Problems Premature Convergence Lack of genetic diversity Selection noise or variance Destructive effects of genetic operators Cloning Introns and Bloat A blessing or a curse?

Lack of Genetic Diversity Duplicate individuals Higher mutation application rates Creation operator Similar individuals Detect lack of diversity Similarity indexes Introducing dissimilar individuals

Example: Similarity Index Tree 1 Tree 2 Is Tree1 similar to Tree2 Index 1: 3 Index 2: 3/7

Selection Noise or Variance What is selection noise? Multiple runs Multiple populations Interbreeding

Destructive Effects of Genetic Operators One of the destructive effects of crossover is that it breaks up good building blocks that could form part of a solution. Another destructive effect is that it may insert a good building block into an individual that does not make proper use of it. Crossover is destructive approximately seventy five percent of the time. The closer a tree is to a solution the more susceptible it is to the destructive effects of crossover. Experiments conducted indicate that the percentage of destructive crossover remains high until the end of a run.

Monitoring the Effects of Crossover Due to the destructive effects of crossover the application of the crossover operator must be monitored during a GP run. Method 1: The average fitness of the parents must be compared with the average fitness of the offspring. Method 2: The fitness of one parent is compared with the fitness of one child. However, this approach presents the problem of how the child and parent should be chosen. Non-destructive operators

Methods for Dealing with Destructive Effects The Macromutation Operator Brood Recombination Similar Parents Intelligent Crossover Context-sensitive Crossover Explicitly Defined Introns (EDIs)

The Macromutation Operator A single parent is selected using the standard selection methods. A new individual is created using the initial population generation process. Crossover is applied to both these individuals. If the offspring has a fitness value greater than or equal to the fitness of its parent it forms part of the new population, else it is discarded. The macromutation operator has not been widely tested and has been successfully applied to only one problem domain.

Brood Recombination GP Parameter: A brood size N must be specified. Two parents are selected. Standard crossover is applied to the parents N times creating N pairs of offspring. The offspring is evaluated for fitness and sorted according to their fitness values. The best two offspring are selected as the result of brood selection and the rest of the offspring are discarded. One of the disadvantages of this method is the time required to evaluate all 2N offspring.

Similar Parents Researchers are of the opinion that the problems experienced with the crossover operator can be attributed to the fact that there are differences between the biological crossover and GP crossover. Biological crossover is only applied to two individuals that are homologous with respect to their function and structure. Similar parents: Arity Node types

Intelligent Crossover An intelligent crossover operator is used in the PADO – The operator is evolved as part of the evolutionary process. Intelligent operator used by Banzhaf: A performance measure is calculated for each subtree. This performance value is used to determine which subtrees to insert into other trees, and which to replace.

Context-Sensitive Crossover A context-sensitive crossover operator will allow only “similar” points to be swapped. Similar points Same arity Same function type Same label How does this effect convergence?

Explicitly Defined Introns This approach involves adding introns to an individual to reduce the destructive effects of crossover. Explicitly defined introns usually take the form of real or integer values inserted between every two nodes in an individual. Example:

Cloning Cloning caused by crossover The use of crossover together with a depth limit can result in the crossover operator merely producing clones of the parents and hence causing the GP process to stagnate. Crossover which swaps terminals Crossover which replaces whole trees Variety

Preventing Cloning Do not use the reproduction operator. An increase in selective pressure. Detect when an offspring is identical to one of its parents. This information can be used to reduce the GP run time or increase the variety. The first of these is achieved by copying the fitness value of parents for offspring that are clones instead of re-evaluating the offspring. The latter is achieved by not allowing the production of duplicates.

Introns and Bloat An intron is redundant code. Examples: Code which does nothing,e.g. NOT(NOT(X)), (+ X 0) Code which is not executed, e.g. (IF (2==1)...X) The emergence of introns has been described as a protective response to the destructive effect of the crossover operator. Introns grow exponentially towards the end of a run. This exponential growth of introns is called bloat and causes the GP algorithm to stagnate.

Types of Introns Local introns - These are functions that have no effect except to pass on the values that were passed to them. Hierarchical introns - These are functions which contain one or more arguments that will be ignored, e.g. an if-else statement. Sibling (horizontal) introns - These functions undo the effect of a function represented by a sibling tree. e.g. when a subtree has its contributions to a memory location overwritten by another subtree after it.

Reducing Introns and Bloat The editing operator (+ x 0) is replaced by x All the introns will not be removed Increased mutation rates Parsimony pressure using a penalty function Weighting size and correctness Pareto fitness When to apply the penalty function The use of Automatically Defined Functions (ADFs)