Deterministic Crowding

Deterministic Crowding #

Name #

Deterministic Crowding (DC)

Taxonomy #

Deterministic Crowding is a niching technique used in Genetic Algorithms, which are a part of Evolutionary Computation, a subfield of Computational Intelligence.

  • Computational Intelligence
    • Evolutionary Computation
      • Evolutionary Algorithms
        • Genetic Algorithms
          • Niching Techniques
            • Deterministic Crowding

Strategy #

Deterministic Crowding aims to maintain population diversity and prevent premature convergence by promoting competition between similar individuals within the population. This is achieved through a specialized replacement strategy that ensures offspring compete directly with their most similar parent for survival.

Similarity Measure #

To determine the similarity between individuals, a distance metric is employed. Common choices include Euclidean distance for continuous-valued problems and Hamming distance for discrete-valued problems. The distance metric quantifies the dissimilarity between two individuals based on their genotypic or phenotypic characteristics.

Replacement Strategy #

During the replacement phase, each offspring competes with its most similar parent for a spot in the next generation. This direct competition between parent and child encourages the formation and maintenance of niches within the population. By allowing offspring to replace only their most similar parent, Deterministic Crowding preserves diversity and prevents a single dominant solution from taking over the entire population.

Procedure #

  1. Initialize the population with N individuals
  2. While termination criteria not met:
    1. Select N/2 pairs of parents from the population using a selection method (e.g., tournament selection)
    2. For each pair of parents:
      1. Apply genetic operators (crossover and/or mutation) to create two offspring
      2. Calculate the similarity between each offspring and each parent using a distance metric
      3. Assign each offspring to compete with its most similar parent
      4. For each parent-offspring pair:
        1. If the offspring has a better fitness than the parent, replace the parent with the offspring in the next generation
        2. Otherwise, retain the parent in the next generation
  3. Return the best solution found

Data Structures #

  • Population: An array or list of individuals representing potential solutions to the problem
  • Individual: Represents a single solution, typically encoded as a string of bits, integers, or real numbers
  • Fitness Function: A function that evaluates the quality or fitness of an individual solution

Parameters #

  • Population Size (N): The number of individuals in the population
  • Crossover Rate: The probability of applying the crossover operator to a pair of parents
  • Mutation Rate: The probability of applying the mutation operator to an individual
  • Distance Metric: The function used to calculate the similarity between individuals (e.g., Euclidean distance, Hamming distance)

Considerations #

Advantages #

  • Maintains population diversity by promoting the formation and preservation of niches
  • Reduces the risk of premature convergence by preventing a single dominant solution from taking over the population
  • Promotes exploration of the search space by allowing multiple promising regions to be investigated simultaneously

Disadvantages #

  • Increased computational complexity due to the need to calculate similarities between individuals
  • The performance of the algorithm can be sensitive to the choice of distance metric
  • May require additional mechanisms to ensure sufficient exploitation of promising solutions within each niche

Heuristics #

Population Size #

  • Choose a population size that balances exploration and exploitation
  • Larger populations can help maintain diversity but may require more computational resources
  • Smaller populations may converge faster but risk getting stuck in suboptimal solutions

Genetic Operators #

  • Use genetic operators that are suitable for the problem representation (e.g., bit-string crossover for binary-encoded problems, real-valued crossover for continuous optimization)
  • Adjust the crossover and mutation rates based on the problem complexity and desired balance between exploration and exploitation
  • Higher crossover rates encourage the exchange of genetic material between individuals, while higher mutation rates introduce new genetic diversity

Distance Metric #

  • Select a distance metric that accurately captures the similarity between individuals in the context of the problem
  • For continuous-valued problems, Euclidean distance is a common choice
  • For discrete-valued problems, Hamming distance can be used to measure the number of differing components between individuals
  • Consider normalizing the distance metric to ensure fair comparisons between individuals with different scales or ranges of values

Termination Criteria #

  • Define termination criteria that reflect the desired level of solution quality or the available computational resources
  • Common criteria include reaching a maximum number of generations, finding a solution with a satisfactory fitness level, or observing convergence of the population
  • Strike a balance between allowing sufficient time for the algorithm to explore the search space and avoiding excessive computation on diminishing returns