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Distribution index

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

A parameter controlling the spread of the probability distribution used by polynomial mutation.

The distribution index, η, controls how polynomial mutation spreads offspring around a parent. Higher values favor exploitation; lower values favor exploration. section 8.2.2

Use the parameter to adjust mutation behavior:

  • Increase η when mutations should remain close to existing candidate solutions. section 8.2.2
  • Decrease η when the search should produce more widely spread offspring. section 8.2.2

Curve-fitting with a real-valued genetic algorithm

When optimizing the coefficients of a third-order polynomial, polynomial mutation uses the distribution index to balance refining promising coefficient vectors against exploring alternatives. section 8.2.2

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

How deep it goes
Defines the qualitative effect of η but stops short of presenting the probability-distribution formula or tuning procedure.
Examples
Illustrates mutation within a curve-fitting problem that optimizes four polynomial coefficients.
What you can do after
Evaluate polynomial-mutation settings by relating η to offspring proximity and search spread.
How it connects
Connects polynomial mutation with probability distributions, exploration, exploitation, and real-valued genetic algorithms.
Cover of Optimization Algorithms: AI techniques for design, planning, and control problems
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