Genetic Programming

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Genetic Programming

• Using Simulated Natural Selection to
  Automatically Write Programs

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Genetic Programming

• John Koza, Stanford University
• Principal proponent of GP
• Has obtained human-competitive results in a
  number of problem domains
• Reproduced existing patents
• Created new patentable designs
• Has written extensively on GP
• Four volume set on Genetic Programming
• Numerous papers on the GP

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Genetic Programming

• Basic Algorithm
• Create a population of programs
• Each program attempts to solve a set of problems
  in a training set.
• Program fitness is determined by success in
  solving training set
• More fit members have better chance to produce
  offspring in the next generation
• Offspring are produced using some form of
  crossover

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Tree Structure of Genetic Programs

• Various structures are used to represent genetic
  programs, but tree structures are the most well
  known.
• Nonterminal nodes are functions that take their
  children as parameters.

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1
5
Tree Structure

• Terminal Nodes, the nodes that make up the leaves
  of a program tree, provide data to the program.
• Constants
• Parameterless functions
• Inputs

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Genetic Program Components

• Terminal Set
• Work as set of primitive data types
• Constants
• Parameterless functions
• Input Values
• Function set
• Set of available functions
• Often tailored specifically for the needs of the
  program domain.

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Initializing the Population

• The following two parameters are specified
• Maximum depth of a program tree
• Maximum number of nodes in a program tree
• Three methods in common use (Koza)
• Full
• Nonterminals are used to build a complete tree up
  to the leaf nodes, which are then completely
  populated with terminals. Every tree is grown to
  maximum depth and has the maximum number of nodes
  allowed.

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Initializing the Population (continued)

• Three methods in common use (Koza)
• Grow
• The root node is chosen from the function set
• All nodes not at maximum depth are chosen
  randomly.
• Growth for a branch ends when a terminal is
  chosen.
• Trees can have irregular shapes.
• Nodes at the maximum depth are chosen from the
  terminal set only.

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Initializing the Population (continued)

• Three methods in common use (Koza)
• Ramped Half and Half
• M is the max depth of deepest partition in the
  population
• The population is separated into M partitions
• The ith partition, (i ranges from 0 to M-1) has
  a max depth of M i.
• Half of each partition is populated with grow,
  the other half is populated with full.

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Genetic Operators Crossover

• Crossover
• Randomly select a node in the mother
• Randomly select a node in the father
• Swap the two nodes along with their subtrees

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Crossover Example
-
Parent 2

Parent 1
/

power
-
13
4
abs
2
1
2
2
-7

-
Child 1
Child 2

1
-
power
/
2
2
abs
2
-7
13
4
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Genetic Operations Mutation

• Mutation
• Randomly select a node in the program tree
• Remove that node and its subtree
• Replace the node with a new subtree, using the
  same method used to initially instantiate the
  population.
• Typically, mutation is applied to a small number
  of offspring after crossover.

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Mutation Example

Left subtree is randomly selected for mutation.


1
3
2
4

The entire subtree is replaced

-
1
2

2
7
4
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Fitness-based Selection

• Gives graded and continuous feedback about how
  well a program performs on the training set
  (Banzhaf et. al.)
• Standardized Fitness
• Fitness scores are transformed so that 0 is the
  fitness of the most fit member.
• Normalized Fitness
• Fitness is transformed to values that always are
  between 0 and 1.

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Different Selection Algorithms

• GA Scenario
• Same as that used in Genetic Algorithms
• Create gene pool by selecting parents based on
  fitness
• Next generation completely replaces current
  generation
• ES Scenario
• Same as used in Evolutionary Strategies
• Generate children first
• Apply fitness function to parents and children
• Select the next generation from children (and
  possibly parents too)
• Selection pressure can be tuned by adjusting the
  ratio of the number of offspring to the number of
  parents.

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Selection Pressure

• Ratio of the best individuals selection
  probability to the average selection probability
• MostFitSelectionProbability / AverageFitSelectionP
  robability
• The larger this ratio, the greater the selection
  pressure.

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Sample Fitness Measures

• Error Fitness
• The sum of the absolute value of the differences
  between the computed result and the desired
  result.

Where fp is the fitness of the pth individual
in the population oi is the desired output for
the ith example in the training set pi is the
output from the pth individual on the ith example
in the training set
Squaring the expressing (pi-oi) can provide
larger penalties for errors.
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Fitness Measures can be as Varied as the
Applications

• Examples
• Number of correct solutions
• Number of wins competing against other members of
  the population.
• Number of errors navigating a maze
• Time required to solve a puzzle

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Truncation or (µ, ?) Selection

• A number of parents (µ) are allowed to breed and
  produce (?) children. The µ best children are
  used to produce the next generation.
• A variation, (µ ?) selection includes the
  parents in those considered for selection into
  the next generation.

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Ranking Selection

• Selection Based on Fitness Order
• The members of the population are ranked from
  best to worst.
• The selection probability is assigned based on
  the rank.

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Tournament Selection

• Select a subset of the population (the tournament
  size) randomly.
• More fit (winning) individuals are used to
  generate replacements for less fit (losing)
  individuals.
• Accelerates processing time (compared with full
  competition)
• Facilitates parallel processing

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The Basic GP Algorithm (from Banzhaf, et. al)

• Define the terminal set
• Define the function set
• Define the fitness function
• Define parameters such as population size,
  maximum individual size, crossover probability,
  selection method, and termination criterion

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Generational GP

• Like what we have seen in GA
• New generation completely replaces the previous
  generation.
• Initialize the population
• Evaluate the individual programs
• Until a new population is fully populated, repeat
• Select an individual or individuals in the
  population using selection algorithm
• Perform genetic operations on the selected
  individual or individuals
• Insert the result of the genetic operations into
  the new population
• Best individual is the resulting program.

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Steady State GP

• There are no generations
• Initialize the population
• Randomly choose a subset of the population to
  take part in the tournament
• Evaluate the fitness value of each competitor in
  the tournament.
• Select the winner or winners from the competitors
  in the tournament using the selection algorithm.
• Apply genetic operators to the winner or winners
  of the tournament

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Steady State GP (continued)

• Replace the losers in the tournament with the
  results of the application of the genetic
  operators to the winners of the tournament.
• Repeat steps 2-6 until the termination criterion
  is met.

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Introns

• Code sections (functions) that provide no real
  value for the problem at hand
• Introns do not directly affect the fitness of the
  individual.
• e.g., j j 0 or j j 1
• Early and middle sections of GP runs might
  include 40-60 introns.
• Later in the run, introns begin to dominate the
  code.
• Introns growth is exponential!

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Why GP Introns Emerge

• Children tend to be less fit than parents
• Crossover and mutation can be extremely
  destructive
• Introns reduce the destructive effects of genetic
  operators
• Parents generate introns when it is easier to
  protect what they already can do, through the
  creation of introns, than improve on what they
  are currently doing.

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Effective Fitness

• Function of at least two factors
• The fitness of the parent
• Likelihood that genetic operators will affect the
  fitness of the parents children

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Effects of Introns

• Introns may have differing effects before and
  after exponential growth of introns begins
• Different systems may generate different types of
  introns with different probabilities.
• The extent to which genetic operatos are
  destructive in their effect is likely to be a
  very important initial condition in intron
  growth.
• Mutation and crossover may affect different types
  of introns differently.

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Problems Caused by Introns

• Run stagnation (no progress)
• Poor results (do nothing code)
• Drain on memory and CPU time (storing and
  executing unnecessary code)

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Possible Beneficial Effects of Introns

• Introns might serve to isolate useful code blocks
• This facilitates the building block model by
  protecting useful building blocks from disruption

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Methods of Handling Introns

• Reduce the destructiveness of genetic operators
• Reducing destructive crossover to 0 results in
  hill climbing
• Attach fitness penalty to the length of the
  program.
• Change the fitness function
• Provides the GP with a way to improve that is
  better than just insulating the current best
  solution.

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References

• Genetic Programming, An Introduction
• Wolfgang Banzhaf, Peter Nordin, Robert E. Keller,
  Frank D. Francone
• Genetic Programming Tutorial
• John Koza, Gecco 2005
• Genetic Programming The Movie
• John Koza