Download soft computing

Massimo Panella
Dipartimento di Scienza e Tecnica dell’Informazione e della Comunicazione
(INFO--COM)
(INFO
Università di Roma “La Sapienza”
Facoltà di Ingegneria dell’Informazione
Via Eudossiana 18,
18, 00184 Roma
[email protected]
[email protected]
1.it
Ministero dello Sviluppo Economico (ISCOM)
Roma, 9 giugno 2010
Soft computing, reti neurali e algoritmi evolutivi
Outline
• Intelligent Systems/Historical Perspective
•Foundation of Soft Computing
•Evolution of Soft Computing
o Neural Network / Neuro Computing
o Fuzzy Logic / Fuzzy Computing
o Genetic Algorithm / Evolutionary Computing
o Hybrid Systems
• Demo
•Conclusions
1
Computation?
• Traditional Sense: Manipulation of Numbers
• Human: Uses Word for Computation and Reasoning
• Conclusions <= Word <== Natural Language
Intelligent System?
The role model for intelligent system is
Human Mind.
Dreyfus:
Minds do not use a theory about the everyday world
Know
Know--how vs know that
Winograd
Intelligent systems act, don't think
2
Computational Intelligence
Knowledge Representation
Predicates
Production rules
Semantic networks
Frames
Inference Engine
Learning
Common Sense & Heuristics
Uncertainty
Computational Intelligence
Applications
Expert tasks
The algorithm does not exist
A medical encyclopedia is not equivalent to a physician
Heuristics
There is an algorithm but it is “useless”
Uncertainty
The algorithm is not possible
Complex problems
The algorithm is too complicated
Technologies
Expert systems
Natural language processing
Symbolic processing
Knowledge engineering
3
Cost
Uncertainty
“As complexity rises, precise statements lose meaning, and
meaningful statements lose precision.” (L.A. Zadeh)
Principle of incompatibility (Pierre Duhem)
The certainty that a proposition is true
decreases with any increase of its precision
The power of a vague assertion rests in its
being vague (“I am not tall”)
A very precise assertion is almost never
certain (“I am 1.71cm tall)
Precision
The Nature of Mind
The Contribution of Information Science
The mind as a symbol processor
Formal study of human knowledge
Knowledge processing
Common--sense knowledge
Common
Neural Networks
4
The Nature of Mind
The Contribution of Psychology
The mind as a processor of concepts
Reconstructive memory
Memory is learning and is reasoning.
Fundamental unity of cognition
The Nature of Mind
The Contribution of Neurophysiology
The brain is an evolutionary system
Mind shaped mainly by genes and experience
Neural--level competition
Neural
Connectionism
5
The Nature of Mind
The Contribution of Physics
Living beings create order from disorder
Non--equilibrium thermodynamics
Non
Self--organizing systems
Self
The mind as a selfself-organizing system
Theories of consciousness based on quantum &
relativity physics
What is Soft Computing?
The basic ideas underlying soft computing in its
current incarnation have links to many earlier
influences, among them Prof. Zadeh’s 1965 paper on
fuzzy sets; the 1973 paper on the analysis of complex
systems and decision processes; and the 1979 report
(1981 paper) on possibility theory and soft data
analysis.
The principal constituents of soft computing (SC) are
fuzzy logic (FL), neural network theory (NN) and
probabilistic reasoning (PR), with the latter subsuming
belief networks, evolutionary computing including DNA
computing, chaos theory and parts of learning theory.
Fuzzy Set: 1965 … Fuzzy Logic: 1973 … Soft Decision: 1981 … BISC: 1990 … HumanHuman-Machine Perception: 2000 - …
6
SOFT COMPUTING
SOFT COMPUTING
“Soft computing is consortium of computing
methodologies which collectively provide a
foundation for the Conception, Design and
Deployment of Intelligent Systems.”
L.A. Zadeh
"...in contrast to traditional hard computing, soft
computing exploits the tolerance for imprecision,
uncertainty, and partial truth to achieve tractability,
robustness, low solution-cost, and better rapport
with reality”
L.A. Zadeh
The role model for Soft Computing is the Human Mind.
7
SOFT COMPUTING
• Neuro-Computing (NC)
• Fuzzy Logic (GL)
• Genetic Computing (GC)
•
Probabilistic Reasoning (PR)
•
Chaotic Systems (CS), Belief Networks (BN),
Learning Theory (LT)
Related Technologies
• Statistics (Stat.)
•Artificial Intelligence (AI):
–Case-Based Reasoning (CBR)
–Rule-Based Expert Systems (RBR)
–Machine Learning (Induction Trees)
–Bayesian Belief Networks (BBN)
SOFT COMPUTING
Neural Networks
Fuzzy Logic
create complicated models without knowing their
structure
gradually adapt existing models using “training
data”
Fuzzy Rules are easy and intuitively
understandable
Genetic Algorithms
find parameters through evolution
(usually when a direct algorithm is unknown)
8
Neural Networks
Ensemble of simple processing units
Connection weights define functionality
Derive weights from “training data”
(usually gradient descent based
algorithms)
Fuzzy Logic
Allow partial membership to sets
Express knowledge through linguistic
terms and rules (“Computing with
Words”)
Derive sets of Fuzzy Rules from data
(usually based on heuristics)
9
Evolutionary Algorithms
Finding an optimal structure
(parameters) for a model is often
complicated (due to large search space,
complex structure)
Find structure (parameters) through
evolution (generate population, evaluate,
breed new pop.)
Why Fuzzy Logic?
•Uncertainty in the data and laws of nature*
•Imprecision due to measurement & human error
•Incomplete and sparse information
•Subjective and Linguistic rules
•So far as the laws of mathematics refer to reality,
they are not certain; and so far as they are certain,
they don’t refer to reality”
Albert Einstein
10
Words are less precise than numbers!
• When information is too imprecise
• Close to reality
• Complex problem
“As complexity rises, precise
statements lose meaning, and
meaningful statements lose
precision.”
Lotfi A. Zadeh
Why Neural Network?
• Structure Free & Nonlinear Mapping
• Multivariable Systems
• Trains Easily Based on Historical Data
• Parallel Processing & Fault Tolerance
*Much Like Human Brain
11
Why Evolutionary Computing?
•For Multi-objectives and Multi-Criteria
Optimization Purposes
• Resolving Conflict
• Capability to learn adaptively and to be self-aware
* Darwinian's law
SOFT COMPUTING
Neural Network
12
Biological Neuron
Biological Neuron
13
Biological vs. Artificial Neuron
Synapse
Axo n
Soma
Dendrites
Synapse
Axo n
Soma
De ndrites
Synapse
14
Analogy between biological and
artificial neural networks
Biological Neural Network
Soma
Dendrite
Axon
Synapse
Artificial Neural Network
Neuron
Input
Output
Weight
Soma
Synapse
Dendrites
Input Signals
Axon
Out put Signals
Synapse
Axon
Soma
Dendrites
Middle Layer
Synapse
Input Layer
Output Layer
Artificial Neuron
Input Signals
Weights
OutputSignals
Neuron
15
Schematic Diagram for Single Neuron
b
1
w1
x1
s=∑
∑xiwi y=f(s)
w22
y
wk
xk
y = f [ b+ w1 x1 + w2 x2 + … + wk xk ] . w22
Activation Functions
f(s)
sgn(s)
1
tanh(s)
s
-1
16
Input Signals
Output Signals
Multilayer perceptron with two hidden layers
Input
layer
First
hidden
layer
Second
hidden
layer
Output
layer
Artificial Neural Network (Feedforward)
Multi Layer Perceptron ANN
X1
Σ
X2
Neural Network
X1
Y
X2
17
Artificial Neural Network vs.
Human Brain
Largest neural computer:
20,000 neurons
Worm’s brain:
1,000 neurons
But the worm’s brain outperforms neural
computers
It’s the connections, not the neurons!
Human brain:
100,000,000,000 neurons
200,000,000,000,000 connections
Brain vs. Computer Processing
• Processing Speed: Milliseconds VS Nanoseconds.
• Processing Order: Massively parallel.VS serially.
• Abundance and Complexity: 1011 and 1014 of neurons operate in
parallel in the brain at any given moment, each with between 103
and 104 abutting connections per neuron.
• Knowledge Storage: Adaptable VS New information destroys old
information.
• Fault Tolerance: Knowledge is retained through the redundant,
distributed encoding information VS the corruption of a conventional
computer's memory is irretrievevable and leads to failure as well.
18
NEURAL NETWORK
Different Non-Linearly
Separable Problems
Structure
Single-Layer
Two-Layer
Three-Layer
Types of
Decision Regions
Exclusive-OR
Problem
Half Plane
Bounded By
Hyperplane
A
B
A
Convex Open
Or
Closed Regions
A
B
Arbitrary
(Complexity
Limited by No.
of Nodes)
Classes with
Most General
Meshed regions Region Shapes
B
B
B
B
A
A
B
B
B
A
A
A
A
19
Learning Paradigms
Supervised learning
Unsupervised learning
network trained by showing a set of input and
output patterns
network is shown only the input patterns
Reinforcement learning
Information on quality of response is available
Neural Network Classification
20
Multilayer
Perceptron
Kohonen
Radial Basis
Functions
Neural Network
Models
Generalised
Regression
Probabilistic
ART
Recurrent
Neural Network Classification
21
Output layer
Output layer
Hidden layer
Hidden layer
Input layer
Input layer
}
Unit delay
operator
Recurrent network
without hidden units
inputs
{
outputs
Recurrent network
with hidden units
Artificial Neural Network (Feedforward and Recurrent)
Other Types of Neural Networks
x1
G
ω1
x2
ωj
G
xm
Input
Layer
SOM
Committee Machines
F (x)
ωN
x m−1
ω = (G T G ) −1 G T d
G
Hidden
layer
of N Green’s
functions
Output
layer
RBFN
ART1
22
Output layer
Hidden layer
Input layer
Artificial Neural Network (recurrent)
SOFT COMPUTING
Fuzzy Logic
23
VARIABLES AND LINGUISTIC VARIABLES
one of the most basic concepts in science is that of a
variable
variable
a linguistic variable is a variable whose values are
words or sentences in a natural or synthetic language
(Zadeh 1973)
the concept of a linguistic variable plays a central role
in fuzzy logic and underlies most of its applications
-numerical (X=5; X=(3, 2); …)
-linguistic (X is small; (X, Y) is much larger)
Fuzzy Sets
Fuzzy Logic
Classical Logic
Element x belongs to set A
or it does not:
µ(x)∈{0,1}
µA(x)
µA(x)
A=“young”
1
0
Element x belongs to set A
with a certain
degree of membership:
µ(x)∈[0,1]
1
x [years]
0
A=“young”
x [years]
24
Membership Functions
Predicate “Old”
Predicate “Old”
1 x ≥ 50 years |
Middle − Aged ( x ) = 
0 x ≤ 50 years
Crisp Set
Fuzzy Set
Other Types of Membership Function
Triangular
Trapezoid
Gaussian
EXAMPLES OF F-GRANULATION (LINGUISTIC VARIABLES)
color: red, blue, green, yellow, …
age: young, middle-aged, old, very old
size: small, big, very big, …
distance: near, far, very, not very far, …
µ
young
1
middle-aged
old
very old
0
Age
25
Fuzzy Logic
Linguistic Rule
Knowledge Base
Crisp
Input
Fuzzifier
Module
Fuzzy Inference
Engine
Defuzzifier
Module
Crisp
Output
Fuzzy Sets
Fuzzy Numbers
Fuzzification Fuzzy Operators
Fuzzy Rules
Fuzzy Inference
Defuzzification
Fuzzy Rule Base
If Age is old then Roya is 70
If Age is milddle-Aged then Roya is 45
If Age is Young then Roya is 20
26
Inferencing
Decision = {20|0, 45|0.75, 70|0.25}
µ
Age
Defuzzification
Output = (20×0 + 45×0.75 + 70×0.25) ÷
(0 + 0.75 + 0.25)
Output = 51.2 Middle-Aged
27
Schema of a Fuzzy Decision
Inference
Fuzzification
Defuzzification
rule-base
µcold µwarm µhot
0.7
if temp is cold
then valve is open
µcold =0.7
if temp is warm
then valve is half
0.2
measured
temperature
t
µopen µhalf µclose
0.7
0.2
µwarm =0.2
if temp is hot
then valve is close
µhot =0.0
v
crisp output
for valve-setting
SOFT COMPUTING
Fuzzy Logic
28
WHAT IS FUZZY LOGIC?
fuzzy logic has been and still is, though to a
lesser degree, an object of controversy
for the most part, the controversies are rooted in
misperceptions, especially a misperception of the
relation between fuzzy logic and probability
theory
a source of confusion is that the label “fuzzy
logic” is used in two different senses
(a) narrow sense: fuzzy logic is a logical system
(b) wide sense: fuzzy logic is coextensive with fuzzy set
theory
today, the label “fuzzy logic” (FL) is used for the
most part in its wide sense
PRINCIPAL APPLICATIONS OF FUZZY LOGIC
control
consumer
products
industrial systems
automotive
decision analysis
medicine
geology
pattern recognition
robotics
FL
CFR
CFR: calculus of fuzzy rules
29
EMERGING APPLICATIONS OF FUZZY LOGIC
computational theory of perceptions
natural language processing
financial engineering
biomedicine
legal reasoning
forecasting
Mamdani Inference System
Output Z
Input MF
A1
B1
X
A2
Y
B2
X
x
C1
C2
Y
y
Z1
Z = (centroid of area)
Z2
Output MF
Input (x,y)
30
First-Order Takagi Sugeno FIS
• Fuzzy Rule base
If X is A1 and Y is B1 then Z = p1*x + q1*y + r1
If X is A2 and Y is B2 then Z = p2*x + q2*y + r2
• Fuzzy reasoning
A1
B1
x=1
B2
X
z1 =
p1*x+q1*y+r1
Y
X
A2
w1
y=3
w2
Y
Π
z2 =
p2*x+q2*y+r2
z=
w1*z1 + w2*z2
w1+w2
SOFT COMPUTING
Neuro-Fuzzy Computing
31
Neuro-Fuzzy Modeling
Hybrid Model
Neural Networks
Fuzzy Inference System
Prior rule-based knowledge cannot be used
Prior rule-based can be incorporated
Learning from scratch
Cannot learn (use linguistic knowledge)
Black box
Interpretable (if-then rules)
Complicated learning algorithms
Simple interpretation and implementation
Difficult to extract knowledge
Knowledge must be available
Adaptive Neuro-Fuzzy Inference System (ANFIS )
Takagi Sugeno FIS
Input partitioning
LSE + gradient descent training
nonlinear
parameters
x
y
A1
Π
A2
Π
B1
Π
B2
Π
w1
linear
parameters
w1*z1
Σ Σ wi*zi
w4
w4*z4
Σ
Σ wi
/
z
Forward pass Backward pass
MF parameter
fixed
steepest descent
(nonlinear)
Coefficient parameter
least-squares
fixed
(linear)
32
Evolutionary Design of Neuro-Fuzzy Systems
SOFT COMPUTING
Evolutionary Computing
66
33
What is a GA?
Genetic Algorithms (GAs) are adaptive heuristic search
algorithm based on the evolutionary ideas of natural
selection and genetics. As such they represent an
intelligent exploitation of a random search used to solve
optimization problems. Although randomized, GAs are by
no means random, instead they exploit historical
information to direct the search into the region of better
performance within the search space. The basic techniques
of the GAs are designed to simulate processes in natural
systems necessary for evolution, specially those follow the
principles first laid down by Charles Darwin of "survival of
the fittest.". Since in nature, competition among individuals
for scanty resources results in the fittest individuals
dominating over the weaker ones.
Evolutionary Algorithms
Evolution
Strategies
Genetic
Programming
Genetic
Algorithms
Classifier
Systems
Evolutionary
Programming
• genetic representation of candidate solutions
• genetic operators
• selection scheme
• problem domain
34
History of GAs
Genetic Algorithms were invented to mimic some of
the processes observed in natural evolution. Many
people, biologists included, are astonished that life
at the level of complexity that we observe could have
evolved in the relatively short time suggested by the
fossil record. The idea with GA is to use this power
of evolution to solve optimization problems. The
father of the original Genetic Algorithm was John
Holland who invented it in the early 1970's.
1970's.
Classes of Search Techniques
DFS, BFS
Tabu Search
Hill Climbing
Genetic Programming
35
The Genetic Algorithm
Directed search algorithms based on the mechanics of
biological evolution
Developed by John Holland, University of Michigan
(1970
1970’s)
’s)
To understand the adaptive processes of natural
systems
To design artificial systems software that retains the
robustness of natural systems
The genetic algorithms, first proposed by Holland (1975
(1975),
), seek to
mimic some of the natural evolution and selection.
The first step of Holland’s genetic algorithm is to represent a legal
solution of a problem by a string of genes known as a chromosome.
Evolutionary Programming
First developed by Lawrence Fogel in 1966
for use in pattern learning
Early experiments dealt with a number of
Finite State Automata
FSA were developed that could recognise
recurring patterns and even primeness of numbers
Later experiments dealt with gaming
problems (coevolution)
More recently has been applied to training of
neural networks, function optimisation & path
planning problems
36
Biological Terminology
• gene
• functional entity that codes for a specific feature e.g. eye color
• set of possible alleles
• allele
• value of a gene e.g. blue, green, brown
• codes for a specific variation of the gene/feature
• locus
• position of a gene on the chromosome
• genome
• set of all genes that define a species
• the genome of a specific individual is called genotype
• the genome of a living organism is composed of several
chromosomes
• population
• set of competing genomes/individuals
Genotype versus Phenotype
• genotype
• blue print that contains the information to construct an
organism e.g. human DNA
• genetic operators such as mutation and recombination
modify the genotype during reproduction
• genotype of an individual is immutable
(no Lamarckian evolution)
• phenotype
• physical make-up of an organism
• selection operates on phenotypes
(Darwin’s principle : “survival of the fittest”)
37
Courtesy of U.S. Department of Energy Human Genome Program , http://www.ornl.gov/hgmis
Genotype Operators
• recombination (crossover)
• combines two parent genotypes into a new offspring
• generates new variants by mixing existing genetic material
• stochastic selection among parent genes
• mutation
• random alteration of genes
• maintain genetic diversity
• in genetic algorithms crossover is the major operator
whereas mutation only plays a minor role
38
Crossover
• crossover applied to parent strings with
probability pc : [0.6..1.0]
• crossover site chosen randomly
• one-point crossover
parent A 1 1 0 1 0
parent B
10001
offspring A
offspring B
11011
offspring A
offspring B
1100 0
10000
• two-point crossover
parent A 1 1 0 1 0
parent B
10001
1001 1
Mutation
• mutation applied to allele/gene with
probability Pm : [0.001..0.1]
• role of mutation is to maintain genetic diversity
offspring:
11000
Mutate fourth allele (bit flip)
mutated offspring: 1 1 010 0
39
Structure of an Evolutionary Algorithm
mutation
population of genotypes
10111
10011
10001
phenotype space
00111
01001
01001
11001
01011
recombination
coding scheme
selection
10011
10
10001
011
001
01001
01
01011
001
011
f
x
10001
10001
fitness
11001
01011
Pseudo Code of an Evolutionary Alg.
Create initial random population
Evaluate fitness of each individual
yes
Termination criteria satisfied ?
no
stop
Select parents according to fitness
Recombine parents to generate offspring
Mutate offspring
Replace population by new offspring
40
Areas EAs Have Been Used In
Design of electronic circuits
Telecommunication network
design
Artificial intelligence
Study of atomic clusters
Study of neuronal behaviour
Neural network training & design
Automatic control
Artificial life
Scheduling
Travelling Salesman Problem
General function optimisation
Bin Packing Problem
Pattern learning
Gaming
Self--adapting computer programs
Self
Classification
Test--data generation
Test
Medical image analysis
Study of earthquakes
Swarm Intelligence
Modelli computazionali (o metaeuristiche)
che imitano il comportamento sociale di
specie biologiche (formiche, api, pesci,
uccelli, …):
“SI is the emergent collective intelligence of
groups of simple agents.”
(Bonabeau et al., 1999)
Roma, 04/03/2008
CATTID, Università di Roma “La Sapienza”
82
41
Swarm intelligence (cnt)
Imitazione: comportamento di gruppi di individui
(sciami), formiche, uccelli, pesci, ….
Prestazione ottimizzata: ricerca del cibo,
movimento del gruppo, ….
Swarm
Intelligence
Vantaggi:
non richiedono il gradiente
possono evitare i minimi locali
ottimizazione distribuita. Non è necessario un
coordinamento centralizzato; ci sono “agenti”
che si influenzano tra di loro per ottenere
l’ottimo.
Inconvenienti: richiedono un alto costo computazionale
ed una certa abilità nell’implementazione
Swarm
Intelligence
Swarm
Intelligence
ACO:
Ant Colony
Optimization
PSO:
Particle Swarm
Optimization
ACO: ant colony optimization
PSO: particle swarm optimization
Swarm intelligence (cnt)
Individuazione del cammino più breve tra il nido ed il cibo
nel superamento di un ostacolo.
Si considera la trasmissione indiretta d’informazione tra
formiche (informazione stigmergetica) ottenuta tramite il
deposito di feromone.
Si considera un insieme di particelle che si muovono nello
spazio soluzione, in cui ogni punto rappresenta una
soluzione del problema d’interesse.
Il movimento di ogni particella è regolato dall’inerzia e
dalla conoscenza delle posizioni in cui essa ha ottenuto in
precedenza la soluzione migliore e l’intero gruppo ha
ottenuto la soluzione migliore in senso assoluto.
42
Illustrazione del meccanismo di superamento di
un ostacolo da parte di una colonia di formiche
con individuazione del cammino più corto
Illustrazione del meccanismo di superamento di
un ostacolo da parte di una colonia di formiche
con individuazione del cammino più corto (cnt)
Evaporazione del
feromone nel
cammino più lungo
43
SOFT COMPUTING
Hybrid Systems
Computing Models
SOFT COMPUTING
HARD COMPUTING
Precise Models
Symbolic
Logic
Reasoning
(Traditional AI)
Probabilistic
Models
Traditional
Numerical
Modeling and
Search
Multivalued &
Fuzzy Logics
Approximate Models
Approximate
Reasoning
Neural
Networks
Functional
Approximation
and Randomized
Search
Evolutionary
Computing
44
Cost
Uncertainty
“As complexity rises, precise statements lose meaning, and
meaningful statements lose precision.” (L.A. Zadeh)
Principle of incompatibility (Pierre Duhem)
The certainty that a proposition is true
decreases with any increase of its precision
The power of a vague assertion rests in its
being vague (“I am not tall”)
A very precise assertion is almost never
certain (“I am 1.71cm tall)
Precision
Soft Computing: Hybrid Probabilistic Systems
Approximate
Reasoning
Multivalued &
Fuzzy Logics
Probabilistic
Models
Bayesian
Belief Nets
DempsterShafer
Probability of
Fuzzy Events
Belief of
Fuzzy Events
Fuzzy Influence
Diagrams
45
Soft Computing: Hybrid FL Systems
Approximate
Reasoning
Functional Approximation/
Randomized Search
Neural
Networks
Multivalued &
Fuzzy Logics
Evolutionary
Computing
Fuzzy
Systems
NN modified by FS
(FNS)
FL Tuned by NN
(NFS)
FL-EA
Soft Computing: Hybrid NN Systems
Approximate
Reasoning
Functional Approximation/
Randomized Search
Multivalued &
Fuzzy Logics
Neural
Networks
RBF
Feedforward
NN
Recurrent
NN
Single/Multiple
Layer Perceptron
Hopfield
NN parameters
controlled by FLC
Evolutionary
Algorithms
SOM
ART
NN structure
Weights
generated by EAs
46
Soft Computing: Hybrid EA Systems
Approximate
Reasoning
Multivalued &
Fuzzy Logics
Functional Approximation/
Randomized Search
Neural
Networks
Evolutionary
Algorithms
Evolution
Strategies
Genetic
Algorithms
Evolutionary
Programs
Genetic
Progr.
EA parameters
(N, Pcr, Pmu )
EA-based search
inter-twined with
EA parameters
controlled by FLC
hill-climbing
controlled by EA
SOFT COMPUTING
47
Conclusions: SC New Directions
• Present -> Short Term Future
- SC technologies will widen beyond its current constituents.
- Artificial Immune Systems (for Information Assurance)
- Fractals (as building blocks in GP or for bacteria identification)
- Development of hybrid SC systems with other AI paradigms
- EA for model/software update
- Evolutionary software agents
- Push for low-cost solutions / intelligent tools will lead to deployment of hybrid
SC systems that efficiently integrate reasoning and search techniques.
• Medium Term Future
- SC technologies are (or will soon be) implemented on alternative, nonstandard computing mechanisms
- Evolvable Hardware (Field Programmable Gate Arrays)
- Bio-inspired Systems: DNA and Molecular Computing
• Great Potential for Hybrid Soft Computing with new computing mechanisms:
DNA and Molecular Computing, Intelligent Matter
Conclusions: SC Experiments
•Bio-inspired Systems: DNA and Molecular Computing (Examples)
- Molecular Genetic Programming (Wasiewicz & Mulawka, 2001)
- Representation of GP graphs by DNA molecules, with crossover and negation operators
implemented using data flow techniques in DNA computing
- DNA-based Fuzzy Systems
(Deaton & Garzon, 2001)
- Encoding of fuzzy membership functions in Gibbs free energy (released upon DNA
hybridization*), leading to the representation of a fuzzy rule set (fuzzy associative memory)
- Fuzzy inference performed by modified hybridization process
- DNA Neural Network Computation (Mills et al., 2001)
- DNA analog neural network in which axons and neuron are replaced by diffusion and
molecular recognition of DNA.
- DNA Evolutionary Computation (Wood et al., 2001)
- Binary-encoded Evolutionary Algorithms, with point-wise mutation and
implemented in molecular computing, evaluating the “OneMax” fitness function.
crossover,
____________________________________________________________________________
*Watson-Crick hybridization of a pair of complementary DNA strands makes possible a representation
of highly parallel selective operations that is key for molecular computing (Adleman 1994)
•Potential for EC: DNA & Molecular Computing process, in parallel, populations
that are billions of time larger than the ones used in conventional computers
•Massive Information Storage (1 g DNA = 2 x1021 bits)
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