1. Genetic Algorithms

2. The Basic Genetic Algorithm 1.[Start] Generate random population of n chromosomes (suitable solutions for the problem) 2.[Fitness] Evaluate the fitness f(x) of each chromosome x in the population 3.[New population] Create a new population by repeating following steps until the new population is complete 1.[Selection] Select two parent chromosomes from a population according to their fitness (the better fitness, the bigger chance to be selected) 2.[Crossover] With a crossover probability cross over the parents to form new offspring (children). If no crossover was performed, offspring is the exact copy of parents. 3.[Mutation] With a mutation probability mutate new offspring at each locus (position in chromosome). 4.[Accepting] Place new offspring in the new population 4.[Replace] Use new generated population for a further run of the algorithm 5.[Test] If the end condition is satisfied, stop, and return the best solution in current population 6.[Loop] Go to step 2

3. Basic principles 1 Coding or Representation –String with all parameters Fitness function –Parent selection Reproduction –Crossover –Mutation Convergence –When to stop

4. Basic principles 2 An individual is characterized by a set of parameters: Genes The genes are joined into a string: Chromosome The chromosome forms the genotype The genotype contains all information to construct an organism: the phenotype Reproduction is a “dumb” process on the chromosome of the genotype Fitness is measured in the real world (‘struggle for life’) of the phenotype

5. Conceptual Algorithm

6. Genetic Algorithm Encoding Fitness Evaluation Reproduction Survivor Selection

7. Reproduction Crossover –Two parents produce two offspring –There is a chance that the chromosomes of the two parents are copied unmodified as offspring –There is a chance that the chromosomes of the two parents are randomly recombined (crossover) to form offspring –Generally the chance of crossover is between 0.6 and 1.0 Mutation –There is a chance that a gene of a child is changed randomly –Generally the chance of mutation is low (e.g. 0.001)

8. One-point crossover Randomly one position in the chromosomes is chosen Child 1 is head of chromosome of parent 1 with tail of chromosome of parent 2 Child 2 is head of 2 with tail of 1 Parents: 10100011100011010010 Offspring: 01010100100011001110 Randomly chosen position

9. Crossover Choose a random point on the two parents Split parents at this crossover point Create children by exchanging tails P c typically in range (0.6, 0.9)

10. Mutation Alter each gene independently with a probability p m p m is called the mutation rate –Typically between 1/pop_size and 1/ chromosome_length

11. Algorithm BEGIN Generate initial population; Compute fitness of each individual; REPEAT /* New generation /* FOR population_size / DO Select two parents from old generation; /* biased to the fitter ones */ Recombine parents for two offspring; Compute fitness of offspring; Insert offspring in new generation END FOR UNTIL population has converged END

12. Parent/Survivor Selection Strategies:Survivor selection Always keep the best one Elitist: deletion of the K worst

13. Worked Example Parent 1Parent 2 Neck: long 11000001Neck : short 11000000 leggs : short 00110000leggs : long 00110001 adaptation : middle

14. After many random crossover-combination, we get the following generation: Sohn 1Sohn 2Sohn 3 Neck: short 11000000 Neck : long 11 000001 Leggs: short 00110000Leggs: long 00110001 Adaptation : BadAdaptation : MiddleAdaptation :Good In a long terme process only sohn three will survive. Sohn 1 and 2 will be eliminate from the existence because of the nature conditions(fitness function)

15. Conclusion The genetic algorithms are very good techniques however the main obstacle is to encode problem, to define a good fitness function! Demo TSM AISteroid