Genetic Programming

Genetic Programming #

Name #

Genetic Programming (GP)

Taxonomy #

Genetic Programming is a branch of Evolutionary Computation, which is a subfield of Computational Intelligence. It is closely related to other Evolutionary Algorithms such as Genetic Algorithms, Evolution Strategies, and Evolutionary Programming.

  • Computational Intelligence
    • Evolutionary Computation
      • Evolutionary Algorithms
        • Genetic Programming

Strategy #

Representation #

In Genetic Programming, solutions are represented as tree structures, where each node in the tree corresponds to a function or a terminal. Functions are internal nodes that perform operations on their child nodes, while terminals are leaf nodes that represent variables or constants. The specific set of functions and terminals used depends on the problem domain and is known as the primitive set.

Initialization #

The initial population of candidate solutions is generated randomly or using a problem-specific heuristic. Each individual in the population is created by recursively selecting functions and terminals from the primitive set until a complete tree is formed. The depth of the trees may be limited to prevent the generation of excessively large individuals.

Evaluation #

Each individual in the population is evaluated using a fitness function that measures how well it solves the given problem. The fitness function assigns a numerical value to each individual, with higher values indicating better solutions. The specific fitness function used depends on the problem and may involve running the evolved program on a set of test cases or evaluating its performance in a simulated environment.

Selection #

Selection is the process of choosing individuals from the current population to serve as parents for the next generation. Common selection methods include tournament selection, where a fixed number of individuals are randomly chosen and the fittest among them is selected, and fitness-proportionate selection, where individuals are chosen with a probability proportional to their fitness.

Genetic Operators #

Genetic operators are applied to the selected parents to create new offspring. The two main operators used in Genetic Programming are:

  1. Crossover: Two parent individuals are selected, and subtrees from each parent are exchanged to create two new offspring. The crossover points are chosen randomly, and the resulting offspring inherit characteristics from both parents.

  2. Mutation: A single parent individual is selected, and a random subtree within the individual is replaced with a newly generated subtree. Mutation introduces new genetic material into the population and helps maintain diversity.

Replacement #

After the new offspring are created, they are evaluated using the fitness function. The offspring then replace some or all of the individuals in the current population. Common replacement strategies include generational replacement, where the entire population is replaced by the offspring, and steady-state replacement, where only a portion of the population is replaced in each generation.

Termination #

The process of evaluation, selection, genetic operations, and replacement continues for a predetermined number of generations or until a satisfactory solution is found. The best individual found during the course of the evolution is typically designated as the final solution.

Procedure #

  1. Define the primitive set:

    1. Specify the set of functions and terminals to be used in the evolved programs.
    2. Ensure that the primitive set is sufficient to express solutions to the given problem.

  2. Initialize the population:

    1. Set the population size and the maximum depth for the initial individuals.
    2. For each individual in the population:
      1. Select a random function from the primitive set as the root node.
      2. Recursively select random functions or terminals for each child node until the maximum depth is reached or all branches end with terminals.

  3. Evaluate the population:

    1. For each individual in the population:
      1. Execute the evolved program represented by the individual.
      2. Compute the fitness value using the specified fitness function.

  4. While the termination criterion is not met:

    1. Select parents:
      1. Choose a subset of individuals from the population using a selection method (e.g., tournament selection or fitness-proportionate selection).
    2. Apply genetic operators:
      1. Crossover:
        1. Select two parent individuals from the chosen subset.
        2. Choose random crossover points in each parent.
        3. Exchange the subtrees rooted at the crossover points to create two offspring.
      2. Mutation:
        1. Select a single parent individual from the chosen subset.
        2. Choose a random mutation point within the individual.
        3. Replace the subtree rooted at the mutation point with a newly generated subtree.
    3. Evaluate the offspring:
      1. For each offspring individual:
        1. Execute the evolved program represented by the individual.
        2. Compute the fitness value using the specified fitness function.
    4. Replace the population:
      1. Select individuals from the current population and the offspring to form the new population based on a replacement strategy (e.g., generational or steady-state).

  5. Return the best individual found during the evolution as the final solution.

Data Structures #

  • Individual: Represents a candidate solution in the population. It is typically implemented as a tree structure, where each node contains a function or a terminal.
  • Population: A collection of individuals. It is usually implemented as an array or a list of individuals.
  • Fitness Function: A function that assigns a numerical value to an individual based on its performance on the given problem. The fitness function is problem-specific and must be defined by the user.

Parameters #

  • Population Size: The number of individuals in the population. A larger population size can explore more of the search space but may require more computational resources.
  • Maximum Depth: The maximum allowed depth for the tree structures representing the individuals. It controls the complexity of the evolved programs.
  • Crossover Rate: The probability of applying the crossover operator to a pair of selected parents. Higher crossover rates promote the exchange of genetic material between individuals.
  • Mutation Rate: The probability of applying the mutation operator to a selected individual. Higher mutation rates introduce more diversity into the population.
  • Tournament Size: The number of individuals participating in each tournament during tournament selection. Larger tournament sizes increase the selection pressure towards fitter individuals.
  • Number of Generations: The maximum number of iterations the evolution process will run for. It determines the computational budget allocated to the search.

Considerations #

Advantages #

  • Flexibility: Genetic Programming can automatically evolve solutions without requiring the user to specify the structure of the solution in advance. It can discover novel and unexpected solutions.
  • Scalability: GP can handle complex problems with large search spaces by efficiently exploring promising regions of the space through the use of genetic operators.
  • Adaptability: GP can adapt to changing problem environments by continuously evolving solutions based on the feedback provided by the fitness function.

Disadvantages #

  • Computational Cost: Evaluating the fitness of each individual in the population can be computationally expensive, especially for problems that require executing the evolved programs on large datasets or in complex simulations.
  • Bloat: GP tends to produce solutions that are larger than necessary, a phenomenon known as bloat. Bloated solutions can be less efficient and harder to interpret.
  • Overfitting: Like other machine learning techniques, GP is susceptible to overfitting, where the evolved solutions perform well on the training data but fail to generalize to unseen instances.

Heuristics #

Function and Terminal Selection #

  • Choose functions and terminals that are relevant to the problem domain and can express meaningful solutions.
  • Ensure that the primitive set is complete, i.e., it can express any possible solution to the problem.
  • Include a diverse set of functions and terminals to allow for the exploration of different solution structures.

Population Initialization #

  • Set the initial maximum depth to a reasonable value (e.g., 5-10) to prevent the generation of excessively large individuals.
  • Consider using problem-specific heuristics or seeding the population with known good solutions to provide a starting point for the evolution.

Fitness Function Design #

  • Define a fitness function that accurately measures the quality of solutions in the context of the problem.
  • Incorporate multiple objectives into the fitness function if the problem requires optimizing several criteria simultaneously.
  • Use a sufficient number of test cases or a representative sample of the problem space to evaluate the individuals.

Genetic Operator 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 diversity without disrupting good solutions too much.
  • Adjust the operator rates based on the problem complexity and the desired balance between exploration and exploitation.

Bloat Control #

  • Implement bloat control measures such as setting a maximum depth limit for the evolved programs.
  • Use parsimony pressure, where the fitness function includes a penalty term for the size of the individuals.
  • Apply simplification or pruning techniques to remove redundant or non-contributing parts of the evolved programs.

Parallelization #

  • Distribute the evaluation of individuals across multiple processors or machines to reduce the overall computation time.
  • Implement island models, where subpopulations evolve independently and occasionally exchange individuals, to maintain diversity and explore different regions of the search space.