# Selection and Reduction

Selectors are HeuristicLab 3.3 operators that implement the ISelector interface. Likewise, Reducers implement the IReducer interface.

Selection and Reduction operators usually work in tandem. To illustrate the application of selection/reduction consider a simple genetic algorithm that has a population of solutions and selects among these solutions those that should be crossed. After selection, the children are crossed (cf. Section on crossover operators) which results in two populations of the same size: The old parent population and the new child population. Finally, after mutating some children with a given probability, the parent population is replaced, i.e., it is reduced to the child population.

## 1. Selection Operators

Common Operator Parameters:

Parameter Description
CopySelected True if the selected sub-scopes should be copied, otherwise false.
CurrentScope The current scope from which sub-scopes should be selected.
Maximization True if the current problem is a maximization problem, otherwise false.
NumberOfSelectedSubScopes The number of sub-scopes which should be selected.
Quality The quality value contained in each sub-scope which is used for selection.

### 1.1 BestSelector

A selection operator which considers a single double quality value and selects the best.

### 1.2 GenderSpecificSelector

Brings two parents together by sampling each with a different selection scheme (Wagner and Affenzeller 2005).

### 1.3 LinearRankSelector

A linear rank selection operator which considers the rank based on a single double quality value for selection.

### 1.4 ProportionalSelector

A quality proportional selection operator which considers a single double quality value for selection.

### 1.5 RandomSelector

A random selection operator.

### 1.6 TournamentSelector

A tournament selection operator which considers a single double quality value for selection.

### 1.7 WorstSelector

A selection operator which considers a single double quality value and selects the worst.

## 2. Reduction Operators

Common Operator Parameters:

Parameter Description
CurrentScope The current scope from which sub-scopes should be selected.

### 2.1 LeftReducer

An operator which reduces to the sub-scopes of the leftmost sub-scope of the current scope.

### 2.2 MergingReducer

An operator which reduces to the sub-scopes of all sub-scopes of the current scope.

### 2.3 RightChildReducer

Merges all sub-scopes generated by successively selecting sub-scopes of the remaining part.

### 2.4 RightReducer

An operator which reduces to the sub-scopes of the rightmost sub-scope of the current scope.

## References

• Wagner, S. and Affenzeller, M. 2005. SexualGA: Gender-Specific Selection for Genetic Algorithms. Proceedings of the 9th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI), pp. 76-81.