1. Genetic Algorithms

2. Idea 5: genetic algorithms
Start with a set of k states Rather than pick from these, create new states by combining states Maintain a “population” of states

3. Idea 5: genetic algorithms
Start with a set of k states Rather than pick from these, create new states by combining states Maintain a “population” of states
Inspired by the biological evolution process
Uses concepts of “Natural Selection” and “Genetic Inheritance” (Darwin 1859)
Originally developed by John Holland (1975)

4. The Algorithm Randomly generate an initial population.
Repeat the following:
Select parents
based on fitness
“reproduce” offspring/next generation
Use crossover + mutation
Evaluate the fitness of the new generation
Discard old generation

5. Genetic Algorithm Crossover
Parent 1
Parent 2
Child 1
Child 2

6. Genetic Algorithm Mutation
Parent 1
Parent 2
Child 1
Mutation
Child 2

7. A Simple Example Goal: Find the binary string 11010010
String can represent a solution to a problem

8. Step 0: Initialization
Start with 5 random binary strings of target length

9. Step 1: Choose Parents (Apply Fitness Function)
Good measure of fitness? (Lower the better).

10. Step 1: Choose Parents (Apply Fitness Function)
Good measure of fitness? (Lower the better).
Negation of: the sum of the differences of digits between string and target.
Target:
fitness( ) =
– ( ) = –3

11. Step 1: Choose Parents (Apply Fitness Function)
The target:
fitness( )= –3
fitness( )= –3
fitness( )= –5
fitness( )= –4
fitness( )= –2

12. Step 1: Choose Parents (based on fitness)
Choose a constant number of parents
Higher the fitness, greater the probability of being chosen
fitness( )= –3
fitness( )= –3
fitness( )= –5
fitness( )= –4
fitness( )= –2

13. Step 1: Parent Selection
Get pairs of parents:
fitness( )= –3
fitness( )= –3
fitness( )= –5
fitness( )= –4
fitness( )= –2

14. Step 2: Reproduce Offspring (Crossover)
Randomly choose a crossover point (ex. 3)
Perform crossover on all pairs of parents
010| |11011
101| |10011

15. Step 2: Reproduce Offspring (Mutation)
For each digit in the offspring string, with low probability (ex. .04), flip the bit) 
New offspring:

16. Step 3: Evaluate New Fitnesses
Target:
f( ) = – 3
f( ) = – 2
f( ) = – 3
f( ) = – 3

17. Step 3: Evaluate New Fitnesses
Target:
f( ) = – 3
f( ) = – 2
f( ) = – 3
f( ) = – 3
Previous generation:
f( )= –3
f( )= –3
f( )= –5
f( )= –4
f( )= –2

18. Repeat Repeat for multiple “generations” until some stopping criterion
When target is “Hello World”, target achieved after 65 generations

19. Genetic Algorithm for 8-Queens?

20. Genetic Algorithm for 8-Queens?
Binary string of length 64

21. Genetic Algorithm for 8-Queens?
Binary string of length 64: … Each substring of length 8 is the row # of a queen

22. Genetic Algorithm for 8-Queens?
Binary string of length 64: … Each substring of length 8 is the row # of a queen We want the entire string to match a target (target = board with no attacking queens)

23. Genetic Algorithm for 8-Queens
fitness(state) = # of queens that can be attacked
fitness(state) = 8
fitness(state) = 7

24. After Crossover fitness(state) = # of queens that can be attacked

25. Genetic Algorithm to solve TSP
Traveling Salesperson Problem:
Given a list of cities, find the lowest-cost path that visits every city exactly once (and returns to the start)
NP-hard