Genetic
Algorithms
Evolutionary Methods
Methods inspired by the process of biological evolution.
Main ideas:
Population of
solutions
Generate new
solutions (offspring)
Assign a score or
fitness value to each
solution
Retain the best
solutions (survival
of the fittest)
Figure 7.2
Genetic Algorithms
The fundamental unit of representation is a chromosome.
A chromosome is a bit of strings representing a solution to
our problem.
00010011110011111
In our case, a chromosome will be a classifier or hypothesis.
A hypothesis is good if it has a high fitness value.
What is a fitness value?
In classification, for example, the fitness value could be
the accuracy of the hypothesis on test examples.
Parameters
A genetic algorithm has the following parameters:
 A fitness function that gives a score to every hypothesis.
 Θ: A fitness threshold above which we stop and take the
hypothesis with best fit.
 L: The number of hypothesis in the current population.
 Pco: the fraction of hypothesis replaced by cross-over.
 Pmut: the mutation rate.
Algorithm
Initialize population with L hypotheses at random
Repeat
For each hypothesis h compute its fitness
Rank all hypotheses based on their fitness value
Generate a new population using genetic operators
Until max_fitness > Θ
Return the hypothesis with highest fitness
Figure 7.13
Genetic Operators
The most common operators are crossover, mutation, and replication.
Crossover (exploration):
There are different variations. The most common is called single-point
crossover:
Initial Strings
Crossover Mask
11101001000
Offspring
11101010101
11111000000
00001010101
00001001000
Genetic Operators
Mutation:
The idea is to produce small changes to a string at random.
Under a uniform distribution, we select one bit and switch its value.
00001010101
01001010101
Select second bit.
Replication:
A chromosome is simply reproduced, and left unchanged.
Figure 7.14
New Population
Create a new generation Ps:
1. Replicate (1-Pco)L members of P and add them to Ps
(Exploitation). The probability of selecting a member is
P(hi) = Fitness (hi) / Σj Fitness (hj)
2. Crossover.- select (Pco L)/2 pairs of hypotheses from P
according to P(hi) (Exploration). For each pair (h1,h2)
produce two offspring by applying the Crossover operator.
Add all offspring to Ps.
3. Mutate.- Choose (Pmut L) members of Ps with uniform probability.
Invert one bit in the representation randomly (Exploration).
4. Update P with Ps
Representing Hypotheses
We need to represent each hypothesis as a binary string.
We can encode as bits of strings:
 Neural Networks
 Decision Trees
 etc.
Figure 7.15
Fitness Function and Selection
Selection.
The typical approach is the “fitness proportionate selection” or
“roulette wheel selection”:
P(hi) = Fitness (hi) / Σj Fitness (hj)
Other options are rank selection: Rank according to fitness,
but then select based on rank only.
Further Heuristics
Other heuristics exist to improve performance:
1. Adjust the mutation and crossover rates to ensure that
convergence is fast.
One way to do it is by encoding their values and letting
the genetic algorithm adapt them.
2. Use ternary or n-ary chromosomes (instead of binary).
The advantage is that classifiers become easier to encode.
Exploration vs Exploitation
Exploitation:
Maximize reward by exploiting
optimal and known solutions.
vs
Exploration: Maximize long-term reward
by searching for new solutions.
John H. Holland
Born in Indiana 1929.
Author of “Adaptation in Natural and Artificial Systems”
written in 1975, providing the basis of genetic algorithms.
Recipient of the McArthur Fellowship.
Genetic Programming
Genetic programming is a form of evolutionary computation in
which the individuals in the population are computer programs.
Programs are normally represented by trees. A program is executed
by parsing the tree. Example:
+
F = sin(x) + sqrt( x^2 + y)
sin
sqrt
x
+
^
x
y
2
Vocabulary
To apply genetic programming one has to define the functions
that can be applied:
Example: sin, cos, sqrt, +, -, etc.
A genetic programming algorithm explores the space of
combinations of these functions.
The fitness of an individual is determined by executing
the program on a set of training data.
Cross Over
The crossover operator is performed by replacing subtrees of
one program with subtrees of another program.
+
+
Sin
^
Sin
2
x
+
x
y
sqrt
x
+
^
x
y
2
Cross Over: Result
+
+
Sin
^
Sin
2
x
^
x
y
sqrt
x
+
+
x
y
2
Figure 7.17
J.R. Koza
Author of “Genetic Programming I II III and IV”.
Professor Stanford University
Member of several editorial boards.