Introduction to Genetic Algorithms and Evolutionary Computation

1
Introduction to Genetic Algorithms and
Evolutionary Computation

• Andrew L. Nelson
• Visiting Research Faculty
• University of South Florida

2
Overview

• Outline to the left
• Current topic in red
• Introduction
• Algorithm Formulation
• Example
• Case Study

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

3
References

• Holland, J. J., Adaptation in Natural and
  Artificial Systems, University of Michigan Press,
  Ann Arbor Michigan, 1975.
• D.B. Fogel, Evolutionary Computation, Toward a
  New Philosophy of Machine Intelligence, 2nd Ed.,
  IEEE Press, Piscataway, NJ, 2000.
• M. Mitchell, An Introduction to Genetic
  Algorithms, The MIT Press, Cambridge,
  Massachusetts, 1998.

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

4
Introduction

• Genetic Algorithms
• Base on Natural Evolution
• Stochastic Optimization
• Stochastic Numerical Techniques
• Evolutionary Computation
• Artificial Life
• Machine Learning
• Artificial Evolution

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

5
Introduction

• Population of candidate solutions
• Evaluate the quality of each solution
• Survival (and reproduction) of the fittest
• Crossover and Mutation

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

6
Sample Application Domain

• Finding the best path between two points in "Grid
  World"
• Creatures in world
• Occupy a single cell
• Can move to neighboring cells
• Goal Travel from the gray cell to the green cell
  in the shortest number of steps

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

7
Algorithm Formulation

• Components of a Genetic Algorithm
• Genome
• Fitness metric
• Stochastic modification
• Cycles of generations
• Many variations

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

8
Genome

• The genome is used represent candidate solutions
• Fixed length Bitstrings
• Holland
• Traditional
• Convergence theorems exist
• Real-valued genomes
• Artificial evolution
• Difficult to prove convergence

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

9
Genome

• Example Representation of a path through a
  square maze
• Representation N00, E10, S11,W01

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

10
Population

• Population, P is made up of individuals pn where
  N is the population size

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

11
Fitness Function

• F(p) called Objective Function
• Example Shortest legal path to goal
• F(pn) S(steps)

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

12
Selection

• Selection Methods of selection of the parents of
  the next generation of candidate solutions
• Diverse methods
• Probabilistic
• Chance of be selected is proportional to fitness
• Greedy
• the fittest solutions are selected

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

13
Propagation

• The next generation is generated from the fittest
  members of the current population
• Genetic operators
• Crossover (recombination)
• Mutation

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

14
Propagation Crossover

• Example 1 point crossover
• Two parents generate 1 offspring

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

15
Propagation Mutation

• Example Bitstring point mutation
• Replace randomly selected bits with their
  complements
• One parent generates one offspring

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

16
Worked Example

• World size
• 4X4
• Population size
• N 4
• Genome
• 16 bits
• Fitness
• F(p) (8-Steps before reaching goal)
  (squares from goal)
• Propagation Greedy, Elitist

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

17
Ex Initial Population

• Initial Population P(0) 4 random 16-bit strings

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

18
Ex Fitness Calculation

• Fitness calculations
• F(p1) (8-8) 4 -4
• F(p2) -5
• F(p3) -6
• F(p4) -4

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

19
Ex Selection and Propagation

• Select p1 and p4 as parents of the next
  generation, P(1)
• Produce offspring using crossover and mutation

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

20
Ex Book Keeping...

• The next generation is...

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

21
Ex Repeat for next Generation

• Repeat
• F(p1) -4
• F(p2) -4
• F(p3) 0
• F(p4) -4

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

22
Case Study

• References
• Introduction
• Sample Application
• Formulation
• Genome
• Population
• Fitness Function
• Selection
• Propagation
• Worked Example
• Case Study Evolving Neural Controllers

• Evolution of neural networks for autonomous robot
  control using competitive relative fitness
  evaluation