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This package contains several example programs of
the usage of the JavaPermutationTools (JPT) library. JPT is a Java
library that enables representing and generating permutations and
sequences, as well as performing computation on permutations and
sequences. It includes implementations of a variety of permutation
distance metrics as well as distance metrics on sequences (i.e.,
Strings, arrays, and other ordered data types). In addition to
programs demonstrating the usage of the JPT library, the
jpt-examples package also contains programs for replicating the
experiments from a few published papers that utilized the library
or implementations on which the library is based. JPT's source code
is maintained on GitHub, and the prebuilt jars of the library can
be imported from Maven Central using maven or other build tools.
The purpose of the package jpt-examples is to demonstrate usage of
the major functionality of the JPT library. You can find out
more about the JPT library itself from its
website: https://jpt.cicirello.org/.
The newest version!
/*
* Example programs for JavaPermutationTools library.
* Copyright (C) 2018-2023 Vincent A. Cicirello
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see
* V.A. Cicirello, "Classification of
* Permutation Distance Metrics for Fitness Landscape Analysis," Proceedings of the 11th
* International Conference on Bio-inspired Information and Communications Technologies, March 2019.
*
* @author Vincent A. Cicirello, https://www.cicirello.org/
*/
public class BICT2019 {
/**
* Runs the replication program.
*
* @param args The command line argument is optional. If specified, the first command line
* argument is the permutation length (defaults to 10 if not specified).
*/
public static void main(String[] args) {
ExamplesShared.printCopyrightAndLicense();
final int LENGTH = (args.length > 0) ? Integer.parseInt(args[0]) : 10;
final int COUNT = fact(LENGTH);
// List of distance measures to use in analysis
ArrayList measures = new ArrayList();
measures.add(new ExactMatchDistance());
measures.add(new InterchangeDistance());
measures.add(new AcyclicEdgeDistance());
measures.add(new CyclicEdgeDistance());
measures.add(new RTypeDistance());
measures.add(new CyclicRTypeDistance());
measures.add(new KendallTauDistance());
measures.add(new ReinsertionDistance());
measures.add(new DeviationDistance());
measures.add(new SquaredDeviationDistance());
measures.add(new LeeDistance());
int numMeasures = measures.size();
// Reference permutation
Permutation p1 = new Permutation(LENGTH, 0);
// Array to store distances to reference permutation
int[][] data = new int[numMeasures][COUNT];
// Iterate over all permutations and compute distances (for all distance measures) to reference
// permutation
for (int i = 0; i < COUNT; i++) {
Permutation p2 = new Permutation(LENGTH, i);
for (int j = 0; j < numMeasures; j++) {
data[j][i] = measures.get(j).distance(p1, p2);
}
}
// Compute correlation matrix
double[][] corr = correlationMatrix(data);
System.out.println("Data for the Tables of Section 3 of the paper.");
System.out.println("PCA using all permutations of length " + LENGTH);
System.out.println();
// Output correlation matrix. Matrix is symmetric so just outputting lower triangle.
System.out.println("Correlation Matrix (lower triangle)\n");
for (int i = 0; i < numMeasures; i++) {
System.out.print("\t" + measures.get(i).getClass().getSimpleName());
}
System.out.println();
for (int i = 0; i < numMeasures; i++) {
System.out.print(measures.get(i).getClass().getSimpleName());
for (int j = 0; j <= i; j++) {
System.out.printf("\t%6.3f", corr[i][j]);
}
System.out.println();
}
System.out.println();
// Compute eigenvalues and eigenvectors with Jacobi method.
JacobiDiagonalization j = new JacobiDiagonalization(corr);
boolean converged = j.compute();
// Get the matrix of eigenvectors.
double[][] v = j.eigenvectors();
// Transpose the matrix to make it easier to sort the eigenvectors by eigenvalue.
// i.e., since java 2D arrays are arrays of arrays, having eigenvectors in rows instead of
// columns will make it easier to sort.
v = MatrixOps.transposeSquareMatrixInline(v);
// Nested class used for sorting.
class EigenValueVectorPair implements Comparable {
double value;
double[] vector;
EigenValueVectorPair(double value, double[] vector) {
this.value = value;
this.vector = vector;
}
@Override
public int compareTo(EigenValueVectorPair other) {
return Double.compare(Math.abs(other.value), Math.abs(value));
}
@Override
public boolean equals(Object other) {
if (other == null || !(other instanceof EigenValueVectorPair)) {
return false;
}
EigenValueVectorPair casted = (EigenValueVectorPair) other;
return compareTo(casted) == 0 && Arrays.equals(vector, casted.vector);
}
@Override
public int hashCode() {
return Double.hashCode(value);
}
}
// Sort the eigenvectors by eigenvalue (largest eigenvalue to smallest)
EigenValueVectorPair[] pairs = new EigenValueVectorPair[v.length];
double sumEigenvalues = 0;
for (int i = 0; i < v.length; i++) {
pairs[i] = new EigenValueVectorPair(j.eigenvalues()[i], v[i]);
sumEigenvalues = sumEigenvalues + pairs[i].value;
}
Arrays.sort(pairs);
System.out.println(
converged ? "Convergence Achieved" : "Max Iterations Caused Termination of Jacobi Method");
System.out.println("Eigenvalues and Eigenvectors sorted by absolute value of Eigenvalue:");
System.out.println();
System.out.println("pc\teigenvalue\tproportion\tcumulative");
double runningSum = 0;
int c = 1;
for (EigenValueVectorPair pair : pairs) {
runningSum = runningSum + pair.value;
System.out.printf(
"%3d\t%6.4f\t%6.4f\t%6.4f%n",
c, pair.value, pair.value / sumEigenvalues, runningSum / sumEigenvalues);
c++;
}
System.out.println();
System.out.println();
System.out.print("distance");
for (int i = 1; i <= numMeasures; i++) {
System.out.print("\tpc" + i);
}
System.out.println();
for (int i = 0; i < numMeasures; i++) {
System.out.print(measures.get(i).getClass().getSimpleName());
for (EigenValueVectorPair pair : pairs) {
System.out.printf("\t%6.4f", pair.vector[i]);
}
System.out.println();
}
System.out.println();
// compute and output correlation coefficients between original distances and the principle
// components
System.out.println("Correlation between original distance measures and principle components.");
System.out.print("distance");
for (int i = 1; i <= numMeasures; i++) {
System.out.print("\tpc" + i);
}
System.out.println();
for (int i = 0; i < numMeasures; i++) {
System.out.print(measures.get(i).getClass().getSimpleName());
for (int k = 0; k < numMeasures; k++) {
System.out.printf("\t%6.4f", Math.sqrt(pairs[k].value) * pairs[k].vector[i]);
}
System.out.println();
}
System.out.println();
System.out.println();
System.out.println("Data for the Tables of Section 4 of the paper.");
System.out.println("PCA using sampled permutations of length 50");
System.out.println("IMPORTANT NOTE: Since we're randomly sampling, the data");
System.out.println("generated by this program will vary by run, so may not be");
System.out.println("identical to the data in the paper, but should be consistent");
System.out.println("statistically.");
System.out.println();
// Reference permutation
final int SAMPLED_LENGTH = 50;
p1 = new Permutation(SAMPLED_LENGTH, 0);
// generate randomly sampled permutations of length 50
for (int i = 0; i < COUNT; i++) {
Permutation p2 = new Permutation(SAMPLED_LENGTH);
for (int k = 0; k < numMeasures; k++) {
data[k][i] = measures.get(k).distance(p1, p2);
}
}
corr = correlationMatrix(data);
// Output correlation matrix. Matrix is symmetric so just outputting lower triangle.
System.out.println("Correlation Matrix from sampled data (lower triangle)\n");
for (int i = 0; i < numMeasures; i++) {
System.out.print("\t" + measures.get(i).getClass().getSimpleName());
}
System.out.println();
for (int i = 0; i < numMeasures; i++) {
System.out.print(measures.get(i).getClass().getSimpleName());
for (int k = 0; k <= i; k++) {
System.out.printf("\t&%6.3f", corr[i][k]);
}
System.out.println();
}
System.out.println();
// Compute eigenvalues and eigenvectors with Jacobi method.
j = new JacobiDiagonalization(corr);
converged = j.compute();
// Get the matrix of eigenvectors.
v = j.eigenvectors();
// Transpose the matrix to make it easier to sort the eigenvectors by eigenvalue.
// i.e., since java 2D arrays are arrays of arrays, having eigenvectors in rows instead of
// columns will make it easier to sort.
v = MatrixOps.transposeSquareMatrixInline(v);
// Sort the eigenvectors by eigenvalue (largest eigenvalue to smallest)
pairs = new EigenValueVectorPair[v.length];
sumEigenvalues = 0;
for (int i = 0; i < v.length; i++) {
pairs[i] = new EigenValueVectorPair(j.eigenvalues()[i], v[i]);
sumEigenvalues = sumEigenvalues + pairs[i].value;
}
Arrays.sort(pairs);
System.out.println(
converged ? "Convergence Achieved" : "Max Iterations Caused Termination of Jacobi Method");
System.out.println(
"Eigenvalues and Eigenvectors (using sampled data) sorted by absolute value of Eigenvalue:");
System.out.println();
System.out.println("pc\teigenvalue\tproportion\tcumulative");
runningSum = 0;
c = 1;
for (EigenValueVectorPair pair : pairs) {
runningSum = runningSum + pair.value;
System.out.printf(
"%3d\t%6.4f\t%6.4f\t%6.4f%n",
c, pair.value, pair.value / sumEigenvalues, runningSum / sumEigenvalues);
c++;
}
System.out.println();
System.out.println();
System.out.print("distance");
for (int i = 1; i <= 5 /*numMeasures*/; i++) {
System.out.print("\tpc" + i);
}
System.out.println();
for (int i = 0; i < numMeasures; i++) {
System.out.print(measures.get(i).getClass().getSimpleName());
int x = 0;
for (EigenValueVectorPair pair : pairs) {
System.out.printf("\t&%6.4f", pair.vector[i]);
x++;
if (x == 5) break;
}
System.out.println();
}
System.out.println();
// compute and output correlation coefficients between original distances and the principle
// components
System.out.println("Correlation between original distance measures and principle components.");
System.out.print("distance");
for (int i = 1; i <= 5 /*numMeasures*/; i++) {
System.out.print("\tpc" + i);
}
System.out.println();
for (int i = 0; i < numMeasures; i++) {
System.out.print(measures.get(i).getClass().getSimpleName());
for (int k = 0; k < 5 /*numMeasures*/; k++) {
System.out.printf("\t&%6.4f", Math.sqrt(pairs[k].value) * pairs[k].vector[i]);
}
System.out.println();
}
System.out.println();
System.out.println();
System.out.println();
System.out.println(
"Data for Fitness Distance Correlation Examples from Section 5 of the paper");
System.out.println("Note that the data generated here may not be identical");
System.out.println("to the data in the paper due to random behavior, but should");
System.out.println("be consistent statistically.");
System.out.println();
System.out.println();
System.out.println("Fitness Distance Correlation example 1 (R-permutation landscape): TSP");
System.out.println("Simple TSP example with known optimal: cities arranged on a circle.");
double[][] fdcTable = new double[numMeasures][5];
// Generate city locations: on a circle centered at (0,0).
final int NUM_CITIES = 20;
final double RADIUS = 1;
double[][] cities = new double[NUM_CITIES][2];
double angle = 0.0;
final double DELTA_A = 2.0 * Math.PI / NUM_CITIES;
for (int i = 0; i < NUM_CITIES; i++) {
cities[i][0] = RADIUS * Math.cos(angle);
cities[i][1] = RADIUS * Math.sin(angle);
angle += DELTA_A;
}
int[] optimalAsArray = new int[NUM_CITIES];
for (int i = 0; i < NUM_CITIES; i++) optimalAsArray[i] = i;
Permutation opimalTour = new Permutation(optimalAsArray);
ArrayList cyclicAndReversal =
new ArrayList();
ArrayList cyclic = new ArrayList();
for (PermutationDistanceMeasurer m : measures) {
cyclicAndReversal.add(new CyclicReversalIndependentDistance(m));
cyclic.add(new CyclicIndependentDistance(m));
}
// generate randomly sampled permutations, and other data needed for fitness-distance
// correlation
// Simple TSP
final int NUM_SAMPLES = 100000;
double[] tourLength = new double[NUM_SAMPLES];
double[][] dataD = new double[numMeasures][NUM_SAMPLES];
for (int i = 0; i < NUM_SAMPLES; i++) {
Permutation randomTour = new Permutation(NUM_CITIES);
tourLength[i] = tourCost(cities, randomTour);
for (int k = 0; k < numMeasures; k++) {
dataD[k][i] = cyclicAndReversal.get(k).distance(opimalTour, randomTour);
}
}
System.out.println();
System.out.println("Outputting fitness-distance correlations.");
for (int i = 0; i < numMeasures; i++) {
fdcTable[i][0] = correlation(tourLength, dataD[i]);
System.out.print(measures.get(i).getClass().getSimpleName());
System.out.printf("\t&%6.4f%n", fdcTable[i][0]);
}
System.out.println();
System.out.println();
System.out.println();
System.out.println(
"Fitness Distance Correlation example 2 (R-permutation directed edges): Asymmetric TSP");
System.out.println("Simple ATSP example with known optimal: cities arranged on a circle.");
// generate randomly sampled permutations, and other data needed for fitness-distance
// correlation
// Simple Asymmetric TSP
for (int i = 0; i < NUM_SAMPLES; i++) {
Permutation randomTour = new Permutation(NUM_CITIES);
tourLength[i] = tourCostAsymmetric(cities, randomTour);
for (int k = 0; k < numMeasures; k++) {
dataD[k][i] = cyclic.get(k).distance(opimalTour, randomTour);
}
}
System.out.println();
System.out.println("Outputting fitness-distance correlations.");
for (int i = 0; i < numMeasures; i++) {
fdcTable[i][1] = correlation(tourLength, dataD[i]);
System.out.print(measures.get(i).getClass().getSimpleName());
System.out.printf("\t&%6.4f%n", fdcTable[i][1]);
}
System.out.println();
System.out.println();
System.out.println();
System.out.println("Fitness Distance Correlation example 3: A-permutation landscape");
System.out.println("Simple mapping example with known optimal.");
double[] fitness = new double[NUM_SAMPLES];
final int MAPPING_LENGTH = 10;
optimalAsArray = new int[MAPPING_LENGTH];
for (int i = 0; i < MAPPING_LENGTH; i++) optimalAsArray[i] = i;
Permutation opimalPerm = new Permutation(optimalAsArray);
ExactMatchDistance em = new ExactMatchDistance();
for (int i = 0; i < NUM_SAMPLES; i++) {
Permutation randomPerm = new Permutation(MAPPING_LENGTH);
fitness[i] = em.distance(opimalPerm, randomPerm);
if (fitness[i] > 0.0) {
fitness[i] *= (1.0 + 0.5 * ThreadLocalRandom.current().nextDouble());
}
for (int k = 0; k < numMeasures; k++) {
dataD[k][i] = measures.get(k).distance(opimalPerm, randomPerm);
}
}
System.out.println();
System.out.println("Outputting fitness-distance correlations.");
for (int i = 0; i < numMeasures; i++) {
fdcTable[i][2] = correlation(fitness, dataD[i]);
System.out.print(measures.get(i).getClass().getSimpleName());
System.out.printf("\t&%6.4f%n", fdcTable[i][2]);
}
System.out.println();
System.out.println();
System.out.println();
System.out.println("Fitness Distance Correlation example 4: P-permutation landscape");
System.out.println("Simple ranking example with known optimal.");
KendallTauDistance tau = new KendallTauDistance();
for (int i = 0; i < NUM_SAMPLES; i++) {
Permutation randomPerm = new Permutation(MAPPING_LENGTH);
fitness[i] = tau.distance(opimalPerm, randomPerm);
if (fitness[i] > 0.0) {
fitness[i] *= (1.0 + 0.5 * ThreadLocalRandom.current().nextDouble());
}
for (int k = 0; k < numMeasures; k++) {
dataD[k][i] = measures.get(k).distance(opimalPerm, randomPerm);
}
}
System.out.println();
System.out.println("Outputting fitness-distance correlations.");
for (int i = 0; i < numMeasures; i++) {
fdcTable[i][3] = correlation(fitness, dataD[i]);
System.out.print(measures.get(i).getClass().getSimpleName());
System.out.printf("\t&%6.4f%n", fdcTable[i][3]);
}
System.out.println();
System.out.println();
System.out.println();
System.out.println("Fitness Distance Correlation example 5: P-permutation, cyclic, landscape");
System.out.println("Simple cyclic P-permutation example with known optimal.");
LeeDistance lee = new LeeDistance();
for (int i = 0; i < NUM_SAMPLES; i++) {
Permutation randomPerm = new Permutation(MAPPING_LENGTH);
fitness[i] = lee.distance(opimalPerm, randomPerm);
if (fitness[i] > 0.0) {
fitness[i] *= (1.0 + 0.5 * ThreadLocalRandom.current().nextDouble());
}
for (int k = 0; k < numMeasures; k++) {
dataD[k][i] = measures.get(k).distance(opimalPerm, randomPerm);
}
}
System.out.println();
System.out.println("Outputting fitness-distance correlations.");
for (int i = 0; i < numMeasures; i++) {
fdcTable[i][4] = correlation(fitness, dataD[i]);
System.out.print(measures.get(i).getClass().getSimpleName());
System.out.printf("\t&%6.4f%n", fdcTable[i][4]);
}
System.out.println();
System.out.println();
System.out.println("Outputting All FDC Data as One Table");
System.out.println(
"Distance\t& Landscape 1\t& Landscape 2\t& Landscape 3\t& Landscape 4\t& Landscape 5");
for (int i = 0; i < numMeasures; i++) {
System.out.print(measures.get(i).getClass().getSimpleName());
System.out.printf(
"\t&%6.4f\t&%6.4f\t&%6.4f\t&%6.4f\t&%6.4f%n",
fdcTable[i][0], fdcTable[i][1], fdcTable[i][2], fdcTable[i][3], fdcTable[i][4]);
}
System.out.println();
}
private static double tourCost(double[][] cities, Permutation p) {
double cost = 0;
for (int i = 0; i < p.length(); i++) {
int start = p.get(i);
int end = p.get((i + 1) % p.length());
double deltaX = cities[start][0] - cities[end][0];
double deltaY = cities[start][1] - cities[end][1];
cost = cost + Math.sqrt(deltaX * deltaX + deltaY * deltaY);
}
return cost;
}
private static double tourCostAsymmetric(double[][] cities, Permutation p) {
double cost = 0;
for (int i = 0; i < p.length(); i++) {
int start = p.get(i);
int end = p.get((i + 1) % p.length());
double deltaX = cities[start][0] - cities[end][0];
double deltaY = cities[start][1] - cities[end][1];
double edgeCost =
start < end || (end == 0 && start == p.length() - 1)
? Math.sqrt(deltaX * deltaX + deltaY * deltaY)
: 2.0;
cost = cost + edgeCost;
}
return cost;
}
private static int fact(int N) {
int f = 1;
for (int i = 2; i <= N; i++) {
f *= i;
}
return f;
}
}