Introduction to Soft Computing ECE457 Applied Artificial Intelligence Spring 2007 Lecture #12

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 2 Outline Overview of soft computing Neural networks 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 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 4 Soft vs. Hard Computing Hard ComputingSoft Computing Input Complete and exact data Approximate and incomplete data Output Overly-exact solution Solution that’s “good enough” ReasoningRationalHuman-like

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 5 Soft Computing Probabilistic reasoning Human randomness Artificial neural networks (ANN) Human brain Fuzzy logic (FL) Human knowledge Evolutionary computing Genetic algorithms (GA) Biological evolution

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 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!

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 8 Neurons Receives electric impulse from other neurons through dendrites. If impulse strong enough, travels through axon. Reaches synapses and transmits to other neurons

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 9 Artificial Neuron i th neuron sums inputs a 1 … a j … a n, weighted by weights w i1 … w ij … w in Threshold value  i controls activation If activated, input is transformed by transfer function f i (.) into output a i a i = f i (  j w ij a j -  i ) = [0, 1] ajaj w ij ii aiai  f i (.) Dendrites Axon Synapse Cell body

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 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 x1x1 x2x2 x3x3 o1o1 o2o2 Input layer Hidden layer Output layer

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 12 Examples x1x1 x2x o x1x1 x2x o x1x1 x2x2 o OR Network AND Network XOR Network All these neurons use step functions f(<0) = 0 f(  0) = 1

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 13 Learning Backpropagation 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 14 ANN Topologies Feed-forward topology Information can only move forward through the network Recurrent topology Information can loop back to create feedback loop, or network memory x1x1 x2x2 x3x3 o1o1 x1x1 x2x2 x3x3 o1o1

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 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, …

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 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, … x1x1 x2x2

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 17 Recurrent Networks 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, … x1x1 x2x2 x3x3 o1o1 o2o2 o3o3

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 18 Limits of ANN Black box 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 19 Fuzzy Logic In crisp logic, facts are either true or false Truth value = {0, 1} This is an unnatural way of doing it Temperature 1010 ColdWarmHot

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 20 Temperature 1010 ColdWarmHot Fuzzy Logic In fuzzy logic, facts can be partially true and partially false Truth value = [0, 1] This is closer to human knowledge

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 21 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] = μ Cold (t):   [0,1]

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 22 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 23 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 24 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 25 Fuzzy Controller Example If Hot and Wet then VeryCool If Warm and Humid then Cool T 1010 Hot T 1010 Warm H 1010 H 1010 C 1010 C 1010 th Wet Humid VeryCool Cool

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 26 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 1010 c

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 27 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 28 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 29 Limits of Fuzzy Logic Writing the fuzzy rules Designing the fuzzy membership functions Often requires work by a domain expert

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 30 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 31 Fuzzy Robot Navigation Fuzzy linguistic variables of control system Distance: near, medium, far Direction angle: negative, zero, positive Speed: slow, medium, fast Distance 1010 NearMedium Far Direction 1010 NegativeZeroPositive Speed 1010 SlowMedium Fast

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 32 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)

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 33 Fuzzy Robot Navigation

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 34 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.

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 35 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 36 Genetic Algorithms Simulating biological evolution in AI BiologyGenetic Algorithms Individuals States Solutions to a problem Environment State space to explore Problem to solve FitnessEvaluation function Changes from one generation to the next Operators

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 37 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 38 Operators To evolve, the population must change GA typically use three operators to change the population Crossover (sexual reproduction) Mutation (mutation) Selection (natural selection)

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 39 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 

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 40 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  

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 41 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 42 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

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 43 Evolution Algorithm Individuals are random, but population converges slowly towards solution Population fitness Generation xxx ** * * * * * * * * * ** * * * * *** *

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 44 Genetic Algorithm Example 8-Queen problem Environment: state space Chromosome: encodes position of queens Fitness: number of attacks

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 45 Genetic Algorithm Example  Crossover operation

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 46 Genetic Algorithm Example Mutation operation Complements (1-8, 2-7, 3-6, 4-5) Swap two random genes  

ECE457 Applied Artificial Intelligence R. Khoury (2007)Page 47 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)