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Area of Science:

  • Computer Science
  • Artificial Intelligence
  • Optimization Algorithms

Background:

  • Theoretical analyses of evolutionary algorithms predominantly focus on binary optimization.
  • Black-box optimization in the categorical domain has significant practical applications but is less explored theoretically.
  • Existing algorithms like the compact genetic algorithm (cGA) are efficient for binary domains.

Purpose of the Study:

  • To introduce and theoretically analyze a probabilistic model-based algorithm for categorical black-box optimization.
  • To extend the analysis of the compact genetic algorithm (cGA) to the categorical domain.
  • To investigate the impact of key parameters (categories K, dimensions D, learning rate η) on algorithm runtime.

Main Methods:

  • Developed the categorical compact genetic algorithm (ccGA) using categorical distributions with a sample size of two.
  • Conducted theoretical runtime analysis of the ccGA.
  • Investigated the tail bounds of the runtime on categorical OneMax (COM) and KVal benchmark functions.

Main Results:

  • Derived the runtime complexity for categorical OneMax (COM) as O(Dln(DK)/η) with high probability.
  • Derived the runtime complexity for KVal as Θ(DlnK/η) with high probability.
  • Demonstrated that the ccGA analysis generalizes the cGA analysis for binary domains.

Conclusions:

  • The categorical compact genetic algorithm (ccGA) provides a viable approach for discrete black-box optimization in categorical domains.
  • The theoretical runtime analysis offers valuable insights into the performance of ccGA concerning problem dimensions, categories, and learning rates.
  • This work extends the theoretical understanding of evolutionary algorithms to a broader class of discrete optimization problems.