4. Analogy (ctd)
Super-fit
Evolve according to environment
5. Basic Concept
Set of solutions for a problem
Each solution – fitness score
Reproduce a new set of solutions by
“Cross-breeding”
Most-fit: get selected
Least-fit: not selected – die out
Result?
Offsprings with characteristics from most-
fit
6. What just happened?
Good characteristics of a generation
was spread in a successive
generation
Most promising areas of solution
space are searched
7. Algorithm
BEGIN
Generate population
Calculate fitness for each individual
WHILE NOT CONVERGED DO
BEGIN
FOR population_size/2 DO
BEGIN
Select 2 parents for mating
Combine and produce an offspring
Calculate the fitness for the new individual
Insert the offspring to the new generation
END
END
END
9. Fitness function
Must represent the “fitness to the
environment” or “ability” of a
chromosome’s
Issues of fitness range
Premature convergence
Slow finishing
10. Reproduction
Selection of parents
Random
Favors the fittest
Crossover
Single point crossover
Cut 2 chromosomes at a random point
Swap over tails to create 2 new chromosomes
11. Reproduction (ctd)
Crossover is not the only case!
0.6 - 1.0 chance
Otherwise replicate the parent
Mutation
Alter the genes of crossover-ed with a
small probability
12. Example
0101001100 1011001001
0101001001 1011001100
Before mutation: 0 1 0 1 0 0 1 0 0 1
After mutation: 0101101001
13. Convergence
Fitness of the BEST and AVERAGE
moves to a global optimum
Gene is said to have converged
95% of the population has converged
Population is said to have converged
All the genes have converged
15. “Schemata” and “Scheme”
Definition of Schema
Pattern of gene
String comprise {0,1,#}
Ex: Chromosome 0110 contains following
“Schemata”
#110, #1#0, 01##, etc.
A chromosome is said to contain a schema if
it matches a particular schemata
16. Order of schema – Number of non-#
symbols
Length of schema – Distance
between outer most non-# symbols.
Ex: #1#0
17. Schema Theorem
Individuals in a population are given reproductive
trials
Number of trials α Fitness of an individual
Higher fitness value -> Good schemata
Good Schemata receives
exponentially increasing number of
trials in successive generations!
18. Building Block Hypothesis
Definition
Schemata short in length and tend to
improve performance when incorporated
to an individual
Properties of a successful coding
scheme
Related genes close together
Little interaction between genes
19. Exploration and Exploitation
Exploration
Exploring unknown areas
Exploitation
Utilizing already-learnt to find better solutions
Tradeoff
Ex: Random search and Hill climbing
GA combines both in an optimal way!
21. Parent selection
Individuals are copied to a “mating
pool”
Highly fit – more copies
Less fit – lesser copies
How to determine number of copies?
Explicit fitness remapping
Implicit fitness remapping
22. Explicit fitness remapping
Individual’s fitness
Average fitness of population
Issue: Number of copies should be an
integer
Solution:
Fitness scaling
Fitness windowing
23. Implicit fitness remapping
Tournament selection
2 random individuals
Copy the one with higher fitness value
to the mating pool
Continue until the pool is full
24. Generation gaps and
steady-state replacement
Generation gap
Proportion of individuals in a population
replaced in each generation
Steady-state replacement
Only few individuals are replaced in a
generation
Considerations:
Parent selection – Random, Fitness
Replacement – Random, Inverse fitness
Two parentsAttract matesOther hunting foodChild both characteristicsSuperfit
There should not be too many local maximasThere shouldn’t be a single global maximumTherefore better chromosomes must be closely related.Problem: Preparing a time table.Invalid chromosomes must guide towards valid chromosomes, using fitness valueBetter to invest sub-goals rewarded going for the ultimate goalPremature convergence: Set of highly fit individuals come to dominate the population, making a local maxima. Which in turn make it difficult to converge to more effective solutionSlow finishing: Population might have converged, but might not have found a global maxima
Passing the genes without disruption of crossoverProbability 0.001
Better individuals -> more of their genes to next generationGood schemata - Likelihood of better solution increase
Power of GA – Finding good building blocksInteraction – In a chromosome, contribution of a gene to the fitness value depends on values of other genesIssues: Might not allow closely related genes to be placed togetherInteraction between genes can become high (specially in multi-dimensional data)
AssumptionsPopulation is infiniteFitness function accurately shows the effectiveness of a solutionGenes in a chromosome don’t interact significantlyGenetic drift, mutation rate