Basics of Genetic Algorithms (MidTerm – only in RED material)

1. Basics of Genetic Algorithms (MidTerm – only in RED material) • General introduction to Genetic Algorithms (GA’s) • Biological background • Origin of species • Natural selection • Genetic Algorithm • Search space • Basic algorithm • Coding • Methods • Examples • Possibilities

2. General Introduction to GA’s • Genetic algorithms (GA’s) are a technique to solve problems which need optimization in search • GA’s are a subclass of Evolutionary Computing • GA’s are based on Darwin’s theory of evolution • History of GA’s • Evolutionary computing evolved in the 1960’s. • GA’s were created by John Holland in the mid-70’s.

3. Biological Background (1) – The cell • Every animal cell is a complex of many small “factories” working together • The center of this all is the cell nucleus • The nucleus contains the genetic information

4. Biological Background (2) – Chromosomes • Genetic information is stored in the chromosomes • Each chromosome is build of DNA • Chromosomes in humans form pairs • There are 23 pairs • The chromosome is divided in parts: genes • Genes code for properties • The posibilities of the genes for one property is called: allele • Every gene has an unique position on the chromosome: locus

5. Biological Background (3) – Genetics • The entire combination of genes is called genotype • A genotype develops to a phenotype • Alleles can be either dominant or recessive • Dominant alleles will always express from the genotype to the phenotype • Recessive alleles can survive in the population for many generations, without being expressed.

6. Biological Background (4) – Reproduction • Reproduction of genetical information • Mitosis • Meiosis • Mitosis is copying the same genetic information to new offspring: there is no exchange of information • Mitosis is the normal way of growing of multicell structures, like organs.

7. Biological Background (5) – Reproduction • Meiosis is the basis of sexual reproduction • After meiotic division 2 gametes appear in the process • In reproduction two gametes conjugate to a zygote wich will become the new individual • Hence genetic information is shared between the parents in order to create new offspring

8. Biological Background (6) – Reproduction • During reproduction “errors” occur • Due to these “errors” genetic variation exists • Most important “errors” are: • Recombination (cross-over) • Mutation

9. Biological Background (7) – Natural selection • The origin of species: “Preservation of favourable variations and rejection of unfavourable variations.” • There are more individuals born than can survive, so there is a continuous struggle for life. • Individuals with an advantage have a greater chance for survive: survival of the fittest.

10. Biological Background (8) – Natural selection • Important aspects in natural selection are: • adaptation to the environment • isolation of populations in different groups which cannot mutually mate • If small changes in the genotypes of individuals are expressed easily, especially in small populations, we speak of genetic drift • Mathematical expresses as fitness: success in life

11. Presentation Overview • Purpose of presentation • General introduction to Genetic Algorithms (GA’s) • Biological background • Origin of species • Natural selection • Genetic Algorithm • Search space • Basic algorithm • Coding • Methods • Examples • Possibilities

12. 1 Genetic Algorithm (and GPs) – Search space • Most often one is looking for the best solution in a specific subset of solutions (best?, exploration) • This subset is called the search space (or state space) • Every point in the search space is a possible solution • Therefore every point has a fitness value, depending on the problem definition (higher is closer to best) • GA’s are used to search the search space for the best solution, e.g. a minimum • Difficulties are the local minima and the starting point of the search

13. 2 Genetic Algorithm (and GPs) – Basic algorithm • Starting with a subset of n randomly chosen solutions from the search space (i.e. chromosomes). This is the population • This population is used to produce a next generation of individuals by reproduction • Individuals with a higher fitness have more chance to reproduce (i.e. natural selection)

14. 3 Genetic Algorithm (and GPs) – Basic algorithm • Outline of the basic algorithm 0 START : Create random population of n chromosomes 1 FITNESS : Evaluate fitness f(x) of each chromosome in the population 2 NEW POPULATION (MAIN LOOP) 0 SELECTION : Based on f(x) 1 RECOMBINATION: Cross-over chromosomes 2 MUTATION : Mutatechromosomes 3 ACCEPTATION : Reject or accept new one 3 REPLACE : Replace old with new population: the new generation (Goto MAIN LOOP) 4 TEST : Test problem criterium 5 LOOP : Continue step 1 – 4 until criterium is satisfied

15. 4 Genetic Algorithm – Coding • Chromosomes are encoded by bitstrings ( GPs – code) • Every bitstring therefore is a solution but not necisseraly the best solution • The way bitstrings can code differs from problem to problem • Either: sequence of on/off or the number 9

16. X 5 Genetic Algorithm – Coding • Recombination (cross-over) can when using bitstrings schematically be represented: • Using a specific cross-over point

17. 6 Genetic Algorithm – Coding • Mutation prevents the algorithm to be trapped in a local minimum • In the bitstring approach mutation is simpy the flipping of one of the bits

18. Genetic Algorithm (8) – Coding • Both recombination and mutation depend a lot on the exact definition of the problem and the choice of representing the chromosomes (e.g. no bitstrings) • Different encodings can be used: • Binary encoding • Permutation encoding • Value encoding • Tree encoding (GPs - if trees are programming code) • Focus in this presentation stays with binary encoding