1. Introduction to Genetic Algorithms
Son Kuswadi
Robotics and Automation Based on Biologically-Inspired Technology (RABBIT) Research Groups
Electronic Engineering Polytechnic Institute of Surabaya (EEPIS)
Institut Teknologi Sepuluh Nopember (ITS)

2. Road Map Basic Idea Quick Review Classes of Search Techniques
Simple GA
State of The Art

3. Road Map Basic Idea Quick Review Classes of Search Techniques
Simple GA
State of The Art

4. Basic Idea Suppose you have a problem You don’t know how to solve it
What can you do?
Can you use a computer to somehow find a solution for you?
This would be nice! Can it be done?

5. Basic Idea A dumb solution A “blind generate and test” algorithm:
Repeat
Generate a random possible solution
Test the solution and see how good it is
Until solution is good enough

6. Basic Idea Can we used this dumb idea? Sometimes - yes:
if there are only a few possible solutions
and you have enough time
then such a method could be used
For most problems - no:
many possible solutions
with no time to try them all
so this method can not be used

7. Basic Idea
Dumb Idea… but it was works…. M l h

8. Basic Idea A “less-dumb” idea (GA) Generate a set of random solutions
Repeat
Test each solution in the set (rank them)
Remove some bad solutions from set
Duplicate some good solutions
make small changes to some of them
Until best solution is good enough

9. How do you encode a solution?
Basic Idea
How do you encode a solution?
Obviously this depends on the problem!
GA’s often encode solutions as fixed length “bitstrings” (e.g , , )
Each bit represents some aspect of the proposed solution to the problem
For GA’s to work, we need to be able to “test” any string and get a “score” indicating how “good” that solution is

10. Silly Example - Drilling for Oil
Basic Idea
Silly Example - Drilling for Oil
Imagine you had to drill for oil somewhere along a single 1km desert road
Problem: choose the best place on the road that produces the most oil per day
We could represent each solution as a position on the road
Say, a whole number between [ ]

11. Basic Idea Where to drill for oil? 500 1000 Road Solution2 = 900
500
1000
Road
Solution2 = 900
Solution1 = 300

12. Basic Idea
Digging for Oil
The set of all possible solutions [ ] is called the search space or state space
In this case it’s just one number but it could be many numbers or symbols
Often GA’s code numbers in binary producing a bitstring representing a solution
In our example we choose 10 bits which is enough to represent

13. Convert to binary string
Basic Idea
Convert to binary string
512
256
128 64 32 16 8 4 2 1
900
300
1023
In GA’s these encoded strings are sometimes called “genotypes” or “chromosomes” and the individual bits are sometimes called “genes”

14. Basic Idea Drilling for Oil Solution1 = 300 (0100101100)
Road
1000
O I L 30 5
Location

15. Basic Idea We have seen how to:
represent possible solutions as a number
encoded a number into a binary string
generate a score for each number given a function of “how good” each solution is - this is often called a fitness function

16. Back to the (GA) Algorithm
Basic Idea
Back to the (GA) Algorithm
Generate a set of random solutions
Repeat
Test each solution in the set (rank them)
Remove some bad solutions from set
Duplicate some good solutions
make small changes to some of them
Until best solution is good enough

17. Replication and Mutation
Basic Idea
Replication and Mutation
Various method inspired by Darwinian evolution are used to update the set or population of solutions (or chromosomes)
Two high scoring “parent” bit strings or chromosomes are selected and combined
Producing two new offspring (bit strings)
Each offspring may then be changed randomly (mutation)

18. Basic Idea Selecting Parents
Many schemes are possible so long as better scoring chromosomes more likely selected
Score is often termed the fitness
“Roulette Wheel” selection can be used:
Add up the fitness's of all chromosomes
Generate a random number R in that range
Select the first chromosome in the population that - when all previous fitness’s are added - gives you at least the value R

19. Road Map Basic Idea Quick Review Classes of Search Techniques
Simple GA
State of The Art

20. Quick Review A class of probabilistic optimization algorithms
Inspired by the biological evolution process
Uses concepts of “Natural Selection” and “Genetic Inheritance” (Darwin 1859)
Originally developed by John Holland (1975)
Particularly well suited for hard problems where little is known about the underlying search space
Widely-used in business, science and engineering

21. Quick Review Typically applied to: Attributed features:
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

22. Quick Review
Holland’s original GA is now known as the simple genetic algorithm (SGA)
Other GAs use different:
Representations
Mutations
Crossovers
Selection mechanisms

23. Road Map Basic Idea Quick Review Classes of Search Techniques
Simple GA
State of The Art

24. Classes of Search Techniques
Search Techniqes
Calculus Base Techniqes
Enumerative Techniqes
Guided random search techniqes
Sort
Dynamic Programming
Fibonacci
DFS
BFS
Evolutionary Algorithms
Tabu Search
Hill Climbing
Simulated Anealing
Genetic Programming
Genetic Algorithms

25. References
C. Darwin. On the Origin of Species by Means of Natural Selection; or, the Preservation of flavored Races in the Struggle for Life. John Murray, London, 1859.
W. D. Hillis. Co-Evolving Parasites Improve Simulated Evolution as an Optimization Procedure. Artificial Life 2, vol 10, Addison-Wesley, 1991.
J. H. Holland. Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor, Michigan, 1975.
Z. Michalewicz. Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, Berlin, third edition, 1996.
M. Sipper. Machine Nature: The Coming Age of Bio-Inspired Computing. McGraw-Hill, New-York, first edition, 2002.
D. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison Wesley, 1989

26. Road Map Basic Idea Quick Review Classes of Search Techniques
Simple GA
State of The Art

27. Simple GA produce an initial population of individuals
evaluate the fitness of all individuals
while termination condition not met do
select fitter individuals for reproduction
recombine between individuals
mutate individuals
evaluate the fitness of the modified individuals
generate a new population
End while

28. The Evolutionary Cycle
parents
selection
modification
modified
offspring
initiate &
population
evaluation
evaluate
evaluated offspring
deleted
members
discard

29. Simple Example (Goldberg98)
Simple problem: max x2 over {0,1,…,31}
GA approach:
Representation: binary code, e.g  13
Population size: 4
1-point xover, bitwise mutation
Roulette wheel selection
Random initialization
We show one generational cycle done by hand

30. Selection

31. Crossover

32. Mutation

33. Simple GA Has been subject of many (early) studies
still often used as benchmark for novel GAs
Shows many shortcomings, e.g.
Representation is too restrictive
Mutation & crossovers only applicable for bit-string & integer representations
Selection mechanism sensitive for converging populations with close fitness values

34. Road Map Basic Idea Quick Review Classes of Search Techniques
Simple GA
State of The Art

35. State of The Art Crossover: Alternative Operators
Crossover vs Mutation
Other Representation: Gray coding, integer, floating point
Binary Representation: Required Precision Set

36. Crossover – Alternative Operators
Performance with 1 Point Crossover depends on the order that variables occur in the representation
more likely to keep together genes that are near each other
Can never keep together genes from opposite ends of string
This is known as Positional Bias
Can be exploited if we know about the structure of our problem, but this is not usually the case

37. Crossover – Alternative Operators
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)

38. Crossover – Alternative Operators
Uniform crossover
Assign 'heads' to one parent, 'tails' to the other
Flip a coin for each gene of the first child
Make an inverse copy of the gene for the second child
Inheritance is independent of position

39. Crossover vs 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, xover-only-EA would not work

40. Crossover vs Mutation
Exploration: Discovering promising areas in the search space, i.e. gaining information on the problem
Exploitation: Optimising within a promising area, i.e. using information
There is co-operation AND competition between them
Crossover is explorative, it makes a big jump to an area somewhere “in between” two (parent) areas
Mutation is exploitative, it creates random small diversions, thereby staying near (in the area of ) the parent

41. Crossover vs Mutation
Only crossover can combine information from two parents
Only mutation can introduce new information (alleles)
To hit the optimum you often need a ‘lucky’ mutation

42. Other Representation
Gray coding of integers (still binary chromosomes)
Gray coding is a mapping that means that small changes in the genotype cause small changes in the phenotype (unlike binary coding). “Smoother” genotype-phenotype mapping makes life easier for the GA
Nowadays it is generally accepted that it is better to encode numerical variables directly as:
Integers
Floating point variables

43. Integer Representation
Some problems naturally have integer variables, e.g. image processing parameters
Others take categorical values from a fixed set e.g. {blue, green, yellow, pink}
N-point / uniform crossover operators work
Extend bit-flipping mutation to make
“creep” i.e. more likely to move to similar value
Random choice (esp. categorical variables)
For ordinal problems, it is hard to know correct range for creep, so often use two mutation operators in tandem

44. Floating Point Representation
Many problems occur as real valued problems, e.g. continuous parameter optimisation f :  n  
Illustration: Ackley’s function (often used in EC)

45. Binary Representation
For example, search space x [-1..2], with six places after decimal point
Therefore 3x equal size ranges
This means that 22 bit are required since:
=221 < <222=

46. Binary Representation
Mapping from binary string <b21b20…b0> into a real number x from range [-1..2]:
convert the binary string <b21b20…b0> from the base 2 to base 10:
find a corresponding real number x: