ec.gp.build

Class Uniform

java.lang.Object

ec.gp.GPNodeBuilder

ec.gp.build.Uniform

All Implemented Interfaces:

Prototype, Setup, java.io.Serializable, 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.

Pseudocode:

    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
                            NUMCHILDPERMUTATIONS[parent,size,outof,pickchild]

    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)
            FillNodeWithChildren(parent,pickchild+1,outof-size)
        return
   

Func CreateTreeOfType(type,size) Choose node from ROOT_D[type,size] If size > 1 FillNodeWithChildren(node,0,size-1) return node

Parameters

base.true-dist 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?)

Default Base
gp.build.uniform

See Also:

Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
java.util.Hashtable	_functionsets
java.math.BigInteger[][][]	_truesizes
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
ec.gp.build.UniformGPNodeStorage[][][][]	ROOT_D
boolean[][][]	ROOT_D_ZERO
double[][][]	truesizes
boolean	useTrueDistribution

Fields inherited from class ec.gp.GPNodeBuilder

CHECK_BOUNDARY, maxSize, minSize, NOSIZEGIVEN, P_MAXSIZE, P_MINSIZE, P_NUMSIZES, P_SIZE, sizeDistribution

Constructor Summary

Constructors

Constructor and Description
Uniform()

Method Summary

Modifier and Type	Method and Description
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 ec.gp.GPNodeBuilder

canPick, clone, pickSize

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

P_UNIFORM

public static final java.lang.String P_UNIFORM

See Also:

Constant Field Values

P_TRUEDISTRIBUTION

public static final java.lang.String P_TRUEDISTRIBUTION

See Also:

Constant Field Values

functionsets

public GPFunctionSet[] functionsets

_functionsets

public java.util.Hashtable _functionsets

funcnodes

public java.util.Hashtable funcnodes

numfuncnodes

public int numfuncnodes

maxarity

public int maxarity

maxtreesize

public int maxtreesize

_truesizes

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

truesizes

public double[][][] truesizes

useTrueDistribution

public boolean useTrueDistribution

NUMTREESOFTYPE

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

NUMTREESROOTEDBYNODE

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

NUMCHILDPERMUTATIONS

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

ROOT_D

public ec.gp.build.UniformGPNodeStorage[][][][] ROOT_D

ROOT_D_ZERO

public boolean[][][] ROOT_D_ZERO

CHILD_D

public double[][][][][] CHILD_D

Constructor Detail

Uniform

public Uniform()

Method Detail

defaultBase

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(...).

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

Overrides:

setup in class GPNodeBuilder

pickSize

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

preprocess

public void preprocess(EvolutionState state,
                       int _maxtreesize)

intForNode

public final int intForNode(GPNode node)

numTreesOfType

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

numTreesRootedByNode

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

numChildPermutations

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

computePercentages

public void computePercentages()

newRootedTree

public GPNode newRootedTree(EvolutionState state,
                            GPType type,
                            int thread,
                            GPNodeParent parent,
                            GPFunctionSet set,
                            int argposition,
                            int requestedSize)

Specified by:

newRootedTree in class GPNodeBuilder