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Cauchy mutation

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

A mutation method that adds a random value sampled from a Cauchy distribution to a real-valued gene.

Cauchy mutation changes a real-valued gene by adding a random value sampled from a Cauchy, or Lorentz, distribution. Its heavier tails make larger mutations more likely than Gaussian mutation, helping preserve diversity and escape local optima. section 8.2.2

Use Cauchy mutation when a real-valued genetic algorithm needs occasional broader moves:

  • Contrast it with Gaussian mutation: both add random perturbations, but Cauchy mutation gives larger mutations a higher probability. section 8.2.2
  • Treat it as an exploration-oriented alternative when small perturbations may leave the search trapped near a local optimum. section 8.2.2

Curve-fitting with real-valued genes

A real-valued genetic algorithm can represent the four coefficients of a third-order polynomial as genes. Cauchy mutation can perturb those coefficients while the population searches for a fit to the supplied x–y data. section 8.2.2

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes
Defines the distributional difference and search rationale, but does not provide Cauchy-specific pseudocode, parameter guidance, or implementation.
Examples
Uses third-order polynomial curve fitting, four coefficient genes, and tabulated x–y observations as the concrete application.
What you can do after
Evaluate Cauchy mutation as an exploration-oriented choice for perturbing continuous genes in a genetic algorithm.
How it connects
Connects Cauchy mutation to real-valued genetic algorithms, Gaussian mutation, local optima, and population diversity.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
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