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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

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overview
Overview
  • Search Algorithms
  • Learning Algorithms
  • GA
  • Example
brief history
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
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
notion of search space
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
Learning Algorithms
  • Finding (through search) a suitable program, algorithm, function for a given problem

Learning Algorithm

Training Data

(Experience)

Program

learning algorithms function optimizations
Learning Algorithms (function Optimizations)

Problem instance

Set of Hypothesis

The One??

Hypothesis Space

Program Space

Function Space

learning algorithms digression
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
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
Evolution is a search process

From the Tree of the Life Website,University of Arizona

Orangutan

Human

Gorilla

Chimpanzee

evolution is parallel search

AGTGACCA

TGGACTA

AAGACTT

AGGACTA

AGGGCAA

CAGCACCA

AGCACTA

AAGGCCT

TGGACTT

TAGCCCT

AGCACTT

AGGGCAT

TCGCCCA

AGTACAA

AAGGCAA

TAGGCCTA

AGTGCTA

AGGGCAT

TAGCCCA

TAGACTT

AGCACAA

AGCGCTT

Evolution is parallel search
genetic algorithm overview
Genetic Algorithm Overview
  • Starting with a subset of n randomly chosen solutions ( )from the search space (i.e. chromosomes). This is the population
  • This population is used to produce a next generation of individuals by reproduction
  • Individuals with a higher fitness (| - |)have more chance to reproduce (i.e. natural selection)
ga in pseudo code
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 : Mutatechromosomes

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
GA vs. Specialized Alg.

Genetic Algorithms (GAs)

GA

Efficiency

Specialized Algo.

Problems

P

Specialized algorithms – best performance for special problems

Genetic algorithms – good performance over a wide range of problems

randomized algorithms
Randomized Algorithms
  • Guided random search technique
  • Uses the payoff function to guide search

Hill Climbing

local

optima

Global optima

evolutionary algorithms
Evolutionary Algorithms?
  • Search Algorithms?
  • Learning Algorithms?
  • Function Optimization Algorithms?

They are fundamentally the same!!

things needed for gas
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

Chromosome A

10110010110011100101

Chromosome B

11111110000000011111

Chromosome

1.235  5.323  0.454  2.321  2.454

Chromosome A

1  5  3  2  6  4  7  9  8

Chromosome

(left), (back), (left), (right), (forward)

Chromosome B

8  5  6  7  2  3  1  4  9

Encoding Methods

Binary Encoding/Ternary Encoding

Permutation Encoding (TSP)

Real numbers, etc. Specialized

fitness function
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
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
Roulette Wheel Selection

Chromosome # Fitness

1 15.3089

2 15.4091

3 4.8363

4 12.3975

4

3

2

1

Spin

Strings that are fitter are assigned a larger slot and hence have a better chance of appearing in the new population.

fitness for 8 queen
Fitness for 8-Queen?

Minimum conflict fitness function.

theory schema theorem
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
Applications
  • Many many…
  • VLSI, TSP, Function Optimization, Data mining, security, etc.