# Genetic Algorithms, Search Algorithms by LYTBhyq

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```									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
   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?
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.

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