/*
* Written by Doug Lea and Bill Scherer with assistance from members
* of JCP JSR-166 Expert Group and released to the public domain, as
* explained at http://creativecommons.org/licenses/publicdomain
*/
import java.util.*;
import java.util.concurrent.*;
import java.util.concurrent.atomic.*;
import java.util.concurrent.locks.*;
/**
* A parallel Traveling Salesperson Problem (TSP) program based on a
* genetic algorithm using an Exchanger. A population of chromosomes
* is distributed among "pools". The chromosomes represent tours, and
* their fitness is the total tour length. Each chromosome is
* initialized as a random tour. A Task is associated with each pool.
* Each task repeatedly does, for a fixed number of iterations
* (generations):
*
*
* - Select a breeder b from the pool
*
- Create a strand of its tour with a random starting point and length
*
- Offer the strand to the exchanger, receiving a strand from
* another pool
*
- Combine b and the received strand using crossing function to
* create new chromosome c.
*
- Replace a chromosome in the pool with c.
*
*
* See below for more details.
*
*
*/
public class TSPExchangerTest {
static final int DEFAULT_MAX_THREADS =
(Runtime.getRuntime().availableProcessors() + 2);
/**
* The problem size. Each city is a random point. The goal is to
* find a tour among them with smallest total Euclidean distance.
*/
static final int DEFAULT_CITIES = 144;
// Tuning parameters.
/**
* The number of chromosomes per pool. Must be a power of two.
*
* Smaller values lead to faster iterations but poorer quality
* results
*/
static final int DEFAULT_POOL_SIZE = 32;
/**
* The number of iterations per task. Convergence appears
* to be roughly proportional to #cities-squared
*/
static final int DEFAULT_GENERATIONS = DEFAULT_CITIES * DEFAULT_CITIES;
/**
* The number of pools. The total population is #pools * poolSize,
* which should be roughly on the order of #cities-squared
*
* Smaller values lead to faster total runs but poorer quality
* results
*/
static final int DEFAULT_NPOOLS = DEFAULT_GENERATIONS / DEFAULT_POOL_SIZE;
/**
* The minimum length for a random chromosome strand.
* Must be at least 1.
*/
static final int MIN_STRAND_LENGTH = 3;
/**
* The probablility mask value for creating random strands,
* that have lengths at least MIN_STRAND_LENGTH, and grow
* with exposnential decay 2^(-(1/(RANDOM_STRAND_MASK + 1)
* Must be 1 less than a power of two.
*/
static final int RANDOM_STRAND_MASK = 7;
/**
* Probablility control for selecting breeders.
* Breeders are selected starting at the best-fitness chromosome,
* with exponentially decaying probablility
* 1 / (poolSize >>> BREEDER_DECAY).
*
* Larger values usually cause faster convergence but poorer
* quality results
*/
static final int BREEDER_DECAY = 1;
/**
* Probablility control for selecting dyers.
* Dyers are selected starting at the worst-fitness chromosome,
* with exponentially decaying probablility
* 1 / (poolSize >>> DYER_DECAY)
*
* Larger values usually cause faster convergence but poorer
* quality results
*/
static final int DYER_DECAY = 1;
/**
* The probability mask for a task to give up running and
* resubmit itself. On each iteration, a task stops iterating
* and resubmits itself with probability 1 / (RESUBMIT_MASK+1).
* This avoids some tasks running to completion before others
* even start when there are more pools than threads.
*
* Must be 1 less than a power of two.
*/
static final int RESUBMIT_MASK = 63;
static final boolean verbose = true;
static final long SNAPSHOT_RATE = 10000; // in milliseconds
/**
* The set of cities. Created once per program run, to
* make it easier to compare solutions across different runs.
*/
static CitySet cities;
public static void main(String[] args) throws Exception {
int maxThreads = DEFAULT_MAX_THREADS;
int nCities = DEFAULT_CITIES;
int poolSize = DEFAULT_POOL_SIZE;
int nGen = nCities * nCities;
int nPools = nCities * nCities / poolSize;
try {
int argc = 0;
while (argc < args.length) {
String option = args[argc++];
if (option.equals("-c")) {
nCities = Integer.parseInt(args[argc]);
nGen = nCities * nCities;
nPools = nCities * nCities / poolSize;
}
else if (option.equals("-p"))
poolSize = Integer.parseInt(args[argc]);
else if (option.equals("-g"))
nGen = Integer.parseInt(args[argc]);
else if (option.equals("-n"))
nPools = Integer.parseInt(args[argc]);
else
maxThreads = Integer.parseInt(option);
argc++;
}
}
catch (Exception e) {
reportUsageErrorAndDie();
}
System.out.print("TSPExchangerTest");
System.out.print(" -c " + nCities);
System.out.print(" -g " + nGen);
System.out.print(" -p " + poolSize);
System.out.print(" -n " + nPools);
System.out.print(" max threads " + maxThreads);
System.out.println();
cities = new CitySet(nCities);
for (int i = 2; i <= maxThreads; i += 2)
oneRun(i, nPools, poolSize, nGen);
}
static void reportUsageErrorAndDie() {
System.out.print("usage: TSPExchangerTest");
System.out.print(" [-c #cities]");
System.out.print(" [-p #poolSize]");
System.out.print(" [-g #generations]");
System.out.print(" [-n #pools]");
System.out.print(" #threads]");
System.out.println();
System.exit(0);
}
/**
* Perform one run with the given parameters. Each run completes
* when all but one of the tasks has finished. The last remaining
* task may have no one left to exchange with, so the pool is
* abruptly terminated.
*/
static void oneRun(int nThreads, int nPools, int poolSize, int nGen)
throws InterruptedException {
Population p = new Population(nThreads, nPools, poolSize, nGen);
ProgressMonitor mon = null;
if (verbose) {
mon = new ProgressMonitor(p);
mon.start();
}
p.printSnapshot(0);
long startTime = System.nanoTime();
p.start();
p.awaitTasks();
long stopTime = System.nanoTime();
if (mon != null)
mon.interrupt();
p.shutdown();
Thread.sleep(100);
long elapsed = stopTime - startTime;
long rate = elapsed / (nPools * nGen);
double secs = (double)elapsed / 1000000000.0;
p.printSnapshot(secs);
System.out.printf("%10d ns per transfer\n", rate);
}
/**
* A Population creates the pools, tasks, and threads for a run
* and has control methods to start, stop, and report progress.
*/
static final class Population {
final Task[] tasks;
final Exchanger exchanger;
final ThreadPoolExecutor exec;
final CountDownLatch done;
final int nGen;
final int poolSize;
final int nThreads;
Population(int nThreads, int nPools, int poolSize, int nGen) {
this.nThreads = nThreads;
this.nGen = nGen;
this.poolSize = poolSize;
this.exchanger = new Exchanger();
this.done = new CountDownLatch(nPools-1);
this.tasks = new Task[nPools];
for (int i = 0; i < nPools; i++)
tasks[i] = new Task(this);
BlockingQueue tq =
new LinkedBlockingQueue();
this.exec = new ThreadPoolExecutor(nThreads, nThreads,
0L, TimeUnit.MILLISECONDS,
tq);
exec.prestartAllCoreThreads();
}
/** Start the tasks */
void start() {
for (int i = 0; i < tasks.length; i++)
exec.execute(tasks[i]);
}
/** Stop the tasks */
void shutdown() {
exec.shutdownNow();
}
/** Called by task upon terminations */
void taskDone() {
done.countDown();
}
/** Wait for (all but one) task to complete */
void awaitTasks() throws InterruptedException {
done.await();
}
/**
* Called by a task to resubmit itself after completing
* fewer than nGen iterations.
*/
void resubmit(Task task) {
exec.execute(task);
}
void printSnapshot(double secs) {
int gens = 0;
double best = Double.MAX_VALUE;
double worst = 0;
for (int k = 0; k < tasks.length; ++k) {
gens += tasks[k].gen;
Chromosome[] cs = tasks[k].chromosomes;
float b = cs[0].fitness;
if (b < best)
best = b;
float w = cs[cs.length-1].fitness;
if (w > worst)
worst = w;
}
int avegen = (done.getCount() == 0)? nGen : gens / tasks.length;
System.out.printf("Time:%9.3f Best:%9.3f Worst:%9.3f Gen:%6d Threads:%4d\n",
secs, best, worst, avegen, nThreads);
}
float averageFitness() { // currently unused
float total = 0;
int count = 0;
for (int k = 0; k < tasks.length; ++k) {
Chromosome[] cs = tasks[k].chromosomes;
for (int i = 0; i < cs.length; i++)
total += cs[i].fitness;
count += cs.length;
}
return total/(float)count;
}
}
/**
* A Task updates its pool of chromosomes..
*/
static final class Task implements Runnable {
/** The pool of chromosomes, kept in sorted order */
final Chromosome[] chromosomes;
final Population pop;
/** The common exchanger, same for all tasks */
final Exchanger exchanger;
/** The current strand being exchanged */
Strand strand;
/** Bitset used in cross */
final int[] inTour;
final RNG rng;
final int poolSize;
final int nGen;
int gen;
Task(Population pop) {
this.pop = pop;
this.nGen = pop.nGen;
this.gen = 0;
this.poolSize = pop.poolSize;
this.exchanger = pop.exchanger;
this.rng = new RNG();
int length = cities.length;
this.strand = new Strand(length);
this.inTour = new int[(length >>> 5) + 1];
this.chromosomes = new Chromosome[poolSize];
for (int j = 0; j < poolSize; ++j)
chromosomes[j] = new Chromosome(length, rng);
Arrays.sort(chromosomes);
}
/**
* Run one or more update cycles.
*/
public void run() {
try {
for (;;) {
update();
if (++gen >= nGen) {
pop.taskDone();
return;
}
if ((rng.next() & RESUBMIT_MASK) == 1) {
pop.resubmit(this);
return;
}
}
} catch (InterruptedException ie) {
pop.taskDone();
}
}
/**
* Choose a breeder, exchange strand with another pool, and
* cross them to create new chromosome to replace a chosen
* dyer.
*/
void update() throws InterruptedException {
int b = chooseBreeder();
int d = chooseDyer(b);
Chromosome breeder = chromosomes[b];
Chromosome child = chromosomes[d];
chooseStrand(breeder);
strand = exchanger.exchange(strand);
cross(breeder, child);
fixOrder(child, d);
}
/**
* Choose a breeder, with exponentially decreasing probability
* starting at best.
* @return index of selected breeder
*/
int chooseBreeder() {
int mask = (poolSize >>> BREEDER_DECAY) - 1;
int b = 0;
while ((rng.next() & mask) != mask) {
if (++b >= poolSize)
b = 0;
}
return b;
}
/**
* Choose a chromosome that will be replaced, with
* exponentially decreasing probablility starting at
* worst, ignoring the excluded index
* @param exclude index to ignore; use -1 to not exclude any
* @return index of selected dyer
*/
int chooseDyer(int exclude) {
int mask = (poolSize >>> DYER_DECAY) - 1;
int d = poolSize - 1;
while (d == exclude || (rng.next() & mask) != mask) {
if (--d < 0)
d = poolSize - 1;
}
return d;
}
/**
* Select a random strand of b's.
* @param breeder the breeder
*/
void chooseStrand(Chromosome breeder) {
int[] bs = breeder.alleles;
int length = bs.length;
int strandLength = MIN_STRAND_LENGTH;
while (strandLength < length &&
(rng.next() & RANDOM_STRAND_MASK) != RANDOM_STRAND_MASK)
strandLength++;
strand.strandLength = strandLength;
int[] ss = strand.alleles;
int k = (rng.next() & 0x7FFFFFFF) % length;
for (int i = 0; i < strandLength; ++i) {
ss[i] = bs[k];
if (++k >= length) k = 0;
}
}
/**
* Copy current strand to start of c's, and then append all
* remaining b's that aren't in the strand.
* @param breeder the breeder
* @param child the child
*/
void cross(Chromosome breeder, Chromosome child) {
for (int k = 0; k < inTour.length; ++k) // clear bitset
inTour[k] = 0;
// Copy current strand to c
int[] cs = child.alleles;
int ssize = strand.strandLength;
int[] ss = strand.alleles;
int i;
for (i = 0; i < ssize; ++i) {
int x = ss[i];
cs[i] = x;
inTour[x >>> 5] |= 1 << (x & 31); // record in bit set
}
// Find index of matching origin in b
int first = cs[0];
int j = 0;
int[] bs = breeder.alleles;
while (bs[j] != first)
++j;
// Append remaining b's that aren't already in tour
while (i < cs.length) {
if (++j >= bs.length) j = 0;
int x = bs[j];
if ((inTour[x >>> 5] & (1 << (x & 31))) == 0)
cs[i++] = x;
}
}
/**
* Fix the sort order of a changed Chromosome c at position k
* @param c the chromosome
* @param k the index
*/
void fixOrder(Chromosome c, int k) {
Chromosome[] cs = chromosomes;
float oldFitness = c.fitness;
c.recalcFitness();
float newFitness = c.fitness;
if (newFitness < oldFitness) {
int j = k;
int p = j - 1;
while (p >= 0 && cs[p].fitness > newFitness) {
cs[j] = cs[p];
j = p--;
}
cs[j] = c;
} else if (newFitness > oldFitness) {
int j = k;
int n = j + 1;
while (n < cs.length && cs[n].fitness < newFitness) {
cs[j] = cs[n];
j = n++;
}
cs[j] = c;
}
}
}
/**
* A Chromosome is a candidate TSP tour.
*/
static final class Chromosome implements Comparable {
/** Index of cities in tour order */
final int[] alleles;
/** Total tour length */
float fitness;
/**
* Initialize to random tour
*/
Chromosome(int length, RNG random) {
alleles = new int[length];
for (int i = 0; i < length; i++)
alleles[i] = i;
for (int i = length - 1; i > 0; i--) {
int idx = (random.next() & 0x7FFFFFFF) % alleles.length;
int tmp = alleles[i];
alleles[i] = alleles[idx];
alleles[idx] = tmp;
}
recalcFitness();
}
public int compareTo(Object x) { // to enable sorting
float xf = ((Chromosome)x).fitness;
float f = fitness;
return ((f == xf)? 0 :((f < xf)? -1 : 1));
}
void recalcFitness() {
int[] a = alleles;
int len = a.length;
int p = a[0];
float f = cities.distanceBetween(a[len-1], p);
for (int i = 1; i < len; i++) {
int n = a[i];
f += cities.distanceBetween(p, n);
p = n;
}
fitness = f;
}
void validate() { // Ensure that this is a valid tour.
int len = alleles.length;
boolean[] used = new boolean[len];
for (int i = 0; i < len; ++i)
used[alleles[i]] = true;
for (int i = 0; i < len; ++i)
if (!used[i])
throw new Error("Bad tour");
}
}
/**
* A Strand is a random sub-sequence of a Chromosome. Each task
* creates only one strand, and then trades it with others,
* refilling it on each iteration.
*/
static final class Strand {
final int[] alleles;
int strandLength;
Strand(int length) { alleles = new int[length]; }
}
/**
* A collection of (x,y) points that represent cities. Distances
* are scaled in [0,1) to simply checking results. The expected
* optimal TSP for random points is believed to be around 0.76 *
* sqrt(N). For papers discussing this, see
* http://www.densis.fee.unicamp.br/~moscato/TSPBIB_home.html for
*/
static final class CitySet {
// Scale ints to doubles in [0,1)
static final double PSCALE = (double)0x80000000L;
final int length;
final int[] xPts;
final int[] yPts;
final float[][] distances;
CitySet(int n) {
this.length = n;
this.xPts = new int[n];
this.yPts = new int[n];
this.distances = new float[n][n];
RNG random = new RNG();
for (int i = 0; i < n; i++) {
xPts[i] = (random.next() & 0x7FFFFFFF);
yPts[i] = (random.next() & 0x7FFFFFFF);
}
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
double dX = (xPts[i] - xPts[j]) / PSCALE;
double dY = (yPts[i] - yPts[j]) / PSCALE;
distances[i][j] = (float)Math.hypot(dX, dY);
}
}
}
// Retrieve the cached distance between a pair of cities
float distanceBetween(int i, int j) {
return distances[i][j];
}
}
/**
* Cheap XorShift random number generator
*/
static final class RNG {
/** Seed generator for XorShift RNGs */
static final Random seedGenerator = new Random();
int seed;
RNG(int seed) { this.seed = seed; }
RNG() { this.seed = seedGenerator.nextInt(); }
int next() {
int x = seed;
x ^= x << 6;
x ^= x >>> 21;
x ^= x << 7;
seed = x;
return x;
}
}
static final class ProgressMonitor extends Thread {
final Population pop;
ProgressMonitor(Population p) { pop = p; }
public void run() {
double time = 0;
try {
while (!Thread.interrupted()) {
sleep(SNAPSHOT_RATE);
time += SNAPSHOT_RATE;
pop.printSnapshot(time / 1000.0);
}
} catch (InterruptedException ie) {}
}
}
}