A First Course in Genetic Algorithms

1
A First Course in Genetic Algorithms

• Tim Watson
• G6.71
• tw_at_dmu.ac.uk

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 100 2 000 1
• 110 3

• Reproduce 110
• 100
• 110
• Crossover Mutate
• 110
• 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
• 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
• Static or Dynamic?
• Chromosome Size
• Fixed or Variable?
• Crossover Rate
• One-point, two-point or uniform?
• Mutation Rate
• Fixed or Variable?
• 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
• Best17, Worst1, Mean9ish, 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
• Fitness scaling based on raw fitness where if
  fita lt 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
• AB probability of split 1
• Local maxima can occur (e.g. for onemax)
• 11011 fit4 1011000101
• 00100 fit1 0010100000
• 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