saealib.MutationGaussian#

class saealib.MutationGaussian(prob=1.0, *, sigma, prob_var=None)[source]#

Bases: Mutation

Gaussian mutation operator.

Parameters:

  • prob (float)

  • sigma (float)

  • prob_var (float | None)

prob#

Individual-level mutation probability.

Type:

float

sigma#

Standard deviation of the Gaussian perturbation.

Type:

float

prob_var#

Per-variable mutation probability. Defaults to min(0.5, 1/dim) when None.

Type:

float or None

Notes

Originates from Rechenberg (1973); the original (German-language) monograph has not been obtained and is credited here by name only. The survey below summarizes Rechenberg’s (1+1)-ES with Gaussian mutation and its mutation-strength (standard deviation) parameterization, consistent with this operator.

References

[41]: Beyer, H.-G., & Schwefel, H.-P. (2002). Evolution strategies – A comprehensive introduction. Natural Computing, 1, 3-52.

Methods

__init__

Initialize Gaussian mutation operator.

contract

Return the real-valued Gaussian mutation contract.

mutate

Execute mutation for one candidate.

mutate_batch

Execute Gaussian mutation on a batch of candidates at once.

post_mutation

Post-mutation lifecycle hook; override to inject custom processing.

post_mutation_batch

Run the post-mutation lifecycle hook for a batch.

with_post

Return a copy of this operator with fn appended to the hook.

Method Details

MutationGaussian.__init__(prob=1.0, *, sigma, prob_var=None)[source]#

Initialize Gaussian mutation operator.

Parameters:

  • prob (float, optional) – Individual-level mutation probability, by default 1.0.

  • sigma (float) – Standard deviation of the Gaussian perturbation.

  • prob_var (float or None, optional) – Per-variable mutation probability. None uses min(0.5, 1/dim).

MutationGaussian.contract()[source]#

Return the real-valued Gaussian mutation contract.

Return type:

ComponentContract

MutationGaussian.mutate(p, mutate_range, rng=Generator(PCG64) at 0x7F7917914740)#

Execute mutation for one candidate.

This method is derived from mutate_batch() by passing a single-row batch.

Notes

Overriding only this method (not mutate_batch()) has no effect under GA’s default variation_execution="batch": the batch path calls mutate_batch() directly and never calls mutate(). Such an override only takes effect under variation_execution="sequential". To customize behavior under both modes, override mutate_batch().

Parameters:

  • p (np.ndarray) – Parent individual. shape = (dim,)

  • mutate_range (tuple) – Tuple of (lower_bound, upper_bound) for mutation.

  • rng (np.random.Generator, optional) – Random number generator, by default np.random.default_rng()

Returns:

Mutated individual. shape = (dim,). The result is always float64 because mutate_batch() casts its input internally; the result does not preserve the input’s dtype.

Return type:

np.ndarray

MutationGaussian.mutate_batch(candidates_batch, mutate_range, rng=Generator(PCG64) at 0x7F7917915380)[source]#

Execute Gaussian mutation on a batch of candidates at once.

This is the primary Gaussian mutation implementation. An individual-level prob gate (one Bernoulli draw per row via rng.random(n) < self.prob) selects which rows are touched at all; a per-dimension prob_var gate is then drawn only for the selected rows, and only dimensions passing that gate are replaced by adding Normal(0.0, self.sigma) noise. Unlike mutate_batch() and mutate_batch(), the replacement value has no branching formula – it is simply sub + noise – so this is the simplest of the three mutate_batch overrides. Rows that fail the individual-level gate are returned byte-identical to the input; dimensions failing the per-dimension gate on a selected row keep their original value exactly (np.where copies rather than recomputes them). If no row passes the individual-level gate (gate.sum() == 0), no further random draws happen at all and the input is returned unchanged, mirroring MutationUniform.mutate_batch’s empty-gate skip.

Parameters:

  • candidates_batch (np.ndarray) – Batch of candidate individuals. shape = (n, dim)

  • mutate_range (tuple) – Tuple of (lower_bound, upper_bound). Accepted for interface uniformity with the Mutation ABC and the other mutate_batch overrides, but unused. This operator adds unbounded Gaussian noise with no clipping to [lb, ub].

  • rng (np.random.Generator, optional) – Random number generator, by default np.random.default_rng()

Returns:

Mutated individuals. shape = (n, dim)

Return type:

np.ndarray

Notes

For multiple rows, a loop of separate single-row mutate_batch calls (equivalently, separate mutate() calls) does not reproduce the same per-row results as one batched call with the same seeded rng. Separate calls interleave each row’s individual gate, full per-dimension gate array, and full noise array before moving to the next row. One batched call instead draws all individual gates, then the variable-gate arrays for all gated rows, then the noise arrays for all of them. These phases therefore have a different draw order whenever more than one row is involved. Only the statistical and distributional semantics are guaranteed to match.

The output is always float64 (via the internal dtype=float cast), regardless of the input array’s dtype.

MutationGaussian.post_mutation(offspring, mutate_range, rng, ctx=None)#

Post-mutation lifecycle hook; override to inject custom processing.

Parameters:

  • offspring (np.ndarray) – Individual after mutation. shape = (dim,)

  • mutate_range (tuple) – Tuple of (lower_bound, upper_bound) used for mutation.

  • rng (np.random.Generator) – Random number generator.

  • ctx (ExecutionContext or None, optional) – Current optimization context.

Returns:

Processed individual. shape = (dim,)

Return type:

np.ndarray

MutationGaussian.post_mutation_batch(offspring_batch, mutate_range, rng, ctx=None)#

Run the post-mutation lifecycle hook for a batch.

The default implementation calls post_mutation() once per individual, in order. Override this method to provide genuinely vectorized post-processing.

Parameters:

  • offspring_batch (np.ndarray) – Offspring produced by mutation. shape = (n, dim)

  • mutate_range (tuple) – Tuple of (lower_bound, upper_bound) used for mutation.

  • rng (np.random.Generator) – Random number generator.

  • ctx (ExecutionContext or None, optional) – Current optimization context.

Returns:

Processed offspring. shape = (n, dim)

Return type:

np.ndarray

Notes

with_post() reassigns only the instance’s post_mutation() hook. A subclass override of this method is responsible for composing that hook itself. If the override does not call self.post_mutation, a hook installed with with_post() will not run in GA batch mode. It still runs in GA sequential mode, which calls post_mutation() directly.

MutationGaussian.with_post(fn)#

Return a copy of this operator with fn appended to the hook.

Parameters:

fn (callable) – fn(offspring, mutate_range, rng, ctx) -> np.ndarray

Returns:

Shallow copy with the hook registered.

Return type:

Mutation