1. Evolutionary Computational Intelligence
Lecture 3:
Genetic Algorithms
Ferrante Neri
University of Jyväskylä
Lecture 3: Genetic Algorithms

2. Lecture 3: Genetic Algorithms
GA Quick Overview
Developed: USA in the 1970’s
Early names: J. Holland, K. DeJong, D. Goldberg
Typically applied to:
discrete optimization
Attributed features:
not too fast
good heuristic for combinatorial problems
Special Features:
Traditionally emphasizes combining information from good parents (crossover)
many variants, e.g., reproduction models, operators
Lecture 3: Genetic Algorithms

3. Lecture 3: Genetic Algorithms
Holland’s original GA is now known as the simple genetic algorithm (SGA)
Other GAs use different:
Representations
Mutations
Crossovers
Selection mechanisms
Lecture 3: Genetic Algorithms

4. Lecture 3: Genetic Algorithms
GAs in EAs
Representation
Binary strings
Recombination
N-point or uniform
Mutation
Bitwise bit-flipping with fixed probability
Parent selection
Fitness-Proportionate
Survivor selection
All children replace parents
Speciality
Emphasis on crossover
Lecture 3: Genetic Algorithms

5. Lecture 3: Genetic Algorithms
Representation
A chromosome is encoded as a binary number
Due to the inner discretization of the binary encoding GA can turn out more efficient in discrete optimization
Lecture 3: Genetic Algorithms

6. Representation in the population
Thus a population of couple (L,b) can be seen as a matrix of binary numbers
Each line is a chromosome 1
Lecture 3: Genetic Algorithms

7. Parent Selection Mechanisms
The individuals that are undergoing recombination are selected by means of a Selection Mechanism
Classical selection mechanisms are
Fitness Proportionate
Ranking
Tournament
Lecture 3: Genetic Algorithms

8. Fitness Proportionate Selection
It is the first one used in SGA
It is given a probability to be chosen to each solution
Such probability is proportionate to the fitness value taken by each single solution
The sum of the probabilities is clearly one
A random number between 0 and 1 is sampled and in a “roulette stile” the individual is selected
Lecture 3: Genetic Algorithms

9. Lecture 3: Genetic Algorithms
Ranking Selection 1/2
Individuals are sorted accoding to their fitness value and a probability is assigned according to their position in the list (rank)
Then, the a probability is assigned to each solution by means of:
Linear Ranking
Exponential Ranking
Lecture 3: Genetic Algorithms

10. Lecture 3: Genetic Algorithms
Ranking Selection 2/2
Linear: if 1.0 < s  2.0 and μ is the total number of ranks, the probability for the individual ranked i is
Exponential: if c is a normalize constant factor which allows the sum of all the probabilities being equal to 1, the probability of the individual ranked i is
Lecture 3: Genetic Algorithms

11. Lecture 3: Genetic Algorithms
Tournament Selection
Pick up a couple of solutions (at random) and compare their fitness, the better individual is in the mating pool
It can work also with groups of individuals picking up a subset of them
It does not require a sorting or a knowledge of the fitness distribution over the individuals of the population
Lecture 3: Genetic Algorithms

12. Lecture 3: Genetic Algorithms
Selection Pressure
It’s the property of the selection component in following the promising search directions
In other words, a parent selection mechanism which selects the best individuals many times has a high selection pressure
In linear ranking ruled by s
Lecture 3: Genetic Algorithms

13. Lecture 3: Genetic Algorithms
Crossover
The selected parents undergo recombination
In a SGA, the recombination is the crossover
Crossover is an operator which combines two parents in order to produce one, two or more offspring
The analogy of biological crossover in binary encoding is very straightforward
Lecture 3: Genetic Algorithms

14. Lecture 3: Genetic Algorithms
1-point crossover
It’s the original crossover employed by Holland
It selects a random “cut-point” and switch head and tail of two chromosomes
Lecture 3: Genetic Algorithms

15. Lecture 3: Genetic Algorithms
n-point crossover
Choose n random crossover points
Split along those points
Glue parts, alternating between parents
Generalisation of 1 point (still some positional bias)
Lecture 3: Genetic Algorithms

16. Lecture 3: Genetic Algorithms
Uniform crossover
Usually it is performed by means of a randomly generated mask
This mask says which genes must be flipped for generating the first child
Make an inverse copy of the gene for the second child
Lecture 3: Genetic Algorithms

17. Lecture 3: Genetic Algorithms
Mutation
It is usually applied to the newly generated offspring before calculating its fitness value
Alter each gene independently with a probability pm
pm is called the mutation rate
Typically between 1/pop_size and 1/ chromosome_length
Lecture 3: Genetic Algorithms

18. Lecture 3: Genetic Algorithms
Crossover OR mutation?
Decade long debate: which one is better / necessary / main-background
Answer (at least, rather wide agreement):
it depends on the problem, but
in general, it is good to have both
both have another role
mutation-only-EA is possible, crossover-only-EA seems not to work
Lecture 3: Genetic Algorithms

19. Lecture 3: Genetic Algorithms
Survivor Selection
In this course the main feature of a GA is that the algorithm must be generational (also called age-based)
In other words, the parents must be replaced by the newly generated offspring
Some implementation employ elitism: a restricted number of parents, the best, are copied for the subsequent generation
Lecture 3: Genetic Algorithms

20. Lecture 3: Genetic Algorithms
Generation
The loop made up of parent selection, recombination (crossover) mutation, survivor selection is called generation
Lecture 3: Genetic Algorithms

21. Other representations
Gray coding of integers (still binary chromosomes)
The distance between two subsequent decimal numbers is one bit (unlike binary coding).
Integers
Floating point variables
Lecture 3: Genetic Algorithms

22. Integer representations
Some problems naturally have integer variables, e.g. TSP, scheduling problems
Crossover and mutation are similar as in the case of binary encoding
N-point crossover can be applied
Lecture 3: Genetic Algorithms

23. Perturbating mutation
It picks up a small subset of genes
Adds (subtracts) a small quantity to the selected genes
It must be assured that this operation does not generate a perturbed individual outside the decision space
Lecture 3: Genetic Algorithms

24. Lecture 3: Genetic Algorithms
Swap mutation
Pick two alleles at random and swap their positions
Preserves most of adjacency information (4 links broken), disrupts order more
Lecture 3: Genetic Algorithms

25. Lecture 3: Genetic Algorithms
Insert Mutation
Pick two allele values at random
Move the second to follow the first, shifting the rest along to accommodate
Note that this preserves most of the order and the adjacency information
Lecture 3: Genetic Algorithms

26. Inversion mutation for permutations
Pick two alleles at random and then invert the substring between them.
Preserves most adjacency information (only breaks two links) but disruptive of order information
Lecture 3: Genetic Algorithms

27. Scramble mutation for permutations
Pick a subset of genes at random
Randomly rearrange the alleles in those positions
(note subset does not have to be contiguous)
Lecture 3: Genetic Algorithms

28. Crossovers for integer representation
It exists a plenty of crossovers designed for several applications
Order 1 crossover
Partially mapped crossover
Cycle crossover
Edge crossover
Lecture 3: Genetic Algorithms

29. Real Encoded Representation
The original EA with real encoding was Evolution Strategies
Nevertheless in 80’s several real encoded GAs were designed
Details will be shown at the next lecture…..
Lecture 3: Genetic Algorithms