1. The Genetic Algorithm

2. HMS Beagle: The Voyage of the Beagle (1831-36)
What’s This?

3. Charles Darwin ( )
Who’s This?

4. Darwin’s Finches

5. Charles Darwin from The Voyage of the Beagle
“The most curious fact is the perfect gradation in the size of the beaks in the different species of Geospiza…. Seeing this gradation and diversity of structure in one small, intimately related group of birds, one might really fancy that from an original paucity of birds in this archipelago, one species had been taken and modified for different ends”

6. Differential Reproduction
The Tragic Tale of Green Beetles

7. Mendelian Inheritance
We want a cat with with black spots and a black tail
The Mating Pool
Mendelian Inheritance

8. (With apologies to Gregor Mendel)
Mates Selected

9. (and thanks to Dr. Sara Ganzerli)
The Offspring
(and thanks to Dr. Sara Ganzerli)

10. The Genetic Algorithm Developed Widely Applied
John Holland, University of Michigan (~1975)
Widely Applied
Daniel Goldberg (1989)
Metaphor of natural selection applied to optimization problems

11. Truss Bridge

12. Truss Optimization: 64 Bars

13. Optimize? Minimize the Volume of the Truss
sum(X-Sectional Area of Member X Length)
NP-Complete*
*Overbay, S., Ganzerli, S., De Palma, P, Brown, A., Stackle, P. (2006). Trusses, NP-
Completeness, and Genetic Algorithms. Proceedings of the 17th Analysis and Computation Specialty Conference. St. Louis, MO.

14. A Simpler Problem: Word Guess
User thinks of a word
Passes the word to the GA Keeper
GA guesses the word

15. Elements of GA
Idea: Representation selects key items of object for computation
Chromosome
Representation of a candidate solution
Specs for an individual truss
A word
Gene
An element of a chromosome
Specs for a member
A letter
Population
Set of chromosomes
Specs for a set of trusses
Set of letter strings representing candidate solutions

16. Initialize the Population
Idea: Starting point for speciation
Randomly generate a set of chromosomes
Randomly generate specifications for trusses
Randomly generate letter strings of the given size

17. How Large? Large Enough to Incorporate Genetic Diversity
Divisible by 2
64 seems to work

18. Rank Fitness
Idea: Members of the population have characteristics that better suit them for reproduction
Function over the population used to rank the population
Truss: The smaller the cross-sectional area, the higher the fitness
Word Guess: Proximity to correct word

19. match.com for trusses or words (or whatever)
Pair
match.com for trusses or words (or whatever)

20. Zero Population Growth
Idea: Food supply (and memory) cannot tolerate unlimited population growth
Suppose current population is max: m
Current population produces n offspring
Reduce m + n candidate solutions to m
Example: m = 64
Select 32 population members to survive
Group them into 16 breeding pairs
Allow each to produce 2 children

21. Selecting Mating Population
Idea: Differential Reproduction
Random: Any PP (potential parent) could reproduce
Truncation Selection
Top half: survive and reproduce
Bottom half: die
Stochastic:
Spin a roulette wheel
Each element has a slot
Size of slot is proportional to 1) fitness 2) probability of being chosen to reproduce

22. Pairing Idea: Maximize the fitness of offspring Top-Down Tournament
While ( < 16 mating pairs) {
Do twice:
Randomly select subset of the population
Select 1 parent at random from subset
Add parents to set of mating pairs }
Many Others

23. Mate Idea: Children preserve parents’ genetic information
Genetic Recombination
Target: Chipolte
Many Algorithms
Illustrated: single point crossover
PA: CHIP OTLE PB: CHIX LOTL
CA: CHIP LOTL CB: CHIX OTLE

24. Mutation (and genetic drift)
Idea: Population can get stuck in a local minimum
Simulates:
chemical mutagens
radiation
copying errors
random loss of population members
Randomly perturb a fraction of the population

25. Convergence
Idea: No further improvement is possible (within acceptable cost)
Stop after a fixed number of iterations
Stop when a known solution is found
Stop when m% of the population is within n standard deviations of the mean fitness

26. Putting It Together: The GA Loop
GA(population) { Initialize(population) //generate population ComputeCost(population) //compute fitness Sort(population) //rank while (population not converged on a good-enough solution) SelectBreeders(population) //who reproduces? Pair(breeders) //love and marriage Mate(population) //genetic recombination Mutate(population) //jar from local minima Sort(population) //rank TestConvergence(population) //stop? }

27. The Vanity Press Finding a Route A World with Infinite Resources
Evolving Rockets
Evolving Pictures
Learning to Walk