1. Introduction to Soft Computing
ECE457 Applied Artificial Intelligence
Fall 2007
Lecture #12

2. Outline Overview of soft computing Neural networks Fuzzy logic
Russell & Norvig, sections 20.5
Fuzzy logic
Russell & Norvig, pages
Genetic algorithms
Russell & Norvig, pages
 ECE 493 & ECE 750 (Prof. Karray)
ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 2

3. Soft 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
“Soft” reasoning
Computer algorithms require complete and precise information
“Hard” reasoning
Soft computing aims to bridge this gap
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4. Soft vs. Hard Computing Hard Computing Soft Computing Input
Complete and exact data
Approximate and incomplete data
Output
Overly-exact solution
Solution that’s “good enough”
Reasoning
Rational
Human-like
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5. Soft Computing Probabilistic reasoning
Human uncertainty and randomness
Artificial neural networks (ANN)
Human brain
Fuzzy logic (FL)
Human knowledge
Evolutionary computing
Genetic algorithms (GA)
Biological evolution
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6. Artificial Neural Networks
Human Brain
Massively parallel network of neurons
Each individual neuron is not intelligent
Neuron is a simple computing element
But the brain is intelligent!
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7. Human Brain
Brain learns by changing and adjusting the connections between neurons
Information encoded in many ways
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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8. Neuron 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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9. Artificial Neuron aj wij i ai  fi(.)
ith neuron sums inputs a1… aj… an, weighted by weights wi1… wij… win
Threshold value i controls activation
If activated, input is transformed by transfer function fi(.) into output ai
ai = fi( jwijaj - i ) = [0, 1] aj
wij i ai 
fi(.)
Cell body
Axon
Synapse
Dendrites
ECE457 Applied Artificial Intelligence R. Khoury (2007) Page 9

10. Artificial Neural Networks
Large arrangement of inter-connected artificial neurons
Different classes of network
Topology of the network
Transfer function of the neurons
Learning algorithm
Different networks appropriate for different applications
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11. Perceptron Simplest and most commonly-used ANN Feed-forward ANN
Single-layer
No hidden layer
Only linearly-separable problems
Multi-layer
Non-linear problems x1 x2 x3 o1 o2
Input layer
Hidden layer
Output layer
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12. Examples XOR Network AND Network OR Network x1 x2 -1.5 1 o x1 x2 o
All these neurons use step functions
f(<0) = 0
f(0) = 1 x1 x2
-1.5 1 o x1 x2 o
-0.5 1 -1
AND Network
OR Network x1 x2
-0.5 1 o
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13. Learning Backpropagation algorithm Algorithm
Train using a set of input-output pairs
Using the entire set = 1 epoch
Supervised learning
Algorithm
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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14. ANN Topologies Feed-forward topology x1 o1 x2 Recurrent topology x3 x1
Information can only move forward through the network
Recurrent topology
Information can loop back to create feedback loop, or network memory x1 x2 x3 o1 x1 x2 x3 o1
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15. Feed-Forward Networks
Perceptron
Basic network
Any transfer functions
Any number of hidden layers
Radial Basis Function (RBF) Network
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, …
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16. Feed-Forward Networks
Kohonen Self-Organising Map
Fully-connected two-layer network
Unsupervised learning
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, … x1 x2
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17. Recurrent Networks x1 o1 x2 o2 o3 x3 Hopfield Network
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, … x1 o1 x2 o2 o3 x3
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18. Limits of ANN Black box No formal design rules Prone to overfitting
What does each neuron do? What does each weight do?
No formal design rules
How many hidden layers? How many neurons per layer? Which transfer functions?
Prone to overfitting
Backpropagation is slow and can converge on local optimum
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19. ANN Classifier Typical application of ANN Requires
A set of crisp, mutually-exclusive classes
A set of well-defined, measurable attributes relevant to classification
Correctly-classified training data
Compared to Naïve Bayes Classifier
Does not require any probabilities
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20. ANN Classifier Design Pick network architecture based on problem
Or simply pick perceptron
One input neuron per attribute
One output neuron per class
Add hidden layers if classification is non-linear function of input space
Exact number of layers or neurons difficult to discover
Train network
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21. ANN Classifier Example
Paper on website
Classification of pixels in aerial photograph
Classes: lake, forest or land
Input: pixel’s RGB value
Data
180 training pixels
300 testing pixels
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22. ANN Classifier Example
Perceptron network
Good for complex classification problems
Two hidden layers
Number of hidden layers / neurons per hidden layer discovered by trial-and-error
One hidden layer not precise enough
First layer neurons  input neurons
Second layer neurons  max(input neurons, output neurons)
More hidden neurons give higher precision, need more training time
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23. ANN Classifier Example
Classification precision: 93%
Naïve Bayes Classifier: 88%
Network later expanded to 7 classes
Water, marsh, farmland, woodland, grassland, residential area, salina
Still has RGB input, two hidden layers
7 output neurons, more neurons on hidden layers
Precision: 97%
Naïve Bayes Classifier: 89%
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24. Fuzzy Logic In crisp logic, facts are either true or false
Truth value = {0, 1}
This is an unnatural way of doing it
Temperature 1
Cold
Warm
Hot
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25. Fuzzy Logic
In fuzzy logic, facts can be partially true and partially false
Truth value = [0, 1]
This is closer to human knowledge
Temperature 1
Cold
Warm
Hot
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26. Terminology “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
The value of cold (or warm or hot) to which a temperature is mapped is called a membership degree
Fz[t  Cold] = μCold(t):   [0,1]
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27. Fuzzy Sets vs. Probabilities
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
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28. Fuzzy Rules If-then rules like other logics, but with fuzzy sets
If Cold then VentilationHigh
If Warm then VentilationLow
If Hot then VentilationMedium
Variables belong partially to antecedent, therefore consequence activated partially
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29. Fuzzy Controller Typical application of fuzzy logic Set of fuzzy rules
Define the behaviour of a system
Antecedent: variables that affect the system
Consequent: reaction of the system
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30. Fuzzy Controller Example
If Hot and Wet then VeryCool
If Warm and Humid then Cool
Hot
Wet
VentilationHigh T 1 H 1 C 1
VentilationMedium
Warm
Humid T 1 H 1 C 1 t h
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31. Fuzzy Controller Example
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 C 1 c
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32. Advantages of Fuzzy Logic
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
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33. Properties of Fuzzy Controllers
The rule base must be
Complete
Continuous
The rules must
Be consistent
Not interact
The rule base system must be
Robust
Stable
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34. Limits of Fuzzy Logic Writing the fuzzy rules
Designing the fuzzy membership functions
Often requires work by a domain expert
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35. Fuzzy Robot Navigation
Fuzzy controllers are very popular for robot navigation
Eliminates need for complete world model and complex reasoning rules
Basic robot
Known current position and target
Three sensors (front, left, right)
Left and right wheels can turn at different speeds to make robot turn
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36. Fuzzy Robot Navigation
Fuzzy linguistic variables of control system
Distance: near, medium, far
Direction angle: negative, zero, positive
Speed: slow, medium, fast
Distance 1
Near
Medium
Far
Direction 1
Negative
Zero
Positive
Speed 1
Slow
Medium
Fast
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37. Fuzzy Robot Navigation
Going to target
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
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
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
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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38. Fuzzy Robot Navigation
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39. Genetic Algorithms Biological evolution
Species adapt to better survive in environment
Over generations
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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40. Evolutionary Computing
Introduced by John Holland in “Adaptation in Natural and Artificial Systems”, 1975
Stochastic search technique
Like simulated annealing!
Divided in four main classes (different representation of individuals)
Genetic algorithms
Evolution strategies
Evolutionary programming
Genetic programming
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41. Changes from one generation to the next
Genetic Algorithms
Simulating biological evolution in AI
Biology
Genetic Algorithms
Individuals
States
Solutions to a problem
Environment
State space to explore
Problem to solve
Fitness
Evaluation function
Changes from one generation to the next
Operators
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42. Individuals Individuals have a chromosome
String of genes (bits)
Encodes the solution represented by the individual
Often binary representation, but can be anything
Length, nature of bits, meaning, varies according to problem 1
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43. Operators To evolve, the population must change
GA typically use three operators to change the population
Crossover (sexual reproduction)
Mutation (mutation)
Selection (natural selection)
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44.  Crossover 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  1 1
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45.  Mutation  Select random child Select random gene
Switch gene value according to mutation rule
Depends on representation
Typically very rare (low mutation rate)
Causes large leap across state space  1 1 
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46. Selection GA population have zero population growth
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)
Each generation, the population improves
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47. Evolution Algorithm Starts with random population
Evaluate fitness of all individuals
For each generation
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
Generation limit reached
An individual achieves the target fitness
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48. Evolution Algorithm
Individuals are random, but population converges slowly towards solution x * * x x * * * * * * * * * * * * * * * * * * *
Population fitness
Generation
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49. Genetic Algorithm Example
8-Queen problem
Environment: state space
Chromosome: encodes position of queens
Fitness: number of attacks 2 6 7 1 5
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50. Genetic Algorithm Example
Crossover operation 2 6 7 1 5 2 6 7 3 5 1  4 8 5 3 6 1 4 8 5 1 7 2
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51. Genetic Algorithm Example
Mutation operation
Complements (1-8, 2-7, 3-6, 4-5)
Swap two random genes 4 8 5 1 7 2  4 8 5 1 7 2  4 5 1 8 7 2
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52. Limits of Genetic Algorithms
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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