Genetic Algorithms

Genetic Algorithms

The Basic Genetic Algorithm1. [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

Basic principles 1

• Coding or Representation– String with all parameters

• Fitness function– Parent selection

• Reproduction– Crossover– Mutation

• Convergence– When to stop

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

Conceptual AlgorithmConceptual Algorithm

Genetic AlgorithmGenetic Algorithm

• Encoding

• Fitness Evaluation

• Reproduction

• Survivor Selection

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)

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: 1010001110 0011010010

Offspring: 0101010010 0011001110

Randomly chosen position

Crossover• Choose a random point on the two parents

• Split parents at this crossover point

• Create children by exchanging tails

• Pc typically in range (0.6, 0.9)

Mutation

• Alter each gene independently with a probability pm

• pm is called the mutation rate– Typically between 1/pop_size and 1/ chromosome_length

AlgorithmBEGIN 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 convergedEND

Parent/Survivor Selection

• Strategies:Survivor selection

• Always keep the best one

• Elitist: deletion of the K worst

Worked Example

Parent 1 Parent 2

Neck: long 11000001 Neck : short 11000000

leggs : short 00110000 leggs : long 00110001

adaptation : middle adaptation : middle

After many random crossover-combination, we get the following generation:

Sohn 1 Sohn 2 Sohn 3

Neck: short 11000000 Neck : short 11000000 Neck : long 11 000001

Leggs: short 00110000 Leggs: long 00110001 Leggs: long 00110001

Adaptation : Bad Adaptation : Middle Adaptation :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)

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