1. Genetic algorithms Prof Kang Li

2. Last lecture
RBF
This Lecture
Genetic algorithm
Basic GA operations

3. Content What is Genetic Algorithm? How to implement GA? A example
Encoding
Selection
Crossover
Mutation
A example
Matlab demo
Differential evolution

4. What is Genetic Algorithm?
Bio-Inspired artificial intelligence class of probabilistic optimization algorithms
Well-suited for nonlinear/hard problems with a large search space
Influenced by Darwin’s Origin of species
Developed by John Holland， Adaptation in Natural and Artificial Systems, U of Michigan Press, 1975

5. Natural Selection (Darwin’s theory)
Genetic contents -> survival capacity -> features
Reproduction
recombination (or crossover) first occurs. Genes from parents combine to form a whole new chromosome.
Newly created offspring mutated, elements of DNA are changed.  Diversity
Survival of the fittest
Gene of the fittest survive, gene of weaker die out
Elitism
Evolution - change of species’ feature to fit environment

6. Natural Selection

7. Main idea
Produce a population of candidate solutions for a given problem
Use operators inspired by the mechanisms of natural genetic variation
Apply selective pressure toward certain properties
Evolve to a more fit solution

8. Nature to Computer Mapping
Population
Individual
Fitness
Chromosome
Gene
Set of solutions
Solution to a problem
Quality of a solution
Encoding for a Solution
Part of the encoding of a solution

10. Simple Genetic Algorithm
Simple_Genetic_Algorithm() { Initialize the Population; Calculate Fitness Function; While(the number of generation > maximum number) { Selection;//Natural Selection, Survival Of Fittest
Crossover;//Reproduction, Propagate favorable characteristics
Mutation;//Mutation
Calculate Fitness Function; } }

11. Structure of Genetic Algorithm
crossover 1
selection
Search
space 1 1
population A B C D
mutation
Fitness
evaluation 1
reproduction
Substitution

12. Genetic Algorithm Process
2017/4/23
Genetic Algorithm Process
Initial population
5th generation
10th generation

13. Applications of GA Difficult Problems such as NP-class
Nonlinear dynamical systems - predicting, data analysis
Designing neural networks, both architecture and weights
Robot Trajectory Planning
Evolving LISP programs (genetic programming)
Strategy planning
Finding shape of protein molecules
TSP and sequence scheduling
Functions for creating images
VLSI layout planning …

14. GA Process
Crossover
Selection
Encoding
Mutation

15. Encoding
The process of representing the solution in the form of a string that conveys the necessary information.
Just as in a chromosome, each gene controls a particular characteristics of the individual, and each bit in the string represents a characteristics of the solution.

16. Encoding Methods Binary Encoding
Most common method of encoding. Chromosomes are strings of 1s and 0s and a gene of chromosomes represents the a particular characteristics of the problem.
Chromosome B
Chromosome A

17. Encoding Methods (contd.)
Permutation Encoding
Useful in ordering problems such as the Traveling Salesman Problem (TSP). Example. In TSP, every chromosome is a string of numbers, each of which represents a city to be visited.
8  5  6  7  2  3  1  4  9
Chromosome B
1  5  3  2  6  4  7  9  8
Chromosome A

18. Encoding Methods (contd.)
Value Encoding
Used in problems where complicated values, such as real numbers, are used and where binary encoding would not suffice. Good for some problems, but often necessary to develop some specific crossover and mutation techniques for these chromosomes.
(left), (back), (left), (right), (forward)
Chromosome B
1.235  5.323  0.454  2.321  2.454
Chromosome A

19. Selection Based on fitness function:
Determines how ‘good’ an individual is (fitness)
Better fitness, higher probability of survival
Selection of individuals for differential reproduction of offspring in next generation
Favors better solutions
Decreases diversity in population B A C

20. Selection – Roulette Wheel
Each solution gets a region on a roulette wheel according to its fitness
Spin wheel, select solution marked by roulette-wheel pointer
stochastic selection (better fitness = higher chance of reproduction)
Individual i will have a
probability to be chosen

21. Selection - Tournament
randomly select q individuals from current population
Winner:
individual(s) with best fitness among these q individuals
Example:
select the best two individuals as parents for recombination
q=6
selection

22. Crossover Crossover is a critical feature of genetic algorithms:
Crossover process simulates the exchange of genetic material that occurs during biological reproduction
In this process pairs in the breeding population are mated randomly with a crossover rate, Pc
Typical crossover properties include that an offspring inherits the common feature from the parents along with the ability of the offspring to inherit two completely different features
Popular crossover techniques: one point, two point and uniform crossover
Chromosome A
Chromosome B
Chromosome A*
Chromosome B* …

23. Example-Bit string Crossover
Single point crossover
Two point Crossover = =

24. Bit string Crossover
Uniform crossover : bits are randomly copied from the parents =
if random-number > Crossover-rate then Crossover
otherwise remain unaltered

25. Mutation
Mutation consists of making small alterations to the values of one or more genes in a chromosome
Mutation randomly perturbs the population’s characteristics, and prevents evolutionary dead ends
Most mutations are damaging rather than beneficial and hence mutation rate must be low to avoid the destruction of species
It works by randomly selecting a bit with a certain mutation rate in the string and reversing its value 42 58
Offspring
Mutated Offspring

26. Fitness Function
A measure of how successful an individual is in the environment
Problem dependent
Given chromosome, the fitness function returns a number
f : S  R
Smooth and regular
Similar chromosomes produce close fitness values
Not have too many local extremes and isolated global extreme

27. Example（1） Finding the maximum of a function: f(x) = x²
Range [0, 31] Goal: find max (31² = 961)
Binary representation: string length 5 = 32 numbers (0-31)
= f(x)

28. Start Population Typical parameter values population size : 30 -100
crossover rate :
mutation rate : 1
00001
String 5
441 21
10101
String 4
100 10
01010
String 3 9 3
00011
String 2 36 6
00110
String 1
fitness
value
binary

29. Selection Worst one removed 1 00001 String 5 441 21 10101 String 4 100
01010
String 3 9 3
00011
String 2 36 6
00110
String 1
fitness
value
binary
6.13%
1.53%
17.04%
75.13%
0.17%
Worst one removed

30. Selection
Best individual: reproduces twice  keep population size constant 1
00001
String 5
441 21
10101
String 4
100 10
01010
String 3 9 3
00011
String 2 36 6
00110
String 1
fitness
value
binary

31. Selection All others are reproduced once 441 10101 String 5 21
100 10
01010
String 3 9 3
00011
String 2 36 6
00110
String 1
fitness
value
binary
All others are reproduced once

32. Crossover Parents and x-position randomly selected 1 1 1 1 1 1 1 1 1 12
String 4
String 3 4
String 2
String 1
x-position
partner
Parents and x-position randomly selected 1 1 1 1 1 6 7
String 1: 1 1 1
String 2: 3 23 1 1 1 1 1 10 21
String 3: 1 1 1 1 1
String 4: 21 17

33. Mutation bit-flip Offspring -String 1: 00111 (7) 10111 (23)

34. New population
All individuals in the parent population are replaced by offspring in the new generation
(generations are discrete!)
New population (Offspring):
binary
value
fitness
String 1
00111 7 49
String 2
10111 23
529
String 3
10101 21
441
String 4
10001 17
289
String 5
10101 21
441

35. End Iterate until termination condition reached, e.g.:
Number of generations
Best fitness
Process time
No improvements after a number of generations
Result after one generation:
Best individual: (23) – fitness 529
Best solution after 100 generation:
Best solution: (31) – fitness 961

36. When to Use a GA
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

37. Summary
Introduction to GA
Basic GA operations