Tree Based Genetic Programming

Tree-based Genetic Programming #

Name #

Tree-based Genetic Programming (GP), Genetic Programming

Taxonomy #

Genetic Programming is a subfield of Evolutionary Computation, which itself is a subfield of Computational Intelligence and Biologically Inspired Computation. GP is closely related to other Evolutionary Algorithms such as Genetic Algorithms and Evolution Strategies.

  • Computational Intelligence
    • Biologically Inspired Computation
      • Evolutionary Computation
        • Evolutionary Algorithms
          • Genetic Algorithms
          • Evolution Strategies
          • Genetic Programming
            • Tree-based Genetic Programming

Strategy #

Genetic Programming evolves a population of computer programs, typically represented as syntax trees, to solve a given problem. Each individual in the population represents a candidate solution, and the fitness of each individual is evaluated based on how well it solves the problem at hand.

The evolutionary process in GP mimics natural selection and reproduction. Individuals with higher fitness are more likely to be selected for reproduction, which involves applying genetic operators such as crossover and mutation to create new offspring programs. Crossover combines genetic material from two parent programs to create new offspring, while mutation introduces random changes to a single parent program.

The selection, reproduction, and evaluation process is repeated over multiple generations, gradually improving the overall fitness of the population. As the population evolves, more effective and efficient programs emerge, ultimately leading to a solution or approximation of the desired behavior.

Procedure #

  1. Initialization
    1. Define the problem and the desired behavior or output of the evolved programs
    2. Determine the function and terminal sets for constructing the program trees
    3. Set the population size, maximum number of generations, and other control parameters
    4. Create an initial population of random program trees using the function and terminal sets
  2. Evaluation
    1. For each individual in the population:
      1. Execute the program represented by the individual’s tree
      2. Evaluate the fitness of the individual based on its performance on the given problem
  3. Selection
    1. Select a subset of individuals from the population based on their fitness using a selection method (e.g., tournament selection, roulette wheel selection)
  4. Reproduction
    1. Create new offspring programs by applying genetic operators to the selected individuals
      1. Crossover: Randomly select two parent programs and create new offspring by exchanging subtrees between them
      2. Mutation: Randomly select a single parent program and create a new offspring by modifying its tree structure (e.g., replacing a subtree with a randomly generated one)
    2. Add the new offspring programs to the population
  5. Replacement
    1. Replace a portion of the existing population with the new offspring programs
    2. Optionally, apply elitism to preserve the best individuals from the previous generation
  6. Termination
    1. If the maximum number of generations is reached or a satisfactory solution is found, terminate the algorithm
    2. Otherwise, go back to step 2 (Evaluation)
  7. Return the best individual found during the evolution process as the solution

Data Structures #

  • Individual: Represents a candidate solution in the form of a program tree
  • Population: A collection of individuals (program trees) that evolves over generations
  • Function Set: A set of functions used as internal nodes in the program trees (e.g., arithmetic operators, logical operators, domain-specific functions)
  • Terminal Set: A set of variables, constants, and zero-argument functions used as leaf nodes in the program trees

Parameters #

  • Population Size: The number of individuals in each generation
  • Maximum Number of Generations: The stopping criterion for the evolutionary process
  • Crossover Rate: The probability of applying the crossover operator to create new offspring
  • Mutation Rate: The probability of applying the mutation operator to create new offspring
  • Tournament Size: The number of individuals participating in tournament selection (if used)
  • Tree Depth Limit: The maximum allowed depth of the program trees to control complexity

Considerations #

Advantages #

  • Flexibility: GP can automatically evolve programs for a wide range of problems without requiring explicit programming
  • Creativity: GP can discover novel and unexpected solutions that may not be apparent to human programmers
  • Adaptability: GP can adapt to changing problem requirements by evolving new solutions as needed

Disadvantages #

  • Computational Complexity: GP can be computationally expensive, especially for large populations and complex problems
  • Bloat: Program trees may grow excessively large and complex over generations, reducing interpretability and efficiency
  • Overfitting: GP may evolve programs that perform well on the training data but fail to generalize to unseen cases

Heuristics #

Function and Terminal Set Design #

  • Include a diverse set of functions and terminals relevant to the problem domain
  • Ensure that the function and terminal sets are sufficient to express potential solutions
  • Consider including higher-level functions or building blocks to improve efficiency and scalability

Population Size and Diversity #

  • Use a large enough population size to maintain diversity and explore the search space effectively
  • Apply techniques like niching or speciation to preserve diversity and prevent premature convergence

Crossover and Mutation Rates #

  • Set the crossover rate high (e.g., 0.8-0.9) to promote the exchange of genetic material between individuals
  • Set the mutation rate low (e.g., 0.01-0.1) to introduce small variations without disrupting good solutions too much
  • Adjust the rates based on the problem complexity and desired exploration-exploitation balance

Tree Depth Limit and Bloat Control #

  • Set a reasonable tree depth limit to prevent excessive growth of program trees
  • Apply bloat control techniques such as parsimony pressure or explicit size limits
  • Consider using alternative representations or operators that inherently control bloat (e.g., grammatical evolution, subtree encapsulation)

Fitness Evaluation and Selection #

  • Design a fitness function that accurately measures the performance of individuals on the given problem
  • Use a selection method that balances exploration and exploitation (e.g., tournament selection with moderate tournament size)
  • Consider incorporating problem-specific knowledge or heuristics into the fitness evaluation to guide the search

Termination Criteria #

  • Set a maximum number of generations based on the problem complexity and available computational resources
  • Define additional termination criteria based on the desired solution quality or convergence properties
  • Allow for early termination if a satisfactory solution is found to save computational effort