Genetic Algorithms

1
Genetic Algorithms

• Introduction
• Advanced

2
Simple Genetic Algorithms Introduction

• What is it?
• In a Nutshell
• References
• The Pseudo Code
• Illustrations
• Applications
• Chinese Version of Introduction

3
Simple Genetic Algorithms Illustrations

• An Illustration Based on Portfolio Optimization
• An Illustration Based on Facial Mask Design

4
Simple Genetic Algorithms Applications

• Portfolio Optimization

5
Genetic Algorithms Advanced

• Theory
• Variants of Genetic Algorithms
• Genetic Algorithms and Other Machine Learning
  Tools

6
Variants of Genetic Algorithms

• Adaptive Genetic Algorithms (AGA)
• Niching Genetic Algorithms (NGA)
• Interactive Genetic Algorithms (IGA)
• Adaptive Genetic Algorithms

7
Father of GAs

• Genetic algorithms were originally developed by
  Holland (1975).
• They are a class of adaptive search and
  optimization techniques based on an evolutionary
  process.

8
Chromosomes

• By representing potential or candidate solutions
  to a problem using vectors consisting of binary
  digits or bits, mathematical operations known as
  crossover and mutation, can be performed.
• These operations are analogous to the genetic
  recombinations of the chromosomes in living
  organisms.

9
Genetic Operation

• By performing these operations, generations of
  new candidates can be created and evolved over
  time through an iterative procedure.
• However, there do exist restrictions on the
  process of crossover so as to ensure that better
  performing candidates are evolved over time.

10
What is it?

• Similar to the theory of natural selection or
  survival of the fittest, the better performing
  candidates have a better than average
  probability of surviving and reproducing relative
  to the lower performing candidates which
  eventually get eliminated from the population.

11
Fitness Function and Selection

• The performance of each candidate can be assessed
  using a suitable objective function.
• A selection process based on performance is
  applied to determine which of the candidates
  should participate in crossover, and thereby pass
  on their favorable traits to future generations.

12
Process of Improvement

• It is through this process of survival of the
  fittest'' that better solutions are developed
  over time.
• This evolutionary process continues until the
  best (or better) performing individual(s),
  consisting of hopefully the optimal or near
  optimal solutions, dominate the population.

13
Binary Strings

• Binary representation is convenient but not
  necessary for the application of the
  recombination operations.
• These vectors also known as strings, are linear
  combinations of zeros and ones, for example 0 1
  0 0 1.

14
An Example

• A binary representation
• is based on the binary number system which
  has a corresponding equivalent decimal value
  given by

15
An Example

• For example, the decimal equivalent of the vector
  0 1 0 0 1 is
• 8 1 9

16
Selection Method

• Rank-Based Selection
• Roulette-Wheel Selection
• Tournament Selection

17
Rank-Based Selection

• The Reference
• The Procedure

18
Reference

• Whitley D. (1989), The GENITOR Algorithm and
  Selection Pressure Why Rank-Based Allocation of
  Reproductive Trials is Best, in D. J.
  Schaffer (ed.) Proceedings of the Third
  International Conference on Genetic Algorithms,
  Morgan Kaufmann, San Mateo, pp.116--121.

19
The Procedure

• This approach involves ranking all candidates
  according to performance and then replacing the
  worst performing candidates by copies of the
  better performing candidates.

20
Crossover

• The method by which promising (better performing)
  candidates are combined, is through a process of
  binary recombination known as crossover.
• One-Point Crossover

21
One-Point Crossover

• To illustrate the process of crossover, assume
  that two vectors
• are chosen at random and that the position of
  partitioning is randomly chosen to be between
  the second and third elements of each vector.

A 1 0 1 0 0
B 0 1 0 1 0
22
A 1 0 1 0 0
B 0 1 0 1 0
C 1 0 0 1 0
D 0 1 1 0 0
C 1 0 0 1 0
D 0 1 1 0 0
23
Mutation

• Mutation involves the introduction of random
  shocks into the population, by slightly altering
  the binary representation of candidates.
• This increases the diversity in the population
  and unlike crossover, randomly re-directs the
  search procedure into new areas of the solution
  space which may or may not be beneficial.

24
Mutation

• This action underpins the genetic algorithms
  ability to find novel inconspicuous solutions and
  avoid being anchored at local optimum solutions.
• Mathematically, this operation is represented by
  switching a binary digit from a one to a zero or
  vice versa.

25
Mutation

• However, the probability of this occurrence is
  normally very low, so as to not unnecessarily
  disrupt the search process.
• This operation can be illustrated by an example.

26
An Example

• Assume that the third element in vector C
  undergoes mutation.

C 1 0 0 1 0
E 1 0 1 1 0
27

• The genetic algorithm procedure can be summarized
  by the following steps
• Create an initial population of candidates
  randomly.
• Evaluate the performance of each candidate.
• Select the candidates for recombination.
• Perform crossover and mutation.
• Evaluate the performance of the new candidates.
• Return to step 3, unless a termination criterion
  is satisfied.

28
Termination Criteria

• The last step in the genetic algorithm involves
  checking a well-defined termination criterion.
• The termination criterion adopted, is satisfied
  when either one of the following conditions is
  met

29
Termination Criteria

• The population converges to a unique individual.
• A predetermined maximum number of generations is
  reached.
• There has been no improvement in the population
  for a certain number.

30
In a Nutshell

• The genetic algorithms, first proposed by Holland
  (1975), seek to mimic some of the natural
  evolution and selection.
• The first step of Hollands genetic algorithm is
  to represent a legal solution of a problem by a
  string of genes known as a chromosome.

31
In a Nutshell

• Then an initial population of chromosome is
  generated randomly at the first generation.
• At each generation, the fitness of each
  chromosome in the population is evaluated by a
  fitness function.

32
In a Nutshell

• The chromosomes with higher fitness have a higher
  possibility to be selected to produce offspring
  for the next generation.
• After many generations of evolution, the optimal
  solution of the problem is hopefully be found in
  the population.

33
Goldberg (1989)

• Goldberg D. E. (1989), Genetic Algorithms in
  Search, Optimisation, and Machine Learning.
  Addison-Wesley, Reading.

34
Michalewicz (1996)

• Michalewicz, Z. (1996), Genetic Algorithms Data
  Structures Evolution Programs, Springer.

35
Vose (1999)

• Vose M. D. (1999), The Simple Genetic Algorithm
  Foundations and Theory (Complex Adaptive
  Systems). Bradford Books

36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39
(No Transcript)
40
(No Transcript)
41
(No Transcript)
42
Genetic Algorithms and Other Machine Learning
Tools

• Simulated Annealing

43
(No Transcript)