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Polynomial mutation

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

A mutation method that samples offspring around a real-valued parent using a polynomially shaped probability distribution.

Polynomial mutation creates real-valued offspring near a parent by sampling from a polynomially shaped probability distribution. Its distribution index, η, controls the balance between exploitation and exploration: higher values keep offspring closer, while lower values spread them farther through the search space. section 8.2.2

Use the distribution index to tune the mutation behavior:

  • Choose a higher η when preserving parent solutions and making smaller changes is preferred. section 8.2.2
  • Choose a lower η when broader exploration of the real-valued search space is useful. section 8.2.2

Curve fitting

A real-valued genetic algorithm can search for coefficients a, b, c, and d in y = ax³ + bx² + cx + d. Polynomial mutation perturbs coefficient vectors while mean squared error evaluates the resulting fit. section 8.2.2

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

How deep it goes
Defines the distribution-index trade-off and shows a pymoo configuration, but does not derive the probability distribution.
Examples
Demonstrates coefficient search for third-order polynomial curve fitting using mean squared error and pymoo.
What it assumes
Assumes real-valued genetic-algorithm representations, candidate vectors, objective functions, and bounded variables.
What you can do after
Apply it via pymoo by configuring PolynomialMutation within a real-valued genetic algorithm.
How it connects
Connects polynomial mutation with real-valued genetic algorithms, SBX crossover, exploration, exploitation, and mean squared error.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
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