Introduction to Genetic Algorithms

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Introduction to Genetic Algorithms
2
Genetic Algorithms

• Weve covered enough material that we can write
  programs that use genetic algorithms!
• More advanced example of using arrays
• Could be better written in most cases using
  objects

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Evolution in Computers

• Genetic Algorithms most widely known work by
  John Holland
• Based on Darwinian Evolution
• In a competitive environment, strongest, most
  fit of a species survive, weak die
• Survivors pass their good genes on to offspring
• Occasional mutation

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Evolution in Computers

• Same idea as Darwinian Evolution
• Population of computer program / solution treated
  like biological organisms in a competitive
  environment
• Computer programs / solutions typically encoded
  as a bit string
• Survival Instinct have computer programs
  compete with one another in some environment,
  evolve with mutation and sexual recombination

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The Simple Genetic Algorithm

1. Generate an initial random population of M
   individuals (i.e. programs or solutions)
2. Repeat for N generations
3. Calculate a numeric fitness for each individual
4. Repeat until there are M individuals in the new
   population
5. Choose two parents from the current population
   probabilistically based on fitness
6. Cross them over at random points, i.e. generate
   children based on parents
7. Mutate with some small probability
8. Put offspring into the new population

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Crossover
Bit Strings Genotype representing some
phenotype Individual 1 001010001 Individual
2 100110110 New child 100110001 has
characteristics of both parents, hopefully
better than before
Bit string can represent whatever we want for our
particular problem solution to a complex
equation, logic problem, classification of some
data, aesthetic art, music, etc.
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Chromosome Examples
Node 1 Node 2 Node 3 Output 1
0 6 53 0 2 15 23 3 2 14 129 3 2 1
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Chromosome Examples
Gen 3 AFFFAF-FF-AFFF Gen 5
AFFFAF-FF-F-FF-FFA- Gen 7 A
FFF-FAF-AAF-F-AF
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Code Trees
Samples for Computer Ant
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Code Trees - Crossover
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Program Example

• The Traveling Salesman Problem (TSP)
• Member of a class of problems called NP-Complete
• Hard problems with no known polynomial time
  solution, only exponential time
• Other NP problems map to a NP-Complete problem in
  polynomial time, suggesting these are the hardest
  problems in the class
• NP-Complete problems are good candidates for
  applying genetic algorithms and approximation
  techniques
• Problem space too large to solve exhaustively
• Generally not guaranteed to solve the problem
  optimally

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• Formal definition for the TSP
• Start with a graph G, composed of edges E and
  vertices V, e.g. the following has 5 nodes, 7
  edges, and costs associated with each edge
• Find a loop (tour) that visits each node exactly
  once and whose total cost (sum of the edges) is
  the minimum possible

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15
6
1
7
5
3
13

• Easy on the graph shown on the previous slide
  becomes harder as the number of nodes and edges
  increases
• Adding two new edges results in five new paths to
  examine
• For a fully connected graph with n nodes, n!
  loops possible
• Impractical to search them all for more than
  about 25 nodes
• Excluding degenerate graphs, an exponential
  number of loops possible in terms of the number
  of nodes/edges

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15
4
6
1
3
7
5
3
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• 29 Node Traveling Salesperson Problem
• 29! 8.8 trillion billion billion possible
  asymmetric routes.
• ASCI White, an IBM supercomputer being used by
  Lawrence Livermore National Labs to model nuclear
  explosions, is capable of 12 trillion operations
  per second (TeraFLOPS) peak throughput
• Assuming symmetric routes, ASCI White would take
  11.7 billion years to exhaustively search the
  solution space

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• Genetic algorithms approximation for a solution
• Randomly generate a population of agents
• Each agent represents an entire solution, i.e. a
  random ordering of each node representing a loop
• Given nodes 1-6, we might generate 423651 to
  represent the loop of visiting 4 first, then 2,
  then 3, then 6, then 5, then 1, then back to 4
• Assign each agent a fitness value
• Fitness is just the sum of the edges in the loop
  lower is more fit
• Evolve a new, hopefully better, generation of the
  same number of agents
• Select two parents randomly, but higher
  probability of selection if better fitness
• New generation formed by crossover and mutation

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• Crossover
• Must combine parents in a way that preserves
  valid loops
• Typical cross method, but invalid for this
  problem
• Parent 1 423651 Parent 2 156234
• Child 1 423234 Child 2 156651
• Use a form of order-preserving crossover
• Parent 1 423651 Parent 2 156234
• Child 1 123654
• Copy positions over directly from one parent,
  fill in from left to right from other parent if
  not already in the child
• Mutation
• Randomly swap nodes (may or may not be neighbors)

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• Run the program!
• Describe major components of the code
• If youre interested in more about genetic
  algorithms, there is a ton of information if you
  google genetic algorithms

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TSP Genetic Algorithm

• Cities
• Two arrays, holding X and Y coordinates of each
  city. 40 cities initially.
• Dim cityX(NUMCITIES - 1) As Integer
• Dim cityY(NUMCITIES - 1) As Integer
• Chromosome
• For each individual (initially 200 random ones)
  it is a list of all the cities we visit (0 to
  NUMCITIES-1), in order
• e.g.
• population(0,0) first city individual 0 visits
• population(0,1) second city individual 0 visits
• population(0,2) third city individual 0 visits
• population(0,NUMCITIES-1) last city individual
  0 visits
• population(1,0) first city individual 1 visits
• population(1,1) second city individual 1 visits
• etc.
• Dim population(POPSIZE - 1, NUMCITIES - 1)

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Chromosome Example
10 30 15 50 75
50 60 15 95 35
cityX
cityY
0 1 2 3 4
0 1 2 3 4
Means individual 0 visits cities 0,3,4,2,1 at
coordinates (10,50), (50,95), (75,35), (15,15),
(30,60) then back to (10,50)
population
0 3 4 2 1
4 3 2 1 0
1 3 4 2 0
3 2 1 4 0
Individual 0
Individual 1
Individual 2
Individual 3
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TSP Genetic Algorithm

• Uses crossover and mutation described on previous
  slide
• Fitness is distance for each individual
• Hard-coded to run 1000 generations, display the
  individual that has the shortest path each
  generation