolution Algorithm (CEA) description Data structures encoding of the individuals Evolution process Control functions Testing, experiments Population behavior Conclusion

3 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

4 Individuals encoding x i = a i, p i, s i, b i Separate evolution of structure and parameters of individuals (models, neural networks)

5 Individuals encoding x i = a i, p i, s i, b i age of the individual

6 Individuals encoding x i = a i, p i, s i, b i structural vector

7 Individuals encoding x i = a i, p i, s i, b i structural vector topology of the network

8 Individuals encoding x i = a i, p i, s i, b i structural vector topology of the network activation functions

9 Individuals encoding x i = a i, p i, s i, b i parametric vector behavioral vector

10 Individuals encoding x i = a i, p i, s i, b i parametric vector behavioral vector weights

11 Individuals encoding x i = a i, p i, s i, b i

12 Evolution process Hybrid genetic algorithm combination of genetic and gradient-based methods 2 Dimensional evolution

13 Evolution process

14 Crossover and mutation Individual 1 p 1 s 1 b 1 p 2 s 2 b 2 Offspring Individual 2

15 Crossover and mutation Individual 1 p 1 s 1 b 1 p 2 s 2 b 2 Random mutation Offspring Individual 2

16 Crossover and mutation Individual 1 p 1 s 1 b 1 p 2 s 2 b 2 Random mutation Offspring Individual 2

17 Crossover and mutation Individual 1 p 1 s 1 b 1 p 2 s 2 b 2 Offspring Individual 2

18 Crossover and mutation Individual 1 p 1 s 1 b 1 p 2 s 2 b 2 Offspring Individual 2

19 Crossover and mutation Individual 1 p 1 s 1 b 1 p 2 s 2 b 2 Offspring Individual 2 Random mutation

20 Crossover and mutation Individual 1 p 1 s 1 b 1 p 2 s 2 b 2 Offspring Copy Individual 2

21 Crossover and mutation Individual 1 p 1 s 1 b 1 p 2 s 2 b 2 Offspring p i s i b i Individual 2

22 Time dimension Training the behavioral vector during time using gradient algorithm. Age=0 p i s i b i Time

23 Time dimension Training the behavioral vector during time using gradient algorithm. Age=0 Age=1 p i s i b i Time

24 Time dimension Training the behavioral vector during time using gradient algorithm. Age=0 Age=1 Age=2 p i s i b i Time

25 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.

26 Reproduction probability Raw reproduction probability function * * RP x i = RP a i, F x i Fitness RP* Age Fitness Age

27 Death probability Raw death probability function * * DP x i = DP a i, F x i Fitness DP* Age Fitness Age

28 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

29 Evolution control

30 Evolution control

31 Evolution control

32 Evolution control

33 Evolution control

34 Evolution control

35 Evolution control

36 Testing, experiments Construction of the neural networks. Universal topology based on fully recurrent network. Structure topology adjacency matrix activation functions parametrized Λ-functions Behavior weight matrix

37 Testing, experiments Neural networks based on fully recurrent topology construction using CEA Activation function optimization

38 Testing, experiments Benchmark tasks Learn to oscillate experiment

39 Population behavior

40 Population behavior

41 Fitness Population behavior Iterations

42 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.

43 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