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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.
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package org.apache.commons.math4.ml.neuralnet.sofm;
import java.util.List;
import java.util.ArrayList;
import java.util.Set;
import java.util.HashSet;
import java.util.Collection;
import java.util.Iterator;
import org.apache.commons.math4.analysis.FunctionUtils;
import org.apache.commons.math4.analysis.UnivariateFunction;
import org.apache.commons.math4.analysis.function.Constant;
import org.apache.commons.math4.analysis.function.HarmonicOscillator;
import org.apache.commons.math4.distribution.RealDistribution;
import org.apache.commons.math4.distribution.UniformRealDistribution;
import org.apache.commons.math4.exception.MathUnsupportedOperationException;
import org.apache.commons.math4.ml.distance.DistanceMeasure;
import org.apache.commons.math4.ml.distance.EuclideanDistance;
import org.apache.commons.math4.ml.neuralnet.FeatureInitializer;
import org.apache.commons.math4.ml.neuralnet.FeatureInitializerFactory;
import org.apache.commons.math4.ml.neuralnet.Network;
import org.apache.commons.math4.ml.neuralnet.Neuron;
import org.apache.commons.math4.ml.neuralnet.oned.NeuronString;
import org.apache.commons.math4.ml.neuralnet.sofm.KohonenTrainingTask;
import org.apache.commons.math4.ml.neuralnet.sofm.KohonenUpdateAction;
import org.apache.commons.math4.ml.neuralnet.sofm.LearningFactorFunction;
import org.apache.commons.math4.ml.neuralnet.sofm.LearningFactorFunctionFactory;
import org.apache.commons.math4.ml.neuralnet.sofm.NeighbourhoodSizeFunction;
import org.apache.commons.math4.ml.neuralnet.sofm.NeighbourhoodSizeFunctionFactory;
import org.apache.commons.rng.simple.RandomSource;
import org.apache.commons.rng.UniformRandomProvider;
import org.apache.commons.math4.util.FastMath;
/**
* Solves the "Travelling Salesman's Problem" (i.e. trying to find the
* sequence of cities that minimizes the travel distance) using a 1D
* SOFM.
*/
public class TravellingSalesmanSolver {
private static final long FIRST_NEURON_ID = 0;
/** RNG. */
private final UniformRandomProvider random;
/** Set of cities. */
private final Set<City> cities = new HashSet<>();
/** SOFM. */
private final Network net;
/** Distance function. */
private final DistanceMeasure distance = new EuclideanDistance();
/** Total number of neurons. */
private final int numberOfNeurons;
/**
* @param cityList List of cities to visit in a single travel.
* @param numNeuronsPerCity Number of neurons per city.
*/
public TravellingSalesmanSolver(City[] cityList,
double numNeuronsPerCity) {
this(cityList, numNeuronsPerCity, RandomSource.createLong());
}
/**
* @param cityList List of cities to visit in a single travel.
* @param numNeuronsPerCity Number of neurons per city.
* @param seed Seed for the RNG that is used to present the samples
* to the trainer.
*/
public TravellingSalesmanSolver(City[] cityList,
double numNeuronsPerCity,
long seed) {
random = RandomSource.create(RandomSource.WELL_1024_A, seed);
// Make sure that each city will appear only once in the list.
for (City city : cityList) {
cities.add(city);
}
// Total number of neurons.
numberOfNeurons = (int) numNeuronsPerCity * cities.size();
// Create a network with circle topology.
net = new NeuronString(numberOfNeurons, true, makeInitializers()).getNetwork();
}
/**
* Creates training tasks.
*
* @param numTasks Number of tasks to create.
* @param numSamplesPerTask Number of training samples per task.
* @return the created tasks.
*/
public Runnable[] createParallelTasks(int numTasks,
long numSamplesPerTask) {
final Runnable[] tasks = new Runnable[numTasks];
final LearningFactorFunction learning
= LearningFactorFunctionFactory.exponentialDecay(2e-1,
5e-2,
numSamplesPerTask / 2);
final NeighbourhoodSizeFunction neighbourhood
= NeighbourhoodSizeFunctionFactory.exponentialDecay(0.5 * numberOfNeurons,
0.1 * numberOfNeurons,
numSamplesPerTask / 2);
for (int i = 0; i < numTasks; i++) {
final KohonenUpdateAction action = new KohonenUpdateAction(distance,
learning,
neighbourhood);
tasks[i] = new KohonenTrainingTask(net,
createRandomIterator(numSamplesPerTask),
action);
}
return tasks;
}
/**
* Creates a training task.
*
* @param numSamples Number of training samples.
* @return the created task.
*/
public Runnable createSequentialTask(long numSamples) {
return createParallelTasks(1, numSamples)[0];
}
/**
* Measures the network's concurrent update performance.
*
* @return the ratio between the number of succesful network updates
* and the number of update attempts.
*/
public double getUpdateRatio() {
return computeUpdateRatio(net);
}
/**
* Measures the network's concurrent update performance.
*
* @param net Network to be trained with the SOFM algorithm.
* @return the ratio between the number of successful network updates
* and the number of update attempts.
*/
private static double computeUpdateRatio(Network net) {
long numAttempts = 0;
long numSuccesses = 0;
for (Neuron n : net) {
numAttempts += n.getNumberOfAttemptedUpdates();
numSuccesses += n.getNumberOfSuccessfulUpdates();
}
return (double) numSuccesses / (double) numAttempts;
}
/**
* Creates an iterator that will present a series of city's coordinates in
* a random order.
*
* @param numSamples Number of samples.
* @return the iterator.
*/
private Iterator<double[]> createRandomIterator(final long numSamples) {
final List<City> cityList = new ArrayList<>();
cityList.addAll(cities);
return new Iterator<double[]>() {
/** Number of samples. */
private long n = 0;
/** {@inheritDoc} */
@Override
public boolean hasNext() {
return n < numSamples;
}
/** {@inheritDoc} */
@Override
public double[] next() {
++n;
return cityList.get(random.nextInt(cityList.size())).getCoordinates();
}
/** {@inheritDoc} */
@Override
public void remove() {
throw new MathUnsupportedOperationException();
}
};
}
/**
* @return the list of linked neurons (i.e. the one-dimensional
* SOFM).
*/
private List<Neuron> getNeuronList() {
// Sequence of coordinates.
final List<Neuron> list = new ArrayList<>();
// First neuron.
Neuron current = net.getNeuron(FIRST_NEURON_ID);
while (true) {
list.add(current);
final Collection<Neuron> neighbours
= net.getNeighbours(current, list);
final Iterator<Neuron> iter = neighbours.iterator();
if (!iter.hasNext()) {
// All neurons have been visited.
break;
}
current = iter.next();
}
return list;
}
/**
* @return the list of features (coordinates) of linked neurons.
*/
public List<double[]> getCoordinatesList() {
// Sequence of coordinates.
final List<double[]> coordinatesList = new ArrayList<>();
for (Neuron n : getNeuronList()) {
coordinatesList.add(n.getFeatures());
}
return coordinatesList;
}
/**
* Returns the travel proposed by the solver.
* Note: cities can be missing or duplicated.
*
* @return the list of cities in travel order.
*/
public City[] getCityList() {
final List<double[]> coord = getCoordinatesList();
final City[] cityList = new City[coord.size()];
for (int i = 0; i < cityList.length; i++) {
final double[] c = coord.get(i);
cityList[i] = getClosestCity(c[0], c[1]);
}
return cityList;
}
/**
* @param x x-coordinate.
* @param y y-coordinate.
* @return the city whose coordinates are closest to {@code (x, y)}.
*/
public City getClosestCity(double x,
double y) {
City closest = null;
double min = Double.POSITIVE_INFINITY;
for (City c : cities) {
final double d = c.distance(x, y);
if (d < min) {
min = d;
closest = c;
}
}
return closest;
}
/**
* Computes the barycentre of all city locations.
*
* @param cities City list.
* @return the barycentre.
*/
private static double[] barycentre(Set<City> cities) {
double xB = 0;
double yB = 0;
int count = 0;
for (City c : cities) {
final double[] coord = c.getCoordinates();
xB += coord[0];
yB += coord[1];
++count;
}
return new double[] { xB / count, yB / count };
}
/**
* Computes the largest distance between the point at coordinates
* {@code (x, y)} and any of the cities.
*
* @param x x-coodinate.
* @param y y-coodinate.
* @param cities City list.
* @return the largest distance.
*/
private static double largestDistance(double x,
double y,
Set<City> cities) {
double maxDist = 0;
for (City c : cities) {
final double dist = c.distance(x, y);
if (dist > maxDist) {
maxDist = dist;
}
}
return maxDist;
}
/**
* Creates the features' initializers: an approximate circle around the
* barycentre of the cities.
*
* @return an array containing the two initializers.
*/
private FeatureInitializer[] makeInitializers() {
// Barycentre.
final double[] centre = barycentre(cities);
// Largest distance from centre.
final double radius = 0.5 * largestDistance(centre[0], centre[1], cities);
final double omega = 2 * Math.PI / numberOfNeurons;
final UnivariateFunction h1 = new HarmonicOscillator(radius, omega, 0);
final UnivariateFunction h2 = new HarmonicOscillator(radius, omega, 0.5 * Math.PI);
final UnivariateFunction f1 = FunctionUtils.add(h1, new Constant(centre[0]));
final UnivariateFunction f2 = FunctionUtils.add(h2, new Constant(centre[1]));
final RealDistribution u = new UniformRealDistribution(-0.05 * radius, 0.05 * radius);
return new FeatureInitializer[] {
FeatureInitializerFactory.randomize(u.createSampler(random),
FeatureInitializerFactory.function(f1, 0, 1)),
FeatureInitializerFactory.randomize(u.createSampler(random),
FeatureInitializerFactory.function(f2, 0, 1))
};
}
}
/**
* A city, represented by a name and two-dimensional coordinates.
*/
class City {
/** Identifier. */
final String name;
/** x-coordinate. */
final double x;
/** y-coordinate. */
final double y;
/**
* @param name Name.
* @param x Cartesian x-coordinate.
* @param y Cartesian y-coordinate.
*/
public City(String name,
double x,
double y) {
this.name = name;
this.x = x;
this.y = y;
}
/**
* @retun the name.
*/
public String getName() {
return name;
}
/**
* @return the (x, y) coordinates.
*/
public double[] getCoordinates() {
return new double[] { x, y };
}
/**
* Computes the distance between this city and
* the given point.
*
* @param x x-coodinate.
* @param y y-coodinate.
* @return the distance between {@code (x, y)} and this
* city.
*/
public double distance(double x,
double y) {
final double xDiff = this.x - x;
final double yDiff = this.y - y;
return FastMath.sqrt(xDiff * xDiff + yDiff * yDiff);
}
/** {@inheritDoc} */
@Override
public boolean equals(Object o) {
if (o instanceof City) {
final City other = (City) o;
return x == other.x &&
y == other.y;
}
return false;
}
/** {@inheritDoc} */
@Override
public int hashCode() {
int result = 17;
final long c1 = Double.doubleToLongBits(x);
result = 31 * result + (int) (c1 ^ (c1 >>> 32));
final long c2 = Double.doubleToLongBits(y);
result = 31 * result + (int) (c2 ^ (c2 >>> 32));
return result;
}
}