Evolutionary algorithms

1. Evolutionary algorithms Evolutionary strategies Genetic algorithms Evolutionary programming Genetic programming

2. Evolutionary algorithms mathematical model, for optimization problems are used for problems, which can not be solved by other methods (e.g. gradient-method) uses mechanisms, inspired by biological evolution reproduction mutation recombination natural selection (survival of the fittest)

3. Evolutionary Algorithms – Block diagram how to use evolutionary algorithms initialize population (number of individuals) with all necessary parameters (random values) in a vector of variables (real valued at evolutionary strategies, binary valued at genetic algorithms) = the genome population = first generation select some specific parents from population (which to choose => evolutionary strategies) create/clone some identical copies of the parents (children, offspring) mutate the children (=> mutation) recombinate the children (=> recombination) from mutated children (and maybe the parents) choose the fittest individuals they are the new population iterate the cycle until the break condition is fullfilled

4. Evolutionary Algorithms - Mutation Parameters in genome of the individuals are real valued (or binary) every parameter has to be changed at random xnew = xold + σ * (0,1)N σ...step size (=> evolutionary strategies) (0,1)N...gaussian random number

5. Recombination (1-point x-over) take two children and cut them after a random parameter exchange the opposing parameters

6. Recombination (2-point x-over) take two children and cut them after two random parameters exchange the opposing parameters exchange either the middle-part or the both outer-parts

7. Recombination (n-point x-over) take two children and exchange the corresponding parameters with a probability of 0.5

8. Evolutionary Strategies (Rechenberg, Schwefel) belongs to the ea parameters of the genome real valued (no recombination) mutation and adaptive step size parents are chosen at random or all individuals are parents

9. (1+1) - ES every generation has only one individual (selection which parent is to be cloned is not necessary) it will be only one offspring created after mutation, selection (survival of the fittest) if parent is the fittest, it is parent again(for the next generation) if child is the fittest, it becomes parent (for the next generation)

10. (µ+1) - ES every generation has µ individuals choose one of them at random as parent generate one child choose the individual (of all), which is the worst (fitness is lowest), and delete it

11. (µ+λ) - ES: every generation has µ individuals every individual is parent generate λ children from µ parents ( λ >= µ) calculate the fitness of all individuals µ fittest become member of the next generation

12. (µ,λ) - ES: every generation has µ individuals every individual is parent generate λ children from µ parents ( λ >/= µ) delete parents calculate the fitness of all children µ fittest become member of the next generation

13. Adaptive step size xnew = xold + σ * (0,1)N (x...genome-parameter) σ is an important factor for optimization to increase performance σ can be changed online (means: while algorithm is running) 2 basic possibilities

14. Adaptive step size – 1/5 succes rule step-size σis optimal, if the fitness of 1/5 of the offspring is better than the fitness of best parent if the fitness of more than 1/5 of the offspring is better than the fitness of best parent, the step size will be increased by the factor of 1.5 if the fitness of less than 1/5 of the offspring is better than the fitness of best parent, the step size will be decreased by the factor of 1.5

15. Adaptive step size – mutative step size adaptation every individual gets its own step size for the first individuals it is created at random, like every other parameter befor mutating the offspring, the step size will be changes at random with a probability of 33.3% it will be increased by the factor of 1.5 with a probability of 33.3% it will be decreased by the factor of 1.5 with a probability of 33.3% it remains unchanged now mutate the children

16. Genetic Algorithm (Holland, Goldberg) belongs to the ea parameters of the genome binary valued recombination is the most important part of the genetic algorithm mutation not so important (just inverts the bit) no adaptive step size (because of binary valued genome) parents are chosen by survival of the fittest

17. Evolutionary Programming (Fogel & Son) optimization for artificial intelligence used for problems, when the form of the solution is not known use of finite state machines, instead of variables as genome no recombination after mutation, tournament-selection e.g. q-tounament: every offspring has to compete against q random other offsprings if fitness is better the offspring gets a point the offsprings with the most points at the end become parents for the next generation

18. Genetic Programming (Koza) automatical creation of programs to solve a specific problem (computer should program itself) no binary genome, programs of different length and structure often used: syntax-trees first generation: thousands of automatically build programs first generation of the programs (primordial soup), often have no reference to the problem they only have the number and the type of all needed parameters (what needs to be done) by mutation and recombination of trees, new programs after cycle, survival of the fittest