Download Introduction to Soft Computing Outline Soft Computing Soft vs. Hard

Outline
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Overview of soft computing
Neural networks
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Fuzzy logic
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Introduction to Soft Computing
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ECE457 Applied Artificial Intelligence
Spring 2007
Lecture #12
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Russell & Norvig, sections 20.5
Russell & Norvig, pages 526-527
Genetic algorithms
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Russell & Norvig, pages 116-120
→ ECE 493 & ECE 750 (Prof. Karray)
ECE457 Applied Artificial Intelligence
Soft Computing
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“Soft” reasoning
Computer algorithms require complete and
precise information
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Soft vs. Hard Computing
Branch of AI that deals with systems and
methodologies that can perform approximate,
qualitative, human-like reasoning
Humans can make intelligent decisions using
incomplete and imprecise information
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R. Khoury (2007)
Input
Hard Computing Soft Computing
Complete and Approximate and
exact data
incomplete data
Output
Overly-exact
solution
Solution that’s
“good enough”
Reasoning
Rational
Human-like
“Hard” reasoning
Soft computing aims to bridge this gap
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Soft Computing
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Probabilistic reasoning
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Human brain
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Human Brain
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But the brain is intelligent!
Connection patterns of neurons
Amplification of signals by dendrites
Transfer function and threshold values
controlling whether the cell transmits the
signal
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Neurons
Brain learns by changing and adjusting
the connections between neurons
Information encoded in many ways
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Neuron is a simple computing
element
Genetic algorithms (GA)
Biological evolution
ECE457 Applied Artificial Intelligence
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Massively parallel network of
neurons
Each individual neuron is not
intelligent
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Human knowledge
Evolutionary computing
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Human Brain
Fuzzy logic (FL)
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Human randomness
Artificial neural networks (ANN)
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Artificial Neural Networks
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Receives electric impulse from other
neurons through dendrites.
If impulse strong enough, travels
through axon.
Reaches synapses and transmits to
other neurons
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Artificial Neuron
Artificial Neural Networks
„ ith
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neuron sums inputs a1… aj… an, weighted
by weights wi1… wij… win
Threshold value θi controls activation
If activated, input is transformed by transfer
function fi(.) into output ai
wij
aj
Cell
body
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fi(.)
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ai
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Synapse
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Dendrites
θi
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Topology of the network
Transfer function of the neurons
Learning algorithm
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Axon
∑
Large arrangement of inter-connected
artificial neurons
Different classes of network
Different networks appropriate for
different applications
ai = fi( ∑jwijaj - θi ) = [0, 1]
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ECE457 Applied Artificial Intelligence
Perceptron
x1
o1
o2
x3
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Simplest and most
commonly-used ANN
Feed-forward ANN
Single-layer
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Input Hidden Output
layer layer
layer
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Examples
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x2
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No hidden layer
Only linearlyseparable problems
Multi-layer
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Non-linear problems
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x1 1
o
x2 1
All these neurons
use step functions
f(<0) = 0
XOR Network
x1
AND Network
1
-1
f(≥0) = 1
-1.5
1
-0.5
-1
OR Network
x1 1
x2
o
1
-0.5
1
-0.5
o
x2 1
-0.5
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Learning
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Backpropagation algorithm
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ANN Topologies
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Train using a set of input-output pairs
Using the entire set = 1 epoch
Supervised learning
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Algorithm
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Start with random weights
Forward propagation of each input, to get the
network’s output and compute the network error
Back propagate the network error to the output of
each neuron, to get the neuron error
Update the weights of the input of the neuron to
minimise the neuron error
Repeat until min error or max training epoch
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Information can
loop back to create
feedback loop, or
network memory
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Basic network
Any transfer functions
Any number of hidden layers
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x3
x1
o1
x2
x3
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Fully-connected two-layer network
Unsupervised learning
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Special class of multi-layer perceptron
Single hidden layer with RBF (typically Gaussian)
transfer function
Hidden neuron transformations are symmetric,
bounded and localized
Useful for modelling systems with complex
nonlinear behaviour, control systems, audio-video
signal processing, …
ECE457 Applied Artificial Intelligence
o1
x2
Kohonen Self-Organising Map
Radial Basis Function (RBF) Network
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x1
Feed-Forward Networks
Perceptron
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Information can
only move forward
through the
network
Recurrent topology
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Feed-Forward Networks
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Feed-forward
topology
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x1
x2
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Output neuron compete to activate
Neuron with highest output value wins
Winning neuron and its neighbours
have their weights updated
Creates a 2D topological mapping of
the input vectors to the output layer
Useful for pattern recognition,
image analysis, data mining, …
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Recurrent Networks
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Hopfield Network
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x1
o1
x2
o2
o3
x3
Limits of ANN
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First kind of recurrent ANN
Implements an associative
memory
Previous-stored patterns
“complete” current (noisy or
incomplete) pattern
Network is attracted to stable
pattern in memory
Useful for information retrieval,
pattern/speech recognition, …
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Fuzzy Logic
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Prone to overfitting
Backpropagation is slow and can
converge on local optimum
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Warm
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Truth value = [0, 1]
This is closer to human knowledge
Cold
Hot
Warm
Hot
1
0
0
Temperature
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In fuzzy logic, facts can be partially true
and partially false
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This is an unnatural way of doing it
Cold
How many hidden layers? How many
neurons per layer? Which transfer
functions?
ECE457 Applied Artificial Intelligence
Truth value = {0, 1}
1
No formal design rules
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What does each neuron do? What does
each weight do?
Fuzzy Logic
In crisp logic, facts are either true or
false
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Black box
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Temperature
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Terminology
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Fuzzy Sets vs. Probabilities
“Cold”, “warm” and “hot” are fuzzy set
The triangle function mapping a value
of temperature to a value of cold (or
warm or hot) is called a fuzzy
membership function
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The value of cold (or warm or hot) to
which a temperature is mapped is
called a membership degree
Fz[t ∈ Cold] = µCold(t): ℜ → [0,1]
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Fuzzy Rules
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If Cold then VentilationHigh
If Warm then VentilationLow
If Hot then VentilationMedium
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Typical application of fuzzy logic
Set of fuzzy rules
Define the behaviour of a system
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Variables belong partially to antecedent,
therefore consequence activated
partially
ECE457 Applied Artificial Intelligence
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Membership degrees are not
probabilities
Both are measures over the range [0,1]
Probabilistic view: x is or is not y, and
we have a certain probability of
knowing which
Fuzzy view: x is more or less y, with a
certain degree
Fuzzy Controller
If-then rules like other logics, but with
fuzzy sets
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Antecedent: variables that affect the
system
Consequent: reaction of the system
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Fuzzy Controller Example
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If Hot and Wet then VeryCool
If Warm and Humid then Cool
Hot
1
Fuzzy Controller Example
Wet
1
1
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VeryCool
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0
1
T
Warm
0
0
H
Humid
1
t
T
0
h
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1
C
Cool
H 0
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1
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0
C
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Advantages of Fuzzy Logic
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Defuzzification using centroid technique
Converts fuzzy consequent C into crisp
value that can be used by system
Centroid merges the output fuzzy sets
and finds the center of gravity
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The rule base must be
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Be consistent
Not interact
The rule base system must be
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Complete
Continuous
The rules must
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Properties of Fuzzy Controllers
Partial activation of multiple rules at
once
Achieve complex non-linear behaviour
with simple IF-THEN rules
Use linguistic variables to model words,
rules of thumb, human knowledge
ECE457 Applied Artificial Intelligence
C
c
Robust
Stable
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Limits of Fuzzy Logic
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Fuzzy Robot Navigation
Writing the fuzzy rules
Designing the fuzzy membership
functions
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Often requires work by a domain expert
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Fuzzy controllers are very popular for
robot navigation
Eliminates need for complete world
model and complex reasoning rules
Basic robot
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Fuzzy Robot Navigation
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1
Medium
Distance: near, medium, far
Direction angle: negative, zero, positive
Speed: slow, medium, fast
Far
1
Negative Zero
Positive
1
Slow
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Medium
Fast
0
ECE457 Applied Artificial Intelligence
Direction
0
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Speed
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IF (left obstacle is far) and (front obstacle is near) and (right
obstacle is far) and (angle is zero) THEN (left speed is fast)
and (right speed is slow)
Turning corners
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IF (left obstacle is medium) and (front obstacle is near) and
(right obstacle is near) and (angle is any) THEN (left speed
is slow) and (right speed is fast)
Following edges
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Distance
IF (left obstacle is far) and (front obstacle is far) and (right
obstacle is far) and (angle is zero) THEN (left speed is fast)
and (right speed is fast)
Avoiding obstacles
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Going to target
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Near
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Fuzzy Robot Navigation
Fuzzy linguistic variables of control
system
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Known current position and target
Three sensors (front, left, right)
Left and right wheels can turn at different
speeds to make robot turn
IF (left obstacle is far) and (front obstacle is far) and (right
obstacle is near) and (angle is positive) THEN (left speed is
medium) and (right speed is medium)
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Fuzzy Robot Navigation
Genetic Algorithms
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Biological evolution
Species adapt to better
survive in environment
Over generations
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Pairs of individuals
reproduce
Individuals mutate
Fittest individuals
survive and go on to
reproduce
Source: David M. Hillis, Derrick Zwickl, and Robin Gutell, University of Texas.
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Evolutionary Computing
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Like simulated annealing!
Divided in four main classes (different
representation of individuals)
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Simulating biological evolution in AI
Biology
Individuals
Environment
Genetic algorithms
Evolution strategies
Evolutionary programming
Genetic programming
ECE457 Applied Artificial Intelligence
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Genetic Algorithms
Introduced by John Holland in “Adaptation in
Natural and Artificial Systems”, 1975
Stochastic search technique
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Genetic Algorithms
States
Solutions to a problem
State space to explore
Problem to solve
Fitness
Evaluation function
Changes from one
generation to the next
Operators
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Individuals
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Individuals have a chromosome
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String of genes (bits)
Encodes the solution represented by the
individual
Often binary representation, but can be
anything
1
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Operators
1
0
0
1
0
1
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0
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Crossover
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Crossover (sexual reproduction)
Mutation (mutation)
Selection (natural selection)
Length, nature of bits, meaning, varies
according to problem
ECE457 Applied Artificial Intelligence
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To evolve, the population must change
GA typically use three operators to
change the population
0 1 0 0 0 1 1 0
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Mutation
Select two fittest parents
Select (random) splitting point in the
chromosomes
Recombine the genes to get children
Causes slow move of the population
around state space
1 1 0 0 1 0 1 0
ECE457 Applied Artificial Intelligence
→
1 1 0 0 0 1 1 0
0 1 0 0 1 0 1 0
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Select random child
Select random gene
Switch gene value according to
mutation rule
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Depends on representation
Typically very rare (low mutation rate)
Causes large leap across state space
1 1 0 0 0 1 1 0
↑
ECE457 Applied Artificial Intelligence
→
1 1 0 1 0 1 1 0
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Selection
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GA population have zero population
growth
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Evolution Algorithm
We can’t keep them all (computer limits)
and we don’t want to (they’re useless)
But each crossover operation generates
two more, new individuals
Survival of the fittest!
Evaluate fitness of all individuals
Kill off (i.e. delete) least fit ones,
keeping only the fittest (best solutions)
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Each generation, the population improves
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Evolution Algorithm
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Starts with random population
Evaluate fitness of all individuals
For each generation
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Select fittest parents and crossover
Mutate children according to mutation rate
Evaluate fitness of new individuals
Select individuals that survive for next generation
Repeat until
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Generation limit reached
An individual achieves the target fitness
ECE457 Applied Artificial Intelligence
*
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x
x
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*
*
*
* *
*
*
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***
x*
***
*
*
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Population
fitness
Generation
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Genetic Algorithm Example
Individuals are random, but population
converges slowly towards solution
*
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8-Queen problem
Environment: state
space
Chromosome: encodes
position of queens
Fitness: number of
attacks
2 6 7 1 5 7 2 5
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Genetic Algorithm Example
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Genetic Algorithm Example
Crossover operation
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Mutation operation
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2
6
7
1
5 7 2
5
4
8
5
3
6 5 1
5
→
2
6
7
3
6 5 1
5
4
8
5
1
5 7 2
5
→
4
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Complements (1-8,
2-7, 3-6, 4-5)
Swap two random
genes
8
5
1
5 7 2
↑
4
8
5
1
4 7 2
5
4
5
5
1
8 7 2
5
5
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Limits of Genetic Algorithms
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Not guaranteed to find the optimal
solution
In large complex state spaces, or with a
low mutation rate, might converge to
local optimum (premature convergence)
High mutation rate can prevent
convergence (mutation interference)
Interdependence between genes makes
it hard to find solution (epistasis)
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