Machine Learning 1Genetic Algorithms

Who’s This?

Charles Darwin (1809-1882)

What’s This?

HMS BeagleThe Voyage of the Beagle (1839)

(1831-1836)

Darwin’s Finches

Charles Darwinfrom 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”

Differential Reproduction

The Tragic Tale of Green Beetles

The Genetic Algorithm

Developed◦John Holland, University of Michigan (~1975)

Widely Applied◦Daniel Goldberg (1989)

Metaphor of natural selection applied to optimization problems

Truss Bridge

Truss Optimization: 64 Bars

2 4 6 8

1 3 5 7

16 24 26 28

15 23 25 27

18

20 22

17

19 21

10 12

14

9 11

13

100 K 100 K

70 K

70 K

20 K

20 K

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.

A Simpler Problem: Word Guess

User thinks of a wordPasses the word to the GA KeeperGA guesses the word

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

Initialize the Population

Idea: Starting point for speciationRandomly generate a set of chromosomesRandomly generate specifications for

trussesRandomly generate letter strings of the

given size

How Large?

Large Enough to Incorporate Genetic Diversity

Divisible by 264 seems to work

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

Pair

match.com for trussesor

words(or whatever)

Zero Population Growth

Idea: Food supply (and memory) cannot tolerate unlimited population growthSuppose current population is max: mCurrent population produces n offspringReduce m + n candidate solutions to mExample: m = 64

◦Select 32 population members to survive◦Group them into 16 breeding pairs◦Allow each to produce 2 children

Selecting Mating Population

Idea: Differential ReproductionRandom: Any PP (potential parent) could

reproduceTruncation 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

Pairing

Idea: Maximize the fitness of offspringTop-DownTournament

While ( < 16 mating pairs){ Do twice:

Randomly select subset of the population Select 1 parent at random from subsetAdd parents to set of mating pairs

}Many Others

Mate

Idea: Children preserve parents’ genetic informationGenetic Recombination

Target: ChipolteMany Algorithms

◦Illustrated: single point crossover

PA: CHIP OTLE PB: CHIX LOTL

CA: CHIP LOTL CB: CHIX OTLE

Mutation (and genetic drift)

Idea: Population can get stuck in a local minimumSimulates:

◦chemical mutagens◦radiation◦copying errors◦random loss of population members

Randomly perturb a fraction of the population

Convergence

Idea: No further improvement is possible (within acceptable cost)Stop after a fixed number of iterationsStop when a known solution is foundStop when m% of the population is within

n standard deviations of the mean fitness

Putting It Together: The GA Loop

GA(population){ Initialize(population) //generate population

ComputeCost(population) //compute fitnessSort(population) //rankwhile (population not converged on a good-enough solution){SelectBreeders(population) //who reproduces?Pair(breeders) //love and marriageMate(population) //genetic recombinationMutate(population) //jar from local minimaSort(population) //rankTestConvergence(population) //stop?}

}