Slide Presentation for ICS1020 and ICS1017

1. Foundations in AI
Introduction to Genetic Algorithms
Dr Vanessa Camilleri
Department of AI
October 2018

2. Overview
• Introduction
• GA Algorithm
• Components
• Examples
• Applications

3. Introduction
• Mimics Theory of Evolution
• GAs as a general purpose learning algorithm
• Solving a complex problem of problems
• Uses Natural Selection or Survival of the Fittest

4. Introduction
• Natural Selection:
variations in gene that
increases its chances of
survival

5. Introduction

6. Introduction

7. Introduction

8. Introduction
• NP (nondeterministic polynomial) Hard Problems
• cannot be solved in traditional way
• possible to guess the solution

9. Basic GA algorithm
1. [Start] Generate random population of n chromosomes (suitable solutions for the problem)
2. [Fitness] Evaluate the fitness f(x) of each chromosome x in the population
3. [New population] Create a new population by repeating following steps until the new population is
complete
1. [Selection] Select two parent chromosomes from a population according to their fitness (the
better fitness, the bigger chance to be selected)
2. [Crossover] With a crossover probability cross over the parents to form a new offspring (children).
If no crossover was performed, offspring is an exact copy of parents.
3. [Mutation] With a mutation probability mutate new offspring at each locus (position in
chromosome).
4. [Accept] Place new offspring in a new population
5. [Replace] Use new generated population for a further run of algorithm
6. [Test] If the end condition is satisfied, stop, and return the best solution in current population
[Loop] Go to step 2

10. {
initialize population;
evaluate population;
while TerminationCriteriaNotSatisfied
{
select parents for reproduction;
perform recombination and mutation;
evaluate population;
}
}

11. GA Cycle of Reproduction
Reproduction Modification
EvaluationPopulation
Discard
Children
Modified
Children
Evaluated
Children
Deleted
Members
Parents

12. GA Operators
1. Reproduction: aka selection operator, usually the first
operator applied on the population. Chromosomes are
selected from the population to cross over and produce
offspring
2. Crossover: After reproduction population is enriched
with better individuals.
3. Mutation: Happens after crossover, causing a random
change in the offspring.

13. Chromosomes could be:
– Bit strings (0101 ... 1100)
– Real numbers (43.2 -33.1 ... 0.0 89.2)
– Permutations of element (E11 E3 E7 ... E1 E15)
– Lists of rules (R1 R2 R3 ... R22 R23)
– Program elements (genetic programming)
– Any data structure ...

14. Crossover
Chromosome 1 11011 | 00100110110
Chromosome 2 11011 | 11000011110
Offspring 1 11011 | 11000011110
Offspring 2 11011 | 00100110110
Chromosome 1 1101100100110110
Chromosome 2 1101111000011110

15. Mutation
Original offspring 1 1101111000011110
Original offspring 2 1101100100110110
Mutated offspring 1 1100111000011110
Mutated offspring 2 1101101100110110

16. GA Parameters
• Solving the problem by finding the extreme of a function
• GA Parameters
• Crossover and Mutation Probability
• Population Size

17. GA: Selection
Roulette Wheel Selection Rank Selection
before
after
Steady State Selection
Elitism

18. GA: Encoding
• Binary Encoding
• example Knapsack problem
• Permutation Encoding
• example Travelling Salesman problem
Chromosome A 101100101100101011100101
Chromosome B 111111100000110000011111
Chromosome A 1 5 3 2 6 4 7 9 8
Chromosome B 8 5 6 7 2 3 1 4 9

19. GA: Encoding
• Value Encoding
• example finding weights
for neural network
• Tree Encoding
• example finding a function
from given values
Chromosome A 1.2324 5.3243 0.4556 2.3293 2.4545
Chromosome B ABDJEIFJDHDIERJFDLDFLFEGT
Chromosome C (back), (back), (right), (forward), (left)
Chromosome A Chromosome B
( + x ( / 5 y ) ) ( do_until step wall )

20. • Binary Encoding: Crossover
• Single Point Crossover
• Two Point Crossover
Crossover & Mutation
11001011+11011111 = 11001111
11001011 + 11011111 = 11011111

21. Crossover & Mutation
• Uniform Crossover
• Arithmetic Crossover
11001011 + 11011101 = 11011111
11001011 + 11011111 = 11001001 (AND)

22. Crossover & Mutation
• Mutation: Bit Inversion
11001001 => 10001001

23. • Permutation Encoding
• Crossover: Single Point Crossover
• Mutation: Order Changing
Crossover & Mutation
(1 2 3 4 5 6 7 8 9) + (4 5 3 6 8 9 7 2 1) = (1 2 3 4 5 6 8 9 7)
(1 2 3 4 5 6 8 9 7) => (1 8 3 4 5 6 2 9 7)

24. • Value Encoding
• Crossover: All crossovers from Binary Encoding can
be used
• Mutation: Adding
Crossover & Mutation
1.29 5.68 2.86 4.11 5.55) => (1.29 5.68 2.73 4.22 5.55)

25. • Tree Encoding
• Crossover: Tree Crossover
• Mutation: Changing operator, number
Crossover & Mutation

26. Example
Distribution of Individuals in Generation 0
Distribution of Individuals in Generation N

27. Example: Travelling
Salesman Problem
Problem Space: 30 cities

28. Example: Travelling
Salesman Problem
Solutioni [Distance=941]

29. Example: Travelling
Salesman Problem
Solutionj [Distance=800]

30. Example: Travelling
Salesman Problem
Solutionk [Distance=652]

31. Example: Travelling
Salesman Problem
Best Solution [Distance=420]

32. Applications of GAs
• GAs used to solve NP-hard
problems, but also for art,
evolving pictures and music
• In the first represented image,
a binary tree type of encoding
is used to generate the
images through mathematical
operations:
Source: [http://www.algosome.com/articles/genetic-algorithm-evolution-art.html]

33. Applications of GAs
• Data analysis
• Designing Neural Networks
• Robot trajectory
• Evolving LISP programs
• Strategy Planning
• Finding the shape of protein
molecules
• Sequence Scheduling
• Functions for creating images

34. Issues for GAs
• Choosing basic implementation issues:
• representation
• population size, mutation rate, ...
• selection, deletion policies
• crossover, mutation operators
• Termination Criteria
• Performance, scalability
• Solution is only as good as the evaluation function (often
hardest part)

35. Strengths of GAs
• Concept is easy to understand
• Modular, separate from application
• Supports multi-objective optimization
• Good for “noisy” environments
• Always an answer; answer gets better with time
• Inherently parallel; easily distributed

36. Strengths of GAs
• Many ways to speed up and improve a GA-based
application as knowledge about problem domain is
gained
• Easy to exploit previous or alternate solutions
• Flexible building blocks for hybrid applications
• Substantial history and range of use

37. When to use GAs
• Alternate solutions are too slow or overly complicated
• Need an exploratory tool to examine new approaches
• Problem is similar to one that has already been
successfully solved by using a GA
• Want to hybridize with an existing solution
• Benefits of the GA technology meet key problem
requirements

38. Time for class exercise …