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* Licensed to the Apache Software Foundation (ASF) under one or more
* contributor license agreements. See the NOTICE file distributed with
* this work for additional information regarding copyright ownership.
* The ASF licenses this file to You under the Apache License, Version 2.0
* (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.apache.commons.math3.genetics;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import org.apache.commons.math3.exception.DimensionMismatchException;
import org.apache.commons.math3.exception.MathIllegalArgumentException;
import org.apache.commons.math3.exception.util.LocalizedFormats;
/**
* Random Key chromosome is used for permutation representation. It is a vector
* of a fixed length of real numbers in [0,1] interval. The index of the i-th
* smallest value in the vector represents an i-th member of the permutation.
* <p>
* For example, the random key [0.2, 0.3, 0.8, 0.1] corresponds to the
* permutation of indices (3,0,1,2). If the original (unpermuted) sequence would
* be (a,b,c,d), this would mean the sequence (d,a,b,c).
* <p>
* With this representation, common operators like n-point crossover can be
* used, because any such chromosome represents a valid permutation.
* <p>
* Since the chromosome (and thus its arrayRepresentation) is immutable, the
* array representation is sorted only once in the constructor.
* <p>
* For details, see:
* <ul>
* <li>Bean, J.C.: Genetic algorithms and random keys for sequencing and
* optimization. ORSA Journal on Computing 6 (1994) 154-160</li>
* <li>Rothlauf, F.: Representations for Genetic and Evolutionary Algorithms.
* Volume 104 of Studies in Fuzziness and Soft Computing. Physica-Verlag,
* Heidelberg (2002)</li>
* </ul>
*
* @param <T> type of the permuted objects
* @since 2.0
*/
public abstract class RandomKey<T> extends AbstractListChromosome<Double> implements PermutationChromosome<T> {
/** Cache of sorted representation (unmodifiable). */
private final List<Double> sortedRepresentation;
/**
* Base sequence [0,1,...,n-1], permuted according to the representation (unmodifiable).
*/
private final List<Integer> baseSeqPermutation;
/**
* Constructor.
*
* @param representation list of [0,1] values representing the permutation
* @throws InvalidRepresentationException iff the <code>representation</code> can not represent a valid chromosome
*/
public RandomKey(final List<Double> representation) throws InvalidRepresentationException {
super(representation);
// store the sorted representation
List<Double> sortedRepr = new ArrayList<Double> (getRepresentation());
Collections.sort(sortedRepr);
sortedRepresentation = Collections.unmodifiableList(sortedRepr);
// store the permutation of [0,1,...,n-1] list for toString() and isSame() methods
baseSeqPermutation = Collections.unmodifiableList(
decodeGeneric(baseSequence(getLength()), getRepresentation(), sortedRepresentation)
);
}
/**
* Constructor.
*
* @param representation array of [0,1] values representing the permutation
* @throws InvalidRepresentationException iff the <code>representation</code> can not represent a valid chromosome
*/
public RandomKey(final Double[] representation) throws InvalidRepresentationException {
this(Arrays.asList(representation));
}
/**
* {@inheritDoc}
*/
public List<T> decode(final List<T> sequence) {
return decodeGeneric(sequence, getRepresentation(), sortedRepresentation);
}
/**
* Decodes a permutation represented by <code>representation</code> and
* returns a (generic) list with the permuted values.
*
* @param <S> generic type of the sequence values
* @param sequence the unpermuted sequence
* @param representation representation of the permutation ([0,1] vector)
* @param sortedRepr sorted <code>representation</code>
* @return list with the sequence values permuted according to the representation
* @throws DimensionMismatchException iff the length of the <code>sequence</code>,
* <code>representation</code> or <code>sortedRepr</code> lists are not equal
*/
private static <S> List<S> decodeGeneric(final List<S> sequence, List<Double> representation,
final List<Double> sortedRepr)
throws DimensionMismatchException {
int l = sequence.size();
// the size of the three lists must be equal
if (representation.size() != l) {
throw new DimensionMismatchException(representation.size(), l);
}
if (sortedRepr.size() != l) {
throw new DimensionMismatchException(sortedRepr.size(), l);
}
// do not modify the original representation
List<Double> reprCopy = new ArrayList<Double> (representation);
// now find the indices in the original repr and use them for permuting
List<S> res = new ArrayList<S> (l);
for (int i=0; i<l; i++) {
int index = reprCopy.indexOf(sortedRepr.get(i));
res.add(sequence.get(index));
reprCopy.set(index, null);
}
return res;
}
/**
* Returns <code>true</code> iff <code>another</code> is a RandomKey and
* encodes the same permutation.
*
* @param another chromosome to compare
* @return true iff chromosomes encode the same permutation
*/
@Override
protected boolean isSame(final Chromosome another) {
// type check
if (! (another instanceof RandomKey<?>)) {
return false;
}
RandomKey<?> anotherRk = (RandomKey<?>) another;
// size check
if (getLength() != anotherRk.getLength()) {
return false;
}
// two different representations can still encode the same permutation
// the ordering is what counts
List<Integer> thisPerm = this.baseSeqPermutation;
List<Integer> anotherPerm = anotherRk.baseSeqPermutation;
for (int i=0; i<getLength(); i++) {
if (thisPerm.get(i) != anotherPerm.get(i)) {
return false;
}
}
// the permutations are the same
return true;
}
/**
* {@inheritDoc}
*/
@Override
protected void checkValidity(final List<Double> chromosomeRepresentation)
throws InvalidRepresentationException {
for (double val : chromosomeRepresentation) {
if (val < 0 || val > 1) {
throw new InvalidRepresentationException(LocalizedFormats.OUT_OF_RANGE_SIMPLE,
val, 0, 1);
}
}
}
/**
* Generates a representation corresponding to a random permutation of
* length l which can be passed to the RandomKey constructor.
*
* @param l length of the permutation
* @return representation of a random permutation
*/
public static final List<Double> randomPermutation(final int l) {
List<Double> repr = new ArrayList<Double>(l);
for (int i=0; i<l; i++) {
repr.add(GeneticAlgorithm.getRandomGenerator().nextDouble());
}
return repr;
}
/**
* Generates a representation corresponding to an identity permutation of
* length l which can be passed to the RandomKey constructor.
*
* @param l length of the permutation
* @return representation of an identity permutation
*/
public static final List<Double> identityPermutation(final int l) {
List<Double> repr = new ArrayList<Double>(l);
for (int i=0; i<l; i++) {
repr.add((double)i/l);
}
return repr;
}
/**
* Generates a representation of a permutation corresponding to the
* <code>data</code> sorted by <code>comparator</code>. The
* <code>data</code> is not modified during the process.
*
* This is useful if you want to inject some permutations to the initial
* population.
*
* @param <S> type of the data
* @param data list of data determining the order
* @param comparator how the data will be compared
* @return list representation of the permutation corresponding to the parameters
*/
public static <S> List<Double> comparatorPermutation(final List<S> data,
final Comparator<S> comparator) {
List<S> sortedData = new ArrayList<S>(data);
Collections.sort(sortedData, comparator);
return inducedPermutation(data, sortedData);
}
/**
* Generates a representation of a permutation corresponding to a
* permutation which yields <code>permutedData</code> when applied to
* <code>originalData</code>.
*
* This method can be viewed as an inverse to {@link #decode(List)}.
*
* @param <S> type of the data
* @param originalData the original, unpermuted data
* @param permutedData the data, somehow permuted
* @return representation of a permutation corresponding to the permutation
* <code>originalData -> permutedData</code>
* @throws DimensionMismatchException iff the length of <code>originalData</code>
* and <code>permutedData</code> lists are not equal
* @throws MathIllegalArgumentException iff the <code>permutedData</code> and
* <code>originalData</code> lists contain different data
*/
public static <S> List<Double> inducedPermutation(final List<S> originalData,
final List<S> permutedData)
throws DimensionMismatchException, MathIllegalArgumentException {
if (originalData.size() != permutedData.size()) {
throw new DimensionMismatchException(permutedData.size(), originalData.size());
}
int l = originalData.size();
List<S> origDataCopy = new ArrayList<S> (originalData);
Double[] res = new Double[l];
for (int i=0; i<l; i++) {
int index = origDataCopy.indexOf(permutedData.get(i));
if (index == -1) {
throw new MathIllegalArgumentException(LocalizedFormats.DIFFERENT_ORIG_AND_PERMUTED_DATA);
}
res[index] = (double) i / l;
origDataCopy.set(index, null);
}
return Arrays.asList(res);
}
@Override
public String toString() {
return String.format("(f=%s pi=(%s))", getFitness(), baseSeqPermutation);
}
/**
* Helper for constructor. Generates a list of natural numbers (0,1,...,l-1).
*
* @param l length of list to generate
* @return list of integers from 0 to l-1
*/
private static List<Integer> baseSequence(final int l) {
List<Integer> baseSequence = new ArrayList<Integer> (l);
for (int i=0; i<l; i++) {
baseSequence.add(i);
}
return baseSequence;
}
}