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Genetic Operators

This overview explores key genetic operators used in evolutionary computation, including reproduction, crossover, mutation, permutation, editing, encapsulation, decimation, inversion, hoisting, creation, compression, and expansion. Each operator plays a vital role in maintaining genetic diversity and facilitating the evolution of solutions within a population. The processes involve selecting parents, manipulating subtrees, and applying various techniques to refine and enhance individuals in each generation, contributing to the overall effectiveness of genetic algorithms and programming methods.

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Genetic Operators

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  1. Genetic Operators • Reproduction • Crossover • Mutation • Permutation • Editing • Encapsulation • Decimation • Inversion • Hoist • Create • Compress • Expand

  2. Reproduction • A parent is chosen from the population (using one of the selection methods). • The individual is copied into the next generation. • The fitness of the individual does not have to be calculated.

  3. Crossover • Two parents are selected from the population. • A crossover point is selected in each individual randomly. • The subtrees rooted at the crossover points are swapped. • In some cases the crossover operator can be reduced to mutation or reproduction. • A limit is usually set on the offspring size. • Variations of crossover

  4. Crossover Example Crossover Fragments

  5. Mutation • A parent is selected from the population. • A mutation point is selected at random. • The subtree rooted at this point is removed and replaced with a newly created subtree (could be a terminal). • Variations of mutation. • Can be reduced to reproduction. • Is used to maintain genetic diversity.

  6. Mutation: Example

  7. Permutation • A parent is chosen from the population. • A function node is randomly selected. • A permutation of the function arguments is randomly selected. • If the arity of the function node is two, the arguments are merely swapped.

  8. Permutation Example

  9. Editing • Is used to remove redundant code. • A parent is selected. • Examples • (+ 1 2 ) will be replaced by 3 • (/ x 1) will be replaced with x • (AND T T) will be replaced with T • GP Parameters • A frequency parameter Effect on Diversity

  10. Encapsulation • Selection a parent. • Select a function node at random. • Remove the subtree rooted at this node. • This subtree forms the a new function and is given a label, e.g. E0, E1, etc. • The new function is added to the terminal set as it does not have arguments.

  11. Encapsulation Example

  12. Decimation • Is to prevent loss of genetic diversity. • A percentage of the population is deleted during the specified generations. • Usually starts with a larger population. • GP parameters • Application rate • Frequency Rate

  13. The Inversion Operator • Select a parent. • Select two subtrees randomly. • Swap the subtrees. • Subtrees to be swapped must not be contained in each other

  14. Inversion: Example

  15. Hoist • Select a parent. • Randomly select a subtree within a the parent. • Copy the subtree into the next generation. • Example:

  16. Create • A new tree is created using initial population generation and added to the next generation. • Maintain genetic diversity.

  17. Compress • Select a parent. • Select a subtree. • The part of the subtree up until a certain depth is defined as a new function. • The nodes below the level of the cut-off depth are considered as arguments to the module. • The module is named and added to the function set. • GP Parameters • Cut-off depth

  18. Compress: Example Cut-off Depth = 1 Arity=2

  19. Expand • Select a parent that contains a function node created by the compression operator. • Replace the function node with its corresponding subtree.

  20. Expand: Example

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