1. Genetic Algorithms, Search Algorithms
Jae C. Oh

2. Overview
Search Algorithms
Learning Algorithms GA
Example

3. Brief History Evolutionary Programming Evolutionary Strategies
Fogel in 1960s
Individuals are encoded to be finite state machines
Intellgent Behavior
Evolutionary Strategies
Rechenberg, Schwefel in 1960s
Real-valued parameter optmization
Genetic Algorithms
Holland in 1960s
Adaptive Systems
Crossover Operators

4. Current Status Wide variety of evolutionary algorithms
No one seriously tries to distinguish them except for some cases and purposes.
We will call all Evolutionary Algorithms
And I will call them Genetic Algorithms or Evolutionary Algorithms for generic terms

5. Search

6. Search

7. Search

8. Notion of Search Space Real world problem Search space
Abstraction -> State Space
Exploring the state space for given problem  Search Algorithms
The Peak
Search Space

9. Learning Algorithms
Finding (through search) a suitable program, algorithm, function for a given problem
Learning Algorithm
Training Data
(Experience)
Program

10. Learning Algorithms (function Optimizations)
Problem instance
Set of Hypothesis
The One??
Hypothesis Space
Program Space
Function Space

11. Learning Algorithms (Digression)
How do we know the found hypothesis, program, function, etc. are the one we are looking for?
We don’t know for sure
Is there any mathematical way of telling how good hypothesis is?
I.e., |h(x) – f(x)| = ?
Computational Learning Theory can tell us this
Valiant (1984)

12. What are Genetic Algorithms?
Find solutions for a problem with the idea of evolution. Search and optimization techniques based on Darwin’s Principle of Natural Selection.
Randomized search and optimization algorithms guided by the principle of Darwin’s natural selection: Survival of fittest.
Evolve potential solutions
Step-wise refinement?
Mutations? Randomized, parallel search
Models natural selection
Population based
Uses fitness to guide search

13. Evolution is a search process
From the Tree of the Life Website, University of Arizona
Orangutan
Gorilla
Chimpanzee
Human

14. Evolution is parallel search
AAGACTT
AGGACTA
TGGACTT
AAGGCCT
TGGACTA
AGTGACCA
AGGGCAT
TAGCCCT
AGCACTT
AGGGCAA
CAGCACCA
AGCACTA
TAGCCCA
TAGACTT
AGCGCTT
AGCACAA
AGGGCAT
TCGCCCA
TAGGCCTA
AGTGCTA
AGTACAA
AAGGCAA

15. Genetic Algorithm Overview
Starting with a subset of n randomly chosen solutions ( )from the search space (i.e. chromosomes). This is the population
This population is used to produce a next generation of individuals by reproduction
Individuals with a higher fitness (| |)have more chance to reproduce (i.e. natural selection)

16. GA in Pseudo code 0 START : Create random population of n chromosomes
1 FITNESS : Evaluate fitness f(x) of each chromosome in the population
2 NEW POPULATION
0 SELECTION : Based on f(x)
1 RECOMBINATION : Cross-over chromosomes
2 MUTATION : Mutate chromosomes
3 ACCEPTATION : Reject or accept new one
3 REPLACE : Replace old with new population: the new
generation
4 TEST : Test problem criterium
5 LOOP : Continue step 1 – 4 until criterium is satisfied

17. GA vs. Specialized Alg. Genetic Algorithms (GAs) GA Efficiency
Specialized Algo.
Problems P
Specialized algorithms – best performance for special problems
Genetic algorithms – good performance over a wide range of problems

18. Randomized Algorithms
Guided random search technique
Uses the payoff function to guide search
Hill Climbing
local
optima
Global optima

19. Evolutionary Algorithms?
Search Algorithms?
Learning Algorithms?
Function Optimization Algorithms?
They are fundamentally the same!!

20. Things needed for GAs
How do we represent individuals? Domain Dependent
How do we interpret individuals? Domain Dependent
What is the fitness function? Domain Dependent
How are individual chosen for reproduction? Choose better individuals (probabilistic)
How do individuals reproduce? Crossover, Mutation, etc.
How is the next generation generated? Replace badly performing individuals

21. Encoding Methods 11111110000000011111 Chromosome B
Binary Encoding/Ternary Encoding
Chromosome B
Chromosome A
Permutation Encoding (TSP)
8  5  6  7  2  3  1  4  9
Chromosome B
1  5  3  2  6  4  7  9  8
Chromosome A
Real numbers, etc. Specialized
(left), (back), (left), (right), (forward)
Chromosome
1.235  5.323  0.454  2.321  2.454

22. Fitness Function
A fitness function quantifies the optimality of a solution (chromosome) so that that particular solution may be ranked against all the other solutions.
A fitness value is assigned to each solution depending on how close it actually is to solving the problem.
Ideal fitness function correlates closely to goal + quickly computable.
Example. In TSP, f(x) is sum of distances between the cities in solution. The lesser the value, the fitter the solution is

23. Producing Offspring
The process that determines which solutions are to be preserved and allowed to reproduce and which ones deserve to die out.
The primary objective of the recombination operator is to emphasize the good solutions and eliminate the bad solutions in a population, while keeping the population size constant.
“Selects The Best, Discards The Rest”.

24. Roulette Wheel Selection
Chromosome # Fitness 4 3 2 1
Spin
Strings that are fitter are assigned a larger slot and hence have a better chance of appearing in the new population.

25. GA in Action for 8-Queen

26. Minimum conflict fitness function.
Fitness for 8-Queen?
Minimum conflict fitness function.

27. Theory (Schema Theorem)
Substring where some positions left undecided
246*****
Instance of this schema:
Theorem: if the average of the instances the schema is above the mean fitness of the population, the number of instances of the schema will increase over time.

28. Applications Many many…
VLSI, TSP, Function Optimization, Data mining, security, etc.