ec.gp.build
Class Uniform

java.lang.Object
  extended by ec.gp.GPNodeBuilder
      extended by 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?)

See Also:
Serialized Form

Field Summary
 java.util.Hashtable _functionsets
           
 java.math.BigInteger[][][] _truesizes
           
static int CHECKBOUNDARY
          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
           
 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
Uniform()
           
 
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 ec.gp.GPNodeBuilder
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

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

CHECKBOUNDARY

public static final int CHECKBOUNDARY
CheckBoundary is 8

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