Mutation

QuickSR supports 4 mutation operators.

Subtree Mutation

This mutation strategy randomly selects a subtree in the expression. The selected subtree is then replaced by another randomly generated subtree. This allows for significant changes in the expression structure, potentially leading to new solutions.

  • The max_depth_increment parameter controls the maximum depth of the inserted subtree. This helps in controlling the complexity of the expressions and prevents excessive growth. Default is 3 if not provided.

  • The mutation_probability parameter determines the likelihood of applying the mutation to an individual. Default is 0.7 if not provided.

Usage:

mutation=SubtreeMutation(
    max_depth_increment=3,
    mutation_probability=0.7
)

An example of how subtree mutation is performed with max_depth_increment = 3:

../_images/subtree-mutation.drawio.png

Note that the new subtree (shown in blue) could have had a depth less than three. Three is just an upper bound.

Hoist Mutation

This mutation strategy randomly selects a subtree from the expression and replaces it with a randomly chosen, smaller subtree within that subtree. This can lead to expressions becoming more simple, fighting the bloat problem.

  • The mutation_probability parameter determines the likelihood of applying the mutation to an individual. Default is 0.7 if not provided.

mutation=HoistMutation(mutation_probability=0.7)
../_images/hoist-mutation.drawio.png

Point Mutation

This mutation strategy randomly selects a node in the expression.

If the selected node is a terminal (constant, variable, parameter), it is replaced by another randomly generated terminal.

If the selected node is a unary operation (sin, cos, exp, relu), it is replaced by another randomly chosen unary operation, while its sole operand (child) is preserved.

If the selected node is a binary operation (+, -, *, /), it is replaced by another randomly selected binary operation, while both of its operands (children) are preserved.

This strategy explores new functions without growth in the complexity of the expressions.

  • The mutation_probability parameter determines the likelihood of applying the mutation to an individual. Default is 0.7 if not provided.

mutation=PointMutation(mutation_probability=0.7)
../_images/point-mutation.drawio.png

Distribution Mutation

This mutation strategy randomly applies one of several mutation strategies at every mutation operation according to the specified probabilities.

Parameters

  • mutations List of mutation strategies to be applied.

  • probabilities List of probabilities corresponding to each mutation strategy.

mutation=DistributionMutation(
    [SubtreeMutation(), HoistMutation(), PointMutation()],
    [0.5, 0.25, 0.25]
)