Class Uniform

  extended by
      extended by
All Implemented Interfaces:
Prototype, Setup,, java.lang.Cloneable

public class Uniform
extends GPNodeBuilder

Uniform implements the algorithm described in

Bohm, Walter and Andreas Geyer-Schulz. 1996. "Exact Uniform Initialization for Genetic Programming". In Foundations of Genetic Algorithms IV, Richard Belew and Michael Vose, eds. Morgan Kaufmann. 379-407. (ISBN 1-55860-460-X)

The user-provided requested tree size is either provided directly to the Uniform algorithm, or if the size is NOSIZEGIVEN, then Uniform will pick one at random from the GPNodeBuilder probability distribution system (using either max-depth and min-depth, or using num-sizes).

Further, if the user sets the true-dist parameter, the Uniform will ignore the user's specified probability distribution and instead pick from a distribution between the minimum size and the maximum size the user specified, where the sizes are distributed according to the actual number of trees that can be created with that size. Since many more trees of size 10 than size 3 can be created, for example, size 10 will be picked that much more often.

Uniform also prints out the actual number of trees that exist for a given size, return type, and function set. As if this were useful to you. :-)

The algorithm, which is quite complex, is described in pseudocode below. Basically what the algorithm does is this:

  1. For each function set and return type, determine the number of trees of each size which exist for that function set and tree type. Also determine all the permutations of tree sizes among children of a given node. All this can be done with dynamic programming. Do this just once offline, after the function sets are loaded.
  2. Using these tables, construct distributions of choices of tree size, child tree size permutations, etc.
  3. When you need to create a tree, pick a size, then use the distriutions to recursively create the tree (top-down).

Dealing with Zero Distributions

Some domains have NO tree of a certain size. For example, Artificial Ant's function set can make NO trees of size 2. What happens when we're asked to make a tree of (invalid) size 2 in Artificial Ant then? Uniform presently handles it as follows:

  1. If the system specifically requests a given size that's invalid, Uniform will look for the next larger size which is valid. If it can't find any, it will then look for the next smaller size which is valid.
  2. If a random choice yields a given size that's invalid, Uniform will pick again.
  3. If there is *no* valid size for a given return type, which probably indicates an error, Uniform will halt and complain.


    Func NumTreesOfType(type,size)
        If NUMTREESOFTYPE[type,size] not defined,       // memoize
            N[type] = all nodes compatible with type
            NUMTREESOFTYPE[type,size] = Sum(n in N[type], NumTreesRootedByNode(n,size))
            return NUMTREESOFTYPE[type,size]

    Func NumTreesRootedByNode(node,size)
        If NUMTREESROOTEDBYNODE[node,size] not defined,   // memoize
            count = 0
            left = size - 1
            If node.children.length = 0 and left = 0  // a valid terminal
                count = 1
            Else if node.children.length <= left  // a valid nonterminal
                For s is 1 to left inclusive  // yeah, that allows some illegal stuff, it gets set to 0
                    count += NumChildPermutations(node,s,left,0)
            NUMTREESROOTEDBYNODE[node,size] = count
        return NUMTREESROOTEBYNODE[node,size]

    Func NumChildPermutations(parent,size,outof,pickchild)
    // parent is our parent node
    // size is the size of pickchild's tree that we're considering
    // pickchild is the child we're considering
    // outof is the total number of remaining nodes (including size) yet to fill
        If NUMCHILDPERMUTATIONS[parent,size,outof,pickchild] is not defined,        // memoize
            count = 0
            if pickchild = parent.children.length - 1        and outof==size        // our last child, outof must be size
                count = NumTreesOfType(parent.children[pickchild].type,size)
            else if pickchild < parent.children.length - 1 and 
                                outof-size >= (parent.children.length - pickchild-1)    // maybe we can fill with terminals
                cval = NumTreesOfType(parent.children[pickchild].type,size)
                tot = 0
                For s is 1 to outof-size // some illegal stuff, it gets set to 0
                    tot += NumChildPermutations(parent,s,outof-size,pickchild+1)
                count = cval * tot
            NUMCHILDPERMUTATIONS [parent,size,outof,pickchild] = count            
        return NUMCHILDPERMUTATIONS[parent,size,outof,pickchild]

    For each type type, size size
        ROOT_D[type,size] = probability distribution of nodes of type and size, derived from
                            NUMTREESOFTYPE[type,size], our node list, and NUMTREESROOTEDBYNODE[node,size]

    For each parent,outof,pickchild
        CHILD_D[parent,outof,pickchild] = probability distribution of tree sizes, derived from

    Func FillNodeWithChildren(parent,pickchild,outof)
        If pickchild = parent.children.length - 1               // last child
            Fill parent.children[pickchild] with CreateTreeOfType(parent.children[pickchild].type,outof)
        Else choose size from CHILD_D[parent,outof,pickchild]
            Fill parent.pickchildren[pickchild] with CreateTreeOfType(parent.children[pickchild].type,size)
Func CreateTreeOfType(type,size) Choose node from ROOT_D[type,size] If size > 1 FillNodeWithChildren(node,0,size-1) return node


bool= true or false (default)
(should we use the true numbers of trees for each size as the distribution for picking trees, as opposed to the user-specified distribution?)

See Also:
Serialized Form

Field Summary
 java.util.Hashtable _functionsets
 java.math.BigInteger[][][] _truesizes
          CheckBoundary is 8
 double[][][][][] CHILD_D
 java.util.Hashtable funcnodes
 GPFunctionSet[] functionsets
 int maxarity
 int maxtreesize
 java.math.BigInteger[][][][][] NUMCHILDPERMUTATIONS
 int numfuncnodes
 java.math.BigInteger[][][] NUMTREESOFTYPE
 java.math.BigInteger[][][] NUMTREESROOTEDBYNODE
static java.lang.String P_TRUEDISTRIBUTION
static java.lang.String P_UNIFORM
   [][][][] ROOT_D
 boolean[][][] ROOT_D_ZERO
 double[][][] truesizes
 boolean useTrueDistribution
Fields inherited from class
Constructor Summary
Method Summary
 void computePercentages()
 Parameter defaultBase()
          Returns the default base for this prototype.
 int intForNode(GPNode node)
 GPNode newRootedTree(EvolutionState state, GPType type, int thread, GPNodeParent parent, GPFunctionSet set, int argposition, int requestedSize)
 java.math.BigInteger numChildPermutations(GPInitializer initializer, int functionset, GPNode parent, int size, int outof, int pickchild)
 java.math.BigInteger numTreesOfType(GPInitializer initializer, int functionset, int type, int size)
 java.math.BigInteger numTreesRootedByNode(GPInitializer initializer, int functionset, GPNode node, int size)
 int pickSize(EvolutionState state, int thread, int functionset, int type)
 void preprocess(EvolutionState state, int _maxtreesize)
 void setup(EvolutionState state, Parameter base)
          Sets up the object by reading it from the parameters stored in state, built off of the parameter base base.
Methods inherited from class
canPick, clone, errorAboutNoNodeWithType, pickSize, warnAboutNonterminal, warnAboutNonTerminalWithType, warnAboutNoTerminalWithType
Methods inherited from class java.lang.Object
equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail


public static final java.lang.String P_UNIFORM
See Also:
Constant Field Values


public static final java.lang.String P_TRUEDISTRIBUTION
See Also:
Constant Field Values


public static final int CHECKBOUNDARY
CheckBoundary is 8

See Also:
Constant Field Values


public GPFunctionSet[] functionsets


public java.util.Hashtable _functionsets


public java.util.Hashtable funcnodes


public int numfuncnodes


public int maxarity


public int maxtreesize


public java.math.BigInteger[][][] _truesizes


public double[][][] truesizes


public boolean useTrueDistribution


public java.math.BigInteger[][][] NUMTREESOFTYPE


public java.math.BigInteger[][][] NUMTREESROOTEDBYNODE


public java.math.BigInteger[][][][][] NUMCHILDPERMUTATIONS


public[][][][] ROOT_D


public boolean[][][] ROOT_D_ZERO


public double[][][][][] CHILD_D
Constructor Detail


public Uniform()
Method Detail


public Parameter defaultBase()
Description copied from interface: Prototype
Returns the default base for this prototype. This should generally be implemented by building off of the static base() method on the DefaultsForm object for the prototype's package. This should be callable during setup(...).


public void setup(EvolutionState state,
                  Parameter base)
Description copied from interface: Prototype
Sets up the object by reading it from the parameters stored in state, built off of the parameter base base. If an ancestor implements this method, be sure to call super.setup(state,base); before you do anything else.

For prototypes, setup(...) is typically called once for the prototype instance; cloned instances do not receive the setup(...) call. setup(...) may be called more than once; the only guarantee is that it will get called at least once on an instance or some "parent" object from which it was ultimately cloned.

Specified by:
setup in interface Prototype
Specified by:
setup in interface Setup
setup in class GPNodeBuilder


public int pickSize(EvolutionState state,
                    int thread,
                    int functionset,
                    int type)


public void preprocess(EvolutionState state,
                       int _maxtreesize)


public final int intForNode(GPNode node)


public java.math.BigInteger numTreesOfType(GPInitializer initializer,
                                           int functionset,
                                           int type,
                                           int size)


public java.math.BigInteger numTreesRootedByNode(GPInitializer initializer,
                                                 int functionset,
                                                 GPNode node,
                                                 int size)


public java.math.BigInteger numChildPermutations(GPInitializer initializer,
                                                 int functionset,
                                                 GPNode parent,
                                                 int size,
                                                 int outof,
                                                 int pickchild)


public void computePercentages()


public GPNode newRootedTree(EvolutionState state,
                            GPType type,
                            int thread,
                            GPNodeParent parent,
                            GPFunctionSet set,
                            int argposition,
                            int requestedSize)
Specified by:
newRootedTree in class GPNodeBuilder