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Introduction to Evolutionary Computation

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Title: Introduction to Evolutionary Computation


1
Introduction to Evolutionary Computation
Eastern Michigan University
  • Matthew Evett

2
Evolutionary Computation is.
  • Umbrella term for machine learning techniques
    that are modeled on the processes of
    neo-Darwinian evolution.
  • Genetic algorithms, genetic programming,
    artificial life, evolutionary programming
  • Survival of the fittest, evolutionary pressure
  • Techniques for automatically finding solutions,
    or near solutions, to very difficult problems.

3
Why is EC Cool?
  • EC techniques have found solutions better than
    any previously known for many domains
  • Electronic circuit design, scheduling,
    pharmaceutical design
  • Autonomous solution discovery is fun
  • Look Ma! No hands!

4
Darwinian Evolution
  • Works on population scale, not individual
  • Chance plays a part
  • Variation affects viability
  • Fittest dont always survive!
  • Heredity of traits
  • Finite resources to yield competition

5
EC is not...
  • Real evolution, or real genetics
  • It is modeled on natural genetic systems only in
    a simple sense.
  • Term genetic is really used to mean heredity
  • Real genetics is much more complicated

6
Overview of the Talk
  • Well look at two related techniques...
  • genetic algorithms
  • genetic programming
  • Well look at some demos of evolutionary systems.

7
History of EC
  • Friedbergs induced compilers (1958)
  • Evolutionary Programming (1965)
  • Fogel, Owens Walsh
  • Evolutionary Strategies (Recehenberg 72)
  • Genetic Algorithms (Holland 75)
  • Genetic Programming
  • Tree-based GA (Cramer 85, Koza 89)
  • True GP (Koza 92)

8
Basic evolutionary algorithm
  • Population of individuals, each representing a
    potential solution to the problem in question.

9
Genetic Algorithms (GA)
  • Population individuals are (fixed-length) binary
    strings (genome)
  • Start with a population of random strings.
  • Measure fitness of individuals.
  • Each generation forms a new population from old
    via recombination and mutation.
  • Solutions improve over generations.

10
Three steps to setting up a GA
  • 1) Devise a binary encoding representing the
    potential solutions to a problem.
  • 2) Define a fitness function.
  • Objective measure of quality of individual
  • 3) Set control parameters.
  • population size
  • maximum number of generations
  • probability of mutation and crossover, etc.

11
Example Designing a Truss
  • 10 members
  • 16 diameters avail.
  • Different costs
  • Different strengths
  • Find cheapest that is strong enough
  • 40-bit genome
  • Each 4 bit sequence reps. diam. of 1 member

12
Running a GA
  • Generate an initial population of random binary
    strings
  • Calculate fitness of each individual
  • Fitness is cost of design, penalty for fails
  • Create next generation
  • Select on the basis of fitness
  • Recombination/mating
  • Select some elements for mutation.
  • Typically one or two random bits will be flipped

13
Crossover in GA
  • Single-point crossover
  • There are many other forms
  • Randomly select crossover point
  • Swap crossover fragments
  • Offspring will have a combination of randomly
    selected parts of both parents

Parents
Children
14
Running a GA (continued)
  • Repeatedly create new generations
  • Calculate fitness
  • Terminate when an acceptable solution is been
    found or when the specified maximum number of
    generations is reached.

15
Running a GA/GP
  • Major phases of evolutionary algorithms

16
Results of Truss Example
  • Optimal solution is known, but rare
  • Number of possible designs is 240
  • Typical run
  • 200 individuals/pop. 40 generations
  • Yields answer within 1 of optimal
  • but examines only 8000 individuals! (.0000007
    of designs)

17
Genetic Programming (GP)
  • GP is a domain-independent method for inducing
    programs by searching a space of S-expressions.
  • GPs search technique is similar to GAs.
  • The elements of a population are programs,
    encoded as s-expressions.
  • The Lisp programming language is based on
    s-expressions.
  • Original GP work was done in Lisp.

18
Genetic Programming Elements
  • S-expressions
  • Prefix notation
  • Programs, encoded as trees, evaluated via
    post-order traversal
  • Ex tree corresponding to the S-expression
  • (sqrt ( / ( a b) 2.0 ) )

19
Representation of a Program
  • S-expressions can be converted to C.

float treeFunc(float a) if ( a gt 10.0)
return 20.0 else return
a/2.0
Looping constructs and subroutine calls are also
possible.
20
Three steps to setting up a GP
  • Define appropriate set of functions and
    terminals.
  • Must have closure.
  • Functions and Terminals must be sufficient.
  • Define a fitness function.
  • Set control parameters.
  • GA population size,
  • maximum size or depth of the individual trees
  • size and the shape of the original trees, etc.

terminal set a, b, c, 0, 1, 2 function set
, -, , /, SQRT
21
Starting a GP
  • Generate an initial population of random
    S-expression trees.
  • Calculate fitness value for each individual
  • Often over a set of test cases.

22
Running a GP
  • Create the next generation (population)
  • Select elements for reproduction
  • Random, fitness-proportionate, tournament.
  • Reproduce
  • Direct reproduction (cloning)
  • Mating
  • Mating method differs from GAs.
  • Mutation
  • Also differs from GAs.

23
GP Crossover
  • Randomly choose crossover points.
  • Swap rooted subtrees.
  • Closure property guarantees viability of
    offspring

24
Mutation with GP
  • Elements that are selected for mutation will have
    some randomly selected node (and any subtree
    under it) replaced with a randomly generated
    subtree.
  • Point mutation
  • Tree growth (shown here)

25
Running a GP (continued)
  • Repeatedly create new generations.
  • Terminate when an acceptable solution is found or
    when a specified maximum number of generations is
    reached.
  • The termination criteria is often based on a
    number of hits, where a hit is defined as the
    successful completion of some subgoal.

26
Example Santa Fe Trail
  • Ant animats, acquiring food.
  • Some gaps in trail
  • 89 food pellets
  • Evolve control strategy to consume all pellets
  • In acceptable time

27
Representing Ants
T ahead, left, right F if-food-ahead,
progn2, progn3
  • Terminals are functions, whose evaluation
    causes ant to move.
  • Fitness of pellets consumed in 400 terminal
    evaluations.
  • Prevents infinite runs, and weak solutions.

(if-food-ahead (move) (progn2 (left) (move)))
28
Demo Santa Fe Ant
  • During run, shows path of
  • best-of-generation, best-of-run
  • Chong, 1998

29
Santa Fe Ant Demo (done)
  • http//studentweb.cs.bham.ac.uk/fsc/DGP.html
  • The applet

30
GP Generated Military Tactics
  • Squadron has a destination
  • Ordered either to evade or attack
  • Porto, Fogel Fogel, 1998
  • Population of strategies

31
Generating tactics
  • Every 20 seconds of real time, do GP run, 40
    generations.
  • Predicts 20 mins ahead.
  • Allows adaptation to changing situation.
  • Here, order is changed from evade to attack.

32
Co-evolution
  • Simulation uses GP-developed strategy for both
    squadrons.

33
Real-time success
  • Platform Sparc 20
  • Actual Pentagon military simulation.
  • Blue squad fires on red.

34
Learning to Walk with GP
  • Evolve control strategies for movement of
    arbitrarily articulated animats.
  • Karl Sims, 1995
  • Fitness is rate of travel
  • physics model
  • LOTS of CPU cycles!

35
GA-learned bipedal motion
  • Individual strategies can be observed on the
    applet. (http//www.jsh.net/andy/gat/environ.html
    )
  • User can view all trials, or just the
    best-of-generation.
  • Constrained skeletons.
  • Dick, 1998

36
Financial Symbolic Regression
  • The goal is time series prediction, where the
    target points are a financial time series.
  • In this case we are using a target time series
    derived from the daily closing prices of the SP
    500 from the years 1994 and 1995.
  • Uses 33 independent variables taken from time
    series that that are derived from the SP 500
    itself and from the closing daily prices of 32
    Fidelity Select Mutual Funds.
  • Evett Fernandez, 1996, 1997.

37
Solving Financial Problems
  • The top line in the graph is the daily closing
    price of the SP 500. The solid line below it is
    the graph of the target time series after
    preprocessing.
  • The dotted line is a function evolved using GP.
    It is included here only as an example to
    illustrate that criterion for success does not
    require a great deal of accuracy.

38
The Example Evolved Function
  • y (((0.38)-((-0.20923)-(FSPTX-(((-0.79706)
    /(0.38))((FSUTX-FSCSX)(FSCGX-(-0.34247)))))))
    (SPX((0.82794)/(0.54431))))
  • The independent variables that were used by this
    evolved function are derived from the following
    time series.
  • FSPTX Fidelity select Technology Portfolio.
  • FSUTX Fidelity Select Utility Portfolio
  • FSCSX Fidelity Select Software Portfolio
  • FSCGX Fidelity Select Capital Goods Portfolio
  • SPX SP 500 Index

39
Conclusions
  • Evolutionary algorithms are a powerful technique
    for problem solving in domains that
  • are variable
  • difficult, if not impossible to optimize
  • GP is especially useful for problems for which
    the form of the solution is not known.
  • Evolutionary techniques are becoming widespread.

40
Overview of the Software
  • Object Oriented
  • C.
  • Windows 95 (MS Visual C 5.0)
  • Ported to UNIX. (GNU C)
  • Extended to run cooperatively on multiple
    machines using MPI.

41
Thank You! Are there any Questions?
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