1. A First Course in Genetic Algorithms
Tim Watson
G6.71

2. What is a GA? Evolutionary Algorithm
Create random population of possible solutions in the form of bitstrings
See how good each one is (test fitness)
Produce next generation (fitter are more likely to get into next generation)
Crossover, mutate and make next generation the current one

3. What can they do? Schedule Barcelona Olympics Aircraft Design
Dynamic Routing in Networks
Robot Arm Trajectory Planning
Lab Task Scheduling for US Navy
Aircraft Missile Evasion
Evolving aNN Architecture
Parameter Tuning for Sonar Systems
Conformational Analysis of DNA

4. Example: Onemax Initial population: 100 000 110
Calculate fitness:
110 3
Reproduce: 110
100
110
Crossover & Mutate:
101
010

5. Biological Terminology
Genes etc.
Gene
Locus (plural loci)
Allele (also called gene value)
(Pleiotropic gene)
Genotype (Chromosome)
Phenotype
Fitness Landscape

6. GA Theory Schema Theorem Building Block Hypothesis
GA searches schemata in parallel
10 represents 10, 1#, #0 and ##
The theorem is rubbish!
Building Block Hypothesis
Good, small sequences are found and recombined to form good solutions
No Free Lunch Theorem

7. GA Parameters Population Size Chromosome Size Crossover Rate
Static or Dynamic?
Chromosome Size
Fixed or Variable?
Crossover Rate
One-point, two-point or uniform?
Mutation Rate
Fitness Function
Termination Criteria

8. Prediction Test!
What happens to the population statistics in a standard GA with random fitness, no crossover, no mutation and chromsize equals 16?
Best, Worst, Mean , Std. Dev., column counts
Best=17, Worst=1, Mean=9ish, Std. Dev. constant-ish, pop converges randomly.

9. Reproduction in GAs
Need selective pressure for reproduction to improve the population fitness
None leads to random walk (slow)
Some leads to geometric growth of best (fast)
Infinite populations select individuals on relative fitness: fit/mean(fit)
Finite populations also affected by how many copies are already present

10. Types of Selection Fitness-Proportionate Rank-Order Tournament Elitism
Fitness scaling based on raw fitness where if fita < fitb then scaled(fita)  scaled(fitb)
Scaling can be altered dynamically
Rank-Order
Tournament
Elitism

11. Initialising the Population
Uniformly at random
Best Guesses
Converged to Best Known
From Real World
Hybrid

12. Mutation Goal of selection: survival of the fittest
Goal of mutation: explore lost or never seen alleles
Random reset versus bit flip
Reset rate = ½ bit flip rate
Mutation as a spring
In infinite time every possible population visited an infinite number of times
Alternative to mutation: complement

13. Crossover
Goal: to try out different combinations of good bits of individuals
Crossover point
One-point
Two-point
N-point
Uniform

14. Crossover (2) Closer genes are less likely to be split by crossover
AB###### probability of split with one-point crossover = 1/7
A######B probability of split = 1
Local maxima can occur (e.g. for onemax)
11011 fit=
00100 fit=
All children have lower fitness than parents

15. Design Decisions
If genes are linked then the representaion of an individual ought to keep them close together
Get the balance right:
Popsize too small  premature convergence
Popsize too large  too slow to compute
Mutation rate too low  not enough exploring
Mutation rate too high  too much noise