Genetic Algorithms, Search Algorithms by LYTBhyq

VIEWS: 10 PAGES: 28

									Genetic Algorithms, Search Algorithms




               Jae C. Oh
    Overview
   Search Algorithms
   Learning Algorithms
   GA
   Example
    Brief History
   Evolutionary Programming
       Fogel in 1960s
       Individuals are encoded to be finite state
        machines
       Intellgent Behavior
   Evolutionary Strategies
       Rechenberg, Schwefel in 1960s
       Real-valued parameter optmization
   Genetic Algorithms
       Holland in 1960s
       Adaptive Systems
       Crossover Operators
    Current Status
   Wide variety of evolutionary algorithms
       No one seriously tries to distinguish them
        except for some cases and purposes.
       We will call all Evolutionary Algorithms
       And I will call them Genetic Algorithms or
        Evolutionary Algorithms for generic terms
Search
Search
Search
    Notion of Search Space
   Real world problem
       Search space
       Abstraction -> State Space
       Exploring the state space for given
        problem  Search Algorithms

                                              The Peak
                      Search Space
     Learning Algorithms
    Finding (through search) a suitable
     program, algorithm, function for a given
     problem



Training Data    Learning Algorithm   Program
(Experience)
       Learning Algorithms (function
       Optimizations)
                                 Problem instance


Set of Hypothesis




                                                    The One??
                     Hypothesis Space
                      Program Space
                      Function Space
    Learning Algorithms (Digression)
   How do we know the found hypothesis,
    program, function, etc. are the one we
    are looking for?
       We don’t know for sure
       Is there any mathematical way of telling
        how good hypothesis is?
            I.e., |h(x) – f(x)| = ?
       Computational Learning Theory can tell us
        this
            Valiant (1984)
    What are Genetic Algorithms?
   Find solutions for a problem with the idea of
    evolution. Search and optimization techniques
    based on Darwin’s Principle of Natural
    Selection.
   Randomized search and optimization algorithms
    guided by the principle of Darwin’s natural selection:
    Survival of fittest.
   Evolve potential solutions
           Step-wise refinement?
           Mutations? Randomized, parallel search
           Models natural selection
           Population based
           Uses fitness to guide search
 Evolution is a search process

                         From the Tree of the Life Website,
                                    University of Arizona




Orangutan   Gorilla   Chimpanzee             Human
          Evolution is parallel search

                   AAGACTT                                        AGGACTA

    AAGGCCT                TGGACTT           AGTGACCA                    TGGACTA


AGGGCAT          TAGCCCT        AGCACTT   AGGGCAA             CAGCACCA         AGCACTA




AGGGCAT TAGCCCA TAGACTT AGCACAA AGCGCTT             TCGCCCA              AGTACAA
                                          AAGGCAA             TAGGCCTA             AGTGCTA
Genetic Algorithm Overview
1. Starting with a subset of n randomly chosen
   solutions ( )from the search space (i.e.
   chromosomes). This is the population
2. This population is used to produce a next
   generation of individuals by reproduction
3. Individuals with a higher fitness (| - |)have
   more chance to reproduce (i.e. natural selection)
    GA in Pseudo code
0   START   : Create random population of n chromosomes
1   FITNESS : Evaluate fitness f(x) of each chromosome in
               the population
2   NEW POPULATION
              0 SELECTION     : Based on f(x)
              1 RECOMBINATION : Cross-over chromosomes
              2 MUTATION      : Mutate chromosomes
              3 ACCEPTATION   : Reject or accept new one
3   REPLACE : Replace old with new population: the new
                generation
4   TEST    : Test problem criterium
5   LOOP    : Continue step 1 – 4 until criterium is
                satisfied
      GA vs. Specialized Alg.

                   Genetic Algorithms (GAs)

                           GA

             Specialized Algo.

        Problems                       P


Specialized algorithms – best performance for special problems
Genetic algorithms – good performance over a wide range of problems
    Randomized Algorithms
   Guided random search technique
   Uses the payoff function to guide
    search

                                    Hill Climbing




           local
           optima
                    Global optima
     Evolutionary Algorithms?
    Search Algorithms?
    Learning Algorithms?
    Function Optimization Algorithms?



They are fundamentally the same!!
    Things needed for GAs
   How do we represent individuals? Domain
    Dependent
   How do we interpret individuals?
    Domain Dependent
   What is the fitness function?
    Domain Dependent
   How are individual chosen for reproduction?
    Choose better individuals (probabilistic)
   How do individuals reproduce?
    Crossover, Mutation, etc.
   How is the next generation generated?
    Replace badly performing individuals
    Encoding Methods
Binary Encoding/Ternary Encoding
    Chromosome A       10110010110011100101
    Chromosome B       11111110000000011111



Permutation Encoding (TSP)
    Chromosome A       1 5 3 2 6 4 7 9 8
    Chromosome B       8 5 6 7 2 3 1 4 9


Real numbers, etc. Specialized
       Chromosome      1.235 5.323 0.454 2.321 2.454

       Chromosome        (left), (back), (left), (right), (forward)
    Fitness Function
   A fitness function quantifies the optimality of a
    solution (chromosome) so that that particular
    solution may be ranked against all the other
    solutions.

   A fitness value is assigned to each solution depending
    on how close it actually is to solving the problem.

    Ideal fitness function correlates closely to goal +
    quickly computable.

   Example. In TSP, f(x) is sum of distances between
    the cities in solution. The lesser the value, the fitter
    the solution is
    Producing Offspring
The process that determines which
 solutions are to be preserved and allowed
 to reproduce and which ones deserve to
 die out.

   The primary objective of the recombination
    operator is to emphasize the good solutions and
    eliminate the bad solutions in a population, while
    keeping the population size constant.

   “Selects The Best, Discards The Rest”.
     Roulette Wheel Selection
     Chromosome #     Fitness
        1             15.3089
        2             15.4091            3
                                               4
        3             4.8363
        4             12.3975
                                         2         1
                                                          Spin




Strings that are fitter are assigned a larger slot and hence
have a better chance of appearing in the new population.
GA in Action for 8-Queen
Fitness for 8-Queen?

            Minimum conflict fitness function.
    Theory (Schema Theorem)
   Schema
       Substring where some positions left
        undecided
       246*****
       Instance of this schema: 24613587
       Theorem: if the average of the instances
        the schema is above the mean fitness of
        the population, the number of instances of
        the schema will increase over time.
    Applications
   Many many…
   VLSI, TSP, Function Optimization, Data
    mining, security, etc.

								
To top