GP GEP Presentation

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    OUTLINE

    Evolutionary Algorithms

    Genetic Programming (GP)

    Gene Expression Programming (GEP)

    Applications in the real world problems

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    NP-HARDNESS

    Some problems cannot be solved by exact methodsExample: Bandwidth allocation

    10 bandwidth ranges, 30 antennas

    Supercomputer (109 combinations in 1 s)

    Result in roughly 7000 times age of Earth

    Approximate results are required

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    EVOLUTIONARY

    ALGORITHMS (EA)

    Inspired by the process ofnatural evolution

    Elements

    Chromosome (representation)

    Individual (solution)

    Fitness

    Population

    Modifications depend onrepresentation

    Initialize population P

    Generation g = 0

    P' = selection(P)

    Recombination (P')

    Mutation (P')

    Evaluate P

    Stoppingcondition

    P = P'

    g = g + 1

    No

    Yes

    Finish

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    EVOLUTIONARY

    ALGORITHMS (EA)

    Inspired by the process ofnatural evolution

    Elements

    Chromosome (representation)

    Individual (solution)

    Fitness

    Population

    Modifications depend on

    representation

    Initialize population P

    Generation g = 0

    P' = selection(P)

    Recombination (P')

    Mutation (P')

    Evaluate P

    Stoppingcondition

    P = P'

    g = g + 1

    No

    Yes

    Finish

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    GENETIC ALGORITHMS

    (GA) (1)

    Chromosome is binary string

    Solution is a value encoded by the chromosome

    Fitness is the performance of the solution

    Example:optimize f(x) = x2

    Solution - x value

    Fitness - y value-2 -1 0 1 2

    0.5

    1

    1.5

    2

    s1

    s2

    s3

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    GENETIC ALGORITHMS

    (2)

    Modifications arestraightforward

    Crossover

    Mutation

    10110011100

    00001110001

    Parent 1

    Parent 2

    Crossover point

    00001011100

    10110110001

    Offspring 1

    Offspring 2Crossover point

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    GENETIC ALGORITHMS

    (2)

    Modifications arestraightforward

    Crossover

    Mutation

    10110011100Parent

    Offspring

    Mutation point

    10100011100

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    GA - SUMMARY

    Solution is a point in the search space

    Chromosome encodes the point as a sequence ofsymbols

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    GENETIC

    PROGRAMMING (GP) (1)

    Chromosome is aprogram

    Program treeTerminals - inputs (T)

    Nodes - functions (F)

    Solution is the programFitness is itsperformance

    a b a

    + sin b a

    *

    /

    f = (a + b) sin(a) a

    b

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    GENETIC

    PROGRAMMING (2)

    Example: data modeling

    Solution is a function describing given data set

    Fitness is the sum of relative errors of the solution

    0 1 2 3 4 5 6

    -1

    1

    2

    s1: y = ln(x)

    s2: y = 4/x+2.4

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    GENETIC

    PROGRAMMING (3)

    Modifications areproblematic

    Crossover

    Mutation

    Problems

    Syntactic correctness

    Tree bloat

    a b a

    + b a

    * /

    sin a b

    +

    a a

    /

    Parent 1 Parent 2

    Crossover point

    a b

    + b a

    * /

    b

    +

    a a

    /

    Offspring 1 Offspring 2

    a

    a

    sin

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    GENETIC

    PROGRAMMING (3)

    Modifications areproblematic

    Crossover

    Mutation

    Problems

    Syntactic correctness

    Tree bloat

    a b

    +

    a a

    /

    Parent

    Mutation point

    Offspring +

    a a

    /

    + a

    ln b

    b

    *

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    GENETIC

    PROGRAMMING (3)

    Modifications areproblematic

    Crossover

    Mutation

    Problems

    Syntactic correctness

    Tree bloat

    a b

    +

    a a

    /

    Parent

    Mutation point

    Offspring +

    a a

    /

    + a

    ln b

    b

    *

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    GP - SUMMARY

    Solution is a program of evaluated performance

    Chromosome represents solution as a program tree

    Problems

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    Break (10 min)

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    GENE EXPRESSION

    PROGRAMMING (GEP) (1)

    Chromosome (k-expression) is a sequence of symbolsfrom the set of terminals (T) and functions (F)

    Solution (expression tree) is a program decoded fromk-expression

    a b

    +

    c d

    /

    dcba/+

    Expression

    TreeK - expression

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    GENE EXPRESSION

    PROGRAMMING (2)

    Modifications are straightforward

    Fixed size sequence of symbols

    Karva notation ensures syntactic correctness

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    GENE EXPRESSION

    PROGRAMMING (3)

    a b

    ln

    +Expression

    Tree

    *

    *

    c/

    *d

    dcabadbc/baln+ *

    Head Tail

    Unused part

    b

    Head -F

    andT

    Tail - only T

    A part of the tail may be

    unused

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    GENE EXPRESSION

    PROGRAMMING (4)

    a b

    ln

    +Expression

    Tree

    *

    *

    c/

    *d

    dcabadbc/baln+ *

    Head Tail

    Unused part

    b

    a

    ln

    +Expression

    Tree

    *

    *

    c/

    *b

    dcabadbc/+aln+ *

    Head Tail

    Unused part

    a

    +

    *db

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    GEP - SUMMARY

    Combines properties of GA and GP

    Fixed size sequence of symbols prevents tree bloat

    Karva notation ensures solution correctness

    Offers intensive exploration of the search space

    Interesting for epistatic problems

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    INTRUSION DETECTION

    WITH GEP

    Problem definition

    Fitness calculation

    Results and comparison with regular approach

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    PROBLEM DEFINITION

    Network traffic is described with a set of parameters

    e.g packets/s, bytes/s, etc.

    We search for a classification function g(x)

    g(x) > 1 during attack

    g(x) < 1 during regular traffic

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    FITNESS CALCULATION

    (1)

    Input: time series of monitored parameters

    E.g. two parameters p and b and time windoww = 2 give s = [pt0, pt1, pt2,bt0,bt1,bt2]

    Three parameters taken from traffic clustering

    Size, Number and Ratio (Capacity/Number)

    Seven values ofw = {5, 10 - 60}

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    FITNESS CALCULATION

    (2)

    Fitness is the classification performance

    Sensitivity

    Specificity

    Learning set composed of time series samples

    Training set

    Testing set

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    RESULTS

    Comparison with regular approach (thresholding)

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    FUNCTION FINDING

    WITH GEP

    Problem definition

    Fitness calculation

    Results

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    PROBLEM / FITNESS

    Problem: having set of 3-d points P find a functionfitting these points

    Fitness: sum of relative errors of a given function

    concerning P

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    RESULTS

    Mexican Hat

    f(x, y) = 1 (a2 + b2) ea2+b2

    2

    Found

    f(x, y) =

    ((1 + sin(sin(x ln(y) + 2)) + sin(sin(2sin(y2

    ))))

    (ey2 sin(1 sin(x + y)))) +sin(1)

    eeyx+1

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    SUMMARY

    Evolution of programs is an interesting and useful

    approach to problem solving

    Challenging issues

    Search guidance

    Solution structure

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    THANK YOU

    Questions ?