Outlines

1
Outlines

• Review GAs
• How GAs Work
• Schema Theorem
• Building Block Hypothesis
• Deceptive Problems
• Royal Road Problem

2
Evolutionary Algorithms

• Design an Evolutionary Algorithm
• Choose an appropriate representation
• Design genetic operators mutation and/or
  recombination
• Design selection/reproduction mechanism
• Design a useful objective function

selection
. . . . .
. . . . . . . .. . .
Decoding function( g)
genetic operators
. . . . . . . .. . .
. . . . .
3
Genetic Algorithm- representation

• Problem
• Max f(x)x2
• Bit-string 5-bits

4
GA- Crossover Mutation

• One-point crossover

5
GA- Crossover Mutation

• Mutation
• Two-point crossover

6
Schema Theory

• Short, lower, above average schemata receive
  exponentially increasing

7
Schema Theory

• Schema
• is a similarity template describing a subset of
  strings with similarities at certain string
  positions
• V 0,1, , H110 (length7) dont care
• Ex H110111 ? 1110111, 0110111 (2 strings)
• H11011
• 1010110,
• 1010111,
• 1110110,
• 1110111

H10 ??
8
Schema Theory

• Schema lengthd (H)
• the distance between the first and last specific
  string position
• Ex11011 ? d 6-1
• 110 ? d 5-3
• Schema order o(H)
• The number of none dont care positions
• Ex11011 ? o 5
• 110 ? o 3

9
Schema Theory
10
Schema Theory

• above average schemata receive exponentially
  increasing

11
Schema Theory

• Crossover vs. schema length
• H110
• H210
• The probability of destroying H1 and H2 is
• l7, d(H1)7-2 d(H1)5-4

12
Schema Theory

• Crossover vs. schema length

13
Schema Theory
14
Schema Theory

• Mutation vs. schema order
• H110
• H210
• The survival probability of H1 and H2 is
• l7, o(H1)2 o(H1)2

15
Schema Theory

• Short, lower, above average schemata receive
  exponentially increasing

16
Schema Theory

• Short, lower, above average schemata receive
  exponentially increasing

17
Schema Theory

• Short, lower, above average schemata receive
  exponentially increasing

18
Building Block Hypothesis

• According to the building-block hypothesis and
  schema analysis of Holland the GA is an efficient
  search method.
• Definition
• A GA seeks near-optimal performance through the
  combination of short, low-order, high-performance
  schemata, called blocks

19
Building Block Hypothesis

• crossover GA works well when short, low-order,
  highly fit schemas recombine to form even more
  highly fit, higher-order schemas.
• the ability to produce fitter and fitter partial
  solutions by combining blocks is believed to be
  the primary source of the GA's search power
• Unfortunately, when we come to examine the
  assumptions introduced by the building-block
  hypothesis, we find that they contradict those
  introduced by the schema theorem.

20
Building Block Hypothesis
21
GA Deceptive Problem (Type I)
ProblemsOptimal is 11
f(0)gtf(1) f(0)gtf(1) f11gtf01gtf00gtf10
22
GA Deceptive Problem (Type II)
ProblemsOptimal is 11
f(0)gtf(1) f(0)gtf(1) f11gtf00gtf01gtf10
23
GA Deceptive Problem
Solutions for Type II
24
GA-Hard Problems Royal Road
R1
Fitnessc1c2c8 Optimization value 64
25
GA-Hard Problems Royal Road
R2
Fitnessc1c2c8 Optimization value 192
26
GA-Hard Problems Royal Road

• Which problem GA performs better
• Settings
• Population size 128
• Length64
• Single-point crossover (probability is 0.7)
• Mutation probability is 0.006 per bit

27
GA-Hard Problems Royal Road
28
GA-Hard Problems Royal Road
Compare GA with hill-climbing schemes
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GA-Hard Problems Royal Road
Compare GA with hill-climbing schemes