Genetic Algorithms, Search Algorithms

1
Genetic Algorithms, Search Algorithms

• Jae C. Oh

2
Overview

• Search Algorithms
• Learning Algorithms
• GA
• Example

3
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

4
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

5
Search
6
Search
7
Search
8
Notion of Search Space

• Real world problem
• Search space
• Abstraction -gt State Space
• Exploring the state space for given problem ?
  Search Algorithms

The Peak
Search Space
9
Learning Algorithms

• Finding (through search) a suitable program,
  algorithm, function for a given problem

Learning Algorithm
Training Data (Experience)
Program
10
Learning Algorithms (function Optimizations)
Problem instance
Set of Hypothesis
The One??
Hypothesis Space Program Space Function Space
11
Learning Algorithms (Digression)

• How do we know the found hypothesis, program,
  function, etc. are the one we are looking for?
• We dont 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)

12
What are Genetic Algorithms?

• Find solutions for a problem with the idea of
  evolution. Search and optimization techniques
  based on Darwins Principle of Natural Selection.
• Randomized search and optimization algorithms
  guided by the principle of Darwins 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

13
Evolution is a search process
From the Tree of the Life Website,University of
Arizona
Orangutan
Human
Gorilla
Chimpanzee
14
Evolution is parallel search
15
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)

16
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
17
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
18
Randomized Algorithms

• Guided random search technique
• Uses the payoff function to guide search

Hill Climbing
local optima
Global optima
19
Evolutionary Algorithms?

• Search Algorithms?
• Learning Algorithms?
• Function Optimization Algorithms?

They are fundamentally the same!!
20
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

21
Encoding Methods
Binary Encoding/Ternary Encoding
Permutation Encoding (TSP)
Real numbers, etc. Specialized
22
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

23
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.

24
Roulette Wheel Selection
Chromosome Fitness 1 15.3089 2 15.4091
3 4.8363 4 12.3975
4
3
1
2
Spin
Strings that are fitter are assigned a larger
slot and hence have a better chance of appearing
in the new population.
25
GA in Action for 8-Queen
26
Fitness for 8-Queen?
Minimum conflict fitness function.
27
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.

28
Applications

• Many many
• VLSI, TSP, Function Optimization, Data mining,
  security, etc.