Download Lecture 2 presentation - Ivan Garibay

An Introduction to Genetic
Algorithms
Lecture 2
November, 2010
Ivan Garibay
[email protected]
Introduction
Motivation: learn from nature
• Nature evolve
strikingly complex
organisms in
response to complex
environmental
adaptation problems
with apparent ease
• Localize and extract
principles from nature
• Apply them to design
algorithms
5/5/2017
University of Central Florida,
Department of EECS
2
Evolution
• Charles Darwin (1859): “On the origin of species
by means of natural selection”
• Reproduction does not produce a perfect copy,
always minor variations (mutations)
• Some variations are advantageous some are not
• Individuals with advantageous variations are
more likely to survive and reproduce (natural
selection, or the survival of the fittest)
• The variations are inheritable
• Species are continuously adapting to their
environment
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University of Central Florida,
Department of EECS
3
Basic Evolutionary Process
• Population
• Birth and Dead
• Fitness
• Variational Inheritance
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University of Central Florida,
Department of EECS
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Genetics
• Science of heredity
• Gregor Mendel (1865): units of
inheritance: Genes (“traits”)
• Organisms form by cells
• Each cell has information
necessary to construct a new
organism = genome
• Genome = set of chromosomes
• Chromosome = set of genes
• Genes are DNA segments
associated with a characteristic
(i.e. eye color)
• Allele is a particular gene value
(blue, black, etc)
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University of Central Florida,
Department of EECS
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DNA: Information
• DNA molecule is an information
structure:
– Store information digitally
(chain of nucleotides)
– Nucleotide = deoxyribose
sugar + phosphate +
Nitrogenous base
– 4 Nitrogenous bases: Adenine,
Thymine, Cytosine, Guanine
• DNA is an amazingly efficient,
highly specialized structure for
information storage, replication,
expression and evolution
5/5/2017
University of Central Florida,
Department of EECS
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Historical perspective
Evolutionary Computation
Evolutionary Strategies Evolutionary Programming
Genetic Algorithms
•Rechenberg, 1965
•Population of two
•Only mutation
•Real value parameter
optimization
•Holland, 1975
•Population based
•Crossover and mutation
•Study adaptation
•Schema Theorem
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•Fogel, Owens, and Walsh,
1966
•Only mutation
•Evolving Finite State
Machines
University of Central Florida,
Department of EECS
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GA terminology: from biology
Chromosome (string)
Population
gene
individual
Fitness based
Selection
Crossover
Mutation
Genetic Operators
Generation i
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Generation i+1
University of Central Florida,
Department of EECS
8
Simple Genetic Algorithm
procedure GA
begin
initialize population;
while termination condition not satisfied do
begin
evaluate current population members;
select parents from current population;
apply genetic operators to selected parents;
set offspring equal to current population;
end
end
5/5/2017
University of Central Florida,
Department of EECS
9
Genetic Algorithm Components
• Population of individuals (population)
• Selection Function (birth and dead)
• Fitness Function (fitness)
• Genetic Operators (variational
inheritance)
5/5/2017
University of Central Florida,
Department of EECS
10
Individuals
allele
gene
0 1 0 0 01 1 1 0 0 1 1 0 1 0 1 1 1 1 0 0 0 1 1
• Each individual represent a candidate solution
• String of ‘1’s and ‘0’ (binary representation GAs)
• In general, any information structure can be
subject to evolution (integers, reals, trees, etc.)
• Needs to be decoded to have meaning:
Genotype to Phenotype
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University of Central Florida,
Department of EECS
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Rethinking Evolutionary Computation
Problem Representation
Genotype
Genome (DNA)
Computational
Evolutionary
Structure
Bit String
Logo instructions
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to
• Problem specific
Phenotype • Different representations
are different problems for
Organisms
a GA
Instance of
• Map a string (structure)
Problem
into a instance of a
Solution
solution
Ordering of
cities for TSP • Representation is very
important
Antena
– Define the space to be
explored
– Define the space structure:
variations are meaningful
University of Central Florida,
Department of EECS
12
Binary Representation
•
•
•
•
Example: encoding 4 parameters
Param1 value = 1000 = 8
Param2 value = 1011 = 11
Etc.,
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University of Central Florida,
Department of EECS
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Fitness function
• Problem specific component
• Function takes as input an individual
(chromosome)
• Function return a numerical value that
determines how good the individual is
• Natural Selection: fitness function = environment
• Genetic Algorithm: fitness function is user
defined
• Typically higher is better
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University of Central Florida,
Department of EECS
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Selection
•
•
•
•
Survival of the fittest
Select the best individuals
Based on fitness function
Drives exploitation: exploit good genes
found so far
• Multiple Types
– Proportional
– Rank
– Tournament (most used)
5/5/2017
University of Central Florida,
Department of EECS
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Fitness proportional Selection
• Holland, 1975.
• Expected number of times an individual is
selected to reproduce is proportional to its
fitness relative to the total population fitness.
Ps(i) = f(i) / fsum
– where f(i) is the fitness of individual i and f is
the sum of fitness of all individuals in a pop.
• Actual number of offspring may be far from
expected number
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University of Central Florida,
Department of EECS
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Rank Selection
• Similar to Proportional
• Proportional to their rank instead
Ps(i) = r(i) / rsum
• Rank selection is weaker than proportional
in diverse populations
• Rank is stronger than proportional in
converged populations
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University of Central Florida,
Department of EECS
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Tournament Selection
1. Select two individuals
2. Generate a random number, r, 0 ≤ r ≤ 1
3. If r < k, select the better of the 2 individuals
else,
select the worse of the 2 individuals
where k is a parameter.
• Computationally efficient.
– Previous methods require 2 passes:
• Compute sum
• Calculate expected number of offspring.
– Rank selection also requires a sort.
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University of Central Florida,
Department of EECS
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Genetic Operators
• Crossover
– Biologically inspired
– Combine genes from two individuals to form
an off-spring (sexual reproduction)
• Mutation
– Biologically inspired
– DNA is copied with errors = mutations
– Most of the time mutation = problem
– Some times = advantage
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University of Central Florida,
Department of EECS
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One-point Crossover
• Simplest form of crossover
• Advantage: Fairly large change in
individuals with very little disruption of
information
Parent 1: 11011100
Parent 2: 01100110
11000110Offspring 1
01111100Offspring 2
Crossover point
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University of Central Florida,
Department of EECS
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Other Crossover Ops
• Two point: select two points and exchange
middles
• Uniform: with probability px exchange or
not each bit
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University of Central Florida,
Department of EECS
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Mutation
• Single parent operator
11011100
11011000
• Mutation rate (M) is per bit
– Mutation rate per individual = M * L (individual
length)
– As a start: M = 1/L per bit
• Issues
– Low mutation rate: minimal exploration
– High mutation rate: too disruptive
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University of Central Florida,
Department of EECS
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Initialization
• Initial Populations are randomly generated
• Binary case are all randomly generated
binary strings
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University of Central Florida,
Department of EECS
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GA Convergence
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University of Central Florida,
Department of EECS
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Termination Criteria
• Found solution
• Number of generations
• Stagnation – no more fitness improvement
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University of Central Florida,
Department of EECS
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