/// <summary>
/// Select a subset of items from a superset of a given size.
/// </summary>
/// <param name="supersetCount">The size of the superset to select from.</param>
/// <returns>An array of indexes that are the selected items.</returns>
public int[] SelectSubset(int supersetCount)
{
// Note. Ideally we'd return a sorted list of indexes to improve performance of the code that consumes them,
// however, the sampling process inherently produces samples in randomized order, thus the decision of whether
// to sort or not depends on the cost to the code using the samples. I.e. don't sort here!
int selectionCount = Math.Min(_selectCount, supersetCount);
int[] idxArr = new int[selectionCount];
DiscreteDistributionUtils.SampleUniformWithoutReplacement(supersetCount, idxArr, _rng);
return(idxArr);
}
/// <summary>
/// Move the prey. The prey moves by a simple set of stochastic rules that make it more likely to move away from
/// the agent, and more so when it is close.
/// </summary>
public void MovePrey()
{
// Determine if prey will move in this timestep. (Speed is simulated stochastically)
if (_rng.NextDouble() > _preySpeed)
{
return;
}
// Determine position of agent relative to prey.
PolarPoint relPolarPos = PolarPoint.FromCartesian(_agentPos - _preyPos);
// Calculate probabilities of moving in each of the four directions. This stochastic strategy is taken from:
// Incremental Evolution Of Complex General Behavior, Faustino Gomez and Risto Miikkulainen (1997)
// (http://nn.cs.utexas.edu/downloads/papers/gomez.adaptive-behavior.pdf)
// Essentially the prey moves randomly but we bias the movements so the prey moves away from the agent, and thus
// generally avoids getting eaten through stupidity.
double T = MovePrey_T(relPolarPos.Radial);
double[] probs = new double[4];
probs[0] = Math.Exp((CalcAngleDelta(relPolarPos.Theta, Math.PI / 2.0) / Math.PI) * T * 0.33); // North.
probs[1] = Math.Exp((CalcAngleDelta(relPolarPos.Theta, 0) / Math.PI) * T * 0.33); // East.
probs[2] = Math.Exp((CalcAngleDelta(relPolarPos.Theta, Math.PI * 1.5) / Math.PI) * T * 0.33); // South.
probs[3] = Math.Exp((CalcAngleDelta(relPolarPos.Theta, Math.PI) / Math.PI) * T * 0.33); // West.
DiscreteDistribution rwl = new DiscreteDistribution(probs);
int action = DiscreteDistributionUtils.Sample(rwl, _rng);
switch (action)
{
case 0: // Move north.
_preyPos._y = Math.Min(_preyPos._y + 1, _gridSize - 1);
break;
case 1: // Move east.
_preyPos._x = Math.Min(_preyPos._x + 1, _gridSize - 1);
break;
case 2: // Move south.
_preyPos._y = Math.Max(_preyPos._y - 1, 0);
break;
case 3: // Move west (is the best?)
_preyPos._x = Math.Max(_preyPos._x - 1, 0);
break;
}
}
public void SampleUniformWithoutReplacement_SampleAllChoices()
{
const int size = 5;
XorShiftRandom rng = new XorShiftRandom();
// Sample all of the elements.
int[] sampleArr = new int[size];
DiscreteDistributionUtils.SampleUniformWithoutReplacement(size, sampleArr, rng);
// Sort the samples.
Array.Sort(sampleArr);
// Confirm that all of the choices were selected.
for (int i = 0; i < size; i++)
{
Assert.AreEqual(i, sampleArr[i]);
}
}
/// <summary>
/// Creates a single randomly initialised genome.
/// </summary>
private NeatGenome <T> CreateGenome()
{
// Determine how many connections to create in the new genome, as a proportion of all possible connections
// between the input and output nodes.
int connectionCount = (int)NumericsUtils.ProbabilisticRound(_connectionDefArr.Length * _connectionsProportion, _rng);
// Ensure there is at least one connection.
connectionCount = Math.Max(1, connectionCount);
// Select a random subset of all possible connections between the input and output nodes.
int[] sampleArr = new int[connectionCount];
DiscreteDistributionUtils.SampleUniformWithoutReplacement(
_connectionDefArr.Length, sampleArr, _rng);
// Sort the samples.
// Note. This results in the neural net connections being sorted by sourceID then targetID.
Array.Sort(sampleArr);
// Create the connection gene arrays and populate them.
var connGenes = new ConnectionGenes <T>(connectionCount);
var connArr = connGenes._connArr;
var weightArr = connGenes._weightArr;
for (int i = 0; i < sampleArr.Length; i++)
{
DirectedConnection cdef = _connectionDefArr[sampleArr[i]];
connArr[i] = new DirectedConnection(
cdef.SourceId,
cdef.TargetId);
weightArr[i] = _connWeightDist.Sample(_metaNeatGenome.ConnectionWeightRange, true);
}
// Get create a new genome with a new ID, birth generation of zero.
int id = _genomeIdSeq.Next();
return(_genomeBuilder.Create(id, 0, connGenes));
}
/// <summary>
/// Cross specie mating.
/// </summary>
/// <param name="rwl">RouletteWheelLayout for selecting genomes in the current specie.</param>
/// <param name="rwlArr">Array of RouletteWheelLayout objects for genome selection. One for each specie.</param>
/// <param name="rwlSpecies">RouletteWheelLayout for selecting species. Based on relative fitness of species.</param>
/// <param name="currentSpecieIdx">Current specie's index in _specieList</param>
/// <param name="genomeList">Current specie's genome list.</param>
private TGenome CreateOffspring_CrossSpecieMating(DiscreteDistribution rwl,
DiscreteDistribution[] rwlArr,
DiscreteDistribution rwlSpecies,
int currentSpecieIdx,
IList <TGenome> genomeList)
{
// Select parent from current specie.
int parent1Idx = DiscreteDistributionUtils.Sample(rwl, _rng);
// Select specie other than current one for 2nd parent genome.
DiscreteDistribution rwlSpeciesTmp = rwlSpecies.RemoveOutcome(currentSpecieIdx);
int specie2Idx = DiscreteDistributionUtils.Sample(rwlSpeciesTmp, _rng);
// Select a parent genome from the second specie.
int parent2Idx = DiscreteDistributionUtils.Sample(rwlArr[specie2Idx], _rng);
// Get the two parents to mate.
TGenome parent1 = genomeList[parent1Idx];
TGenome parent2 = _specieList[specie2Idx].GenomeList[parent2Idx];
return(parent1.CreateOffspring(parent2, _currentGeneration));
}
private ConnectionGene <T>?CreateConnectionGene(
ConnectionGenes <T> connGenes1,
ConnectionGenes <T> connGenes2,
int idx1, int idx2,
out bool isSecondaryGene)
{
// Select gene at random if it is present on both parents.
if (-1 != idx1 && -1 != idx2)
{
if (_rng.NextBool())
{
isSecondaryGene = false;
return(CreateConnectionGene(connGenes1, idx1));
}
else
{
isSecondaryGene = true;
return(CreateConnectionGene(connGenes2, idx2));
}
}
// Use the primary parent's gene if it has one.
if (-1 != idx1)
{
isSecondaryGene = false;
return(CreateConnectionGene(connGenes1, idx1));
}
// Otherwise use the secondary parent's gene stochastically.
if (DiscreteDistributionUtils.SampleBinaryDistribution(_metaNeatGenome.SecondaryParentGeneProbability, _rng))
{
isSecondaryGene = true;
return(CreateConnectionGene(connGenes2, idx2));
}
isSecondaryGene = false;
return(null);
}
/// <summary>
/// Create the required number of offspring genomes, using specieStatsArr as the basis for selecting how
/// many offspring are produced from each species.
/// </summary>
private List <TGenome> CreateOffspring(SpecieStats[] specieStatsArr, int offspringCount)
{
// Build a RouletteWheelLayout for selecting species for cross-species reproduction.
// While we're in the loop we also pre-build a RouletteWheelLayout for each specie;
// Doing this before the main loop means we have RouletteWheelLayouts available for
// all species when performing cross-specie matings.
int specieCount = specieStatsArr.Length;
double[] specieFitnessArr = new double[specieCount];
DiscreteDistribution[] rwlArr = new DiscreteDistribution[specieCount];
// Count of species with non-zero selection size.
// If this is exactly 1 then we skip inter-species mating. One is a special case because for 0 the
// species all get an even chance of selection, and for >1 we can just select normally.
int nonZeroSpecieCount = 0;
for (int i = 0; i < specieCount; i++)
{
// Array of probabilities for specie selection. Note that some of these probabilities can be zero, but at least one of them won't be.
SpecieStats inst = specieStatsArr[i];
specieFitnessArr[i] = inst._selectionSizeInt;
if (0 != inst._selectionSizeInt)
{
nonZeroSpecieCount++;
}
// For each specie we build a RouletteWheelLayout for genome selection within
// that specie. Fitter genomes have higher probability of selection.
List <TGenome> genomeList = _specieList[i].GenomeList;
double[] probabilities = new double[inst._selectionSizeInt];
for (int j = 0; j < inst._selectionSizeInt; j++)
{
probabilities[j] = genomeList[j].EvaluationInfo.Fitness;
}
rwlArr[i] = new DiscreteDistribution(probabilities);
}
// Complete construction of RouletteWheelLayout for specie selection.
DiscreteDistribution rwlSpecies = new DiscreteDistribution(specieFitnessArr);
// Produce offspring from each specie in turn and store them in offspringList.
List <TGenome> offspringList = new List <TGenome>(offspringCount);
for (int specieIdx = 0; specieIdx < specieCount; specieIdx++)
{
SpecieStats inst = specieStatsArr[specieIdx];
List <TGenome> genomeList = _specieList[specieIdx].GenomeList;
// Get RouletteWheelLayout for genome selection.
DiscreteDistribution rwl = rwlArr[specieIdx];
// --- Produce the required number of offspring from asexual reproduction.
for (int i = 0; i < inst._offspringAsexualCount; i++)
{
int genomeIdx = DiscreteDistributionUtils.Sample(rwl, _rng);
TGenome offspring = genomeList[genomeIdx].CreateOffspring(_currentGeneration);
offspringList.Add(offspring);
}
_stats._asexualOffspringCount += (ulong)inst._offspringAsexualCount;
// --- Produce the required number of offspring from sexual reproduction.
// Cross-specie mating.
// If nonZeroSpecieCount is exactly 1 then we skip inter-species mating. One is a special case because
// for 0 the species all get an even chance of selection, and for >1 we can just select species normally.
int crossSpecieMatings = nonZeroSpecieCount == 1 ? 0 :
(int)NumericsUtils.ProbabilisticRound(_eaParams.InterspeciesMatingProportion
* inst._offspringSexualCount, _rng);
_stats._sexualOffspringCount += (ulong)(inst._offspringSexualCount - crossSpecieMatings);
_stats._interspeciesOffspringCount += (ulong)crossSpecieMatings;
// An index that keeps track of how many offspring have been produced in total.
int matingsCount = 0;
for (; matingsCount < crossSpecieMatings; matingsCount++)
{
TGenome offspring = CreateOffspring_CrossSpecieMating(rwl, rwlArr, rwlSpecies, specieIdx, genomeList);
offspringList.Add(offspring);
}
// For the remainder we use normal intra-specie mating.
// Test for special case - we only have one genome to select from in the current specie.
if (1 == inst._selectionSizeInt)
{
// Fall-back to asexual reproduction.
for (; matingsCount < inst._offspringSexualCount; matingsCount++)
{
int genomeIdx = DiscreteDistributionUtils.Sample(rwl, _rng);
TGenome offspring = genomeList[genomeIdx].CreateOffspring(_currentGeneration);
offspringList.Add(offspring);
}
}
else
{
// Remainder of matings are normal within-specie.
for (; matingsCount < inst._offspringSexualCount; matingsCount++)
{
// Select parent 1.
int parent1Idx = DiscreteDistributionUtils.Sample(rwl, _rng);
TGenome parent1 = genomeList[parent1Idx];
// Remove selected parent from set of possible outcomes.
DiscreteDistribution rwlTmp = rwl.RemoveOutcome(parent1Idx);
// Test for existence of at least one more parent to select.
if (0 != rwlTmp.Probabilities.Length)
{ // Get the two parents to mate.
int parent2Idx = DiscreteDistributionUtils.Sample(rwlTmp, _rng);
TGenome parent2 = genomeList[parent2Idx];
TGenome offspring = parent1.CreateOffspring(parent2, _currentGeneration);
offspringList.Add(offspring);
}
else
{ // No other parent has a non-zero selection probability (they all have zero fitness).
// Fall back to asexual reproduction of the single genome with a non-zero fitness.
TGenome offspring = parent1.CreateOffspring(_currentGeneration);
offspringList.Add(offspring);
}
}
}
}
_stats._totalOffspringCount += (ulong)offspringCount;
return(offspringList);
}
/// <summary>
/// Calculate statistics for each specie. This method is at the heart of the evolutionary algorithm,
/// the key things that are achieved in this method are - for each specie we calculate:
/// 1) The target size based on fitness of the specie's member genomes.
/// 2) The elite size based on the current size. Potentially this could be higher than the target
/// size, so a target size is taken to be a hard limit.
/// 3) Following (1) and (2) we can calculate the total number offspring that need to be generated
/// for the current generation.
/// </summary>
private SpecieStats[] CalcSpecieStats(out int offspringCount)
{
double totalMeanFitness = 0.0;
// Build stats array and get the mean fitness of each specie.
int specieCount = _specieList.Count;
SpecieStats[] specieStatsArr = new SpecieStats[specieCount];
for (int i = 0; i < specieCount; i++)
{
SpecieStats inst = new SpecieStats();
specieStatsArr[i] = inst;
inst._meanFitness = _specieList[i].CalcMeanFitness();
totalMeanFitness += inst._meanFitness;
}
// Calculate the new target size of each specie using fitness sharing.
// Keep a total of all allocated target sizes, typically this will vary slightly from the
// overall target population size due to rounding of each real/fractional target size.
int totalTargetSizeInt = 0;
if (0.0 == totalMeanFitness)
{ // Handle specific case where all genomes/species have a zero fitness.
// Assign all species an equal targetSize.
double targetSizeReal = (double)_populationSize / (double)specieCount;
for (int i = 0; i < specieCount; i++)
{
SpecieStats inst = specieStatsArr[i];
inst._targetSizeReal = targetSizeReal;
// Stochastic rounding will result in equal allocation if targetSizeReal is a whole
// number, otherwise it will help to distribute allocations evenly.
inst._targetSizeInt = (int)NumericsUtils.ProbabilisticRound(targetSizeReal, _rng);
// Total up discretized target sizes.
totalTargetSizeInt += inst._targetSizeInt;
}
}
else
{
// The size of each specie is based on its fitness relative to the other species.
for (int i = 0; i < specieCount; i++)
{
SpecieStats inst = specieStatsArr[i];
inst._targetSizeReal = (inst._meanFitness / totalMeanFitness) * (double)_populationSize;
// Discretize targetSize (stochastic rounding).
inst._targetSizeInt = (int)NumericsUtils.ProbabilisticRound(inst._targetSizeReal, _rng);
// Total up discretized target sizes.
totalTargetSizeInt += inst._targetSizeInt;
}
}
// Discretized target sizes may total up to a value that is not equal to the required overall population
// size. Here we check this and if there is a difference then we adjust the specie's targetSizeInt values
// to compensate for the difference.
//
// E.g. If we are short of the required populationSize then we add the required additional allocation to
// selected species based on the difference between each specie's targetSizeReal and targetSizeInt values.
// What we're effectively doing here is assigning the additional required target allocation to species based
// on their real target size in relation to their actual (integer) target size.
// Those species that have an actual allocation below there real allocation (the difference will often
// be a fractional amount) will be assigned extra allocation probabilistically, where the probability is
// based on the differences between real and actual target values.
//
// Where the actual target allocation is higher than the required target (due to rounding up), we use the same
// method but we adjust specie target sizes down rather than up.
int targetSizeDeltaInt = totalTargetSizeInt - _populationSize;
if (targetSizeDeltaInt < 0)
{
// Check for special case. If we are short by just 1 then increment targetSizeInt for the specie containing
// the best genome. We always ensure that this specie has a minimum target size of 1 with a final test (below),
// by incrementing here we avoid the probabilistic allocation below followed by a further correction if
// the champ specie ended up with a zero target size.
if (-1 == targetSizeDeltaInt)
{
specieStatsArr[_bestSpecieIdx]._targetSizeInt++;
}
else
{
// We are short of the required populationSize. Add the required additional allocations.
// Determine each specie's relative probability of receiving additional allocation.
double[] probabilities = new double[specieCount];
for (int i = 0; i < specieCount; i++)
{
SpecieStats inst = specieStatsArr[i];
probabilities[i] = Math.Max(0.0, inst._targetSizeReal - (double)inst._targetSizeInt);
}
// Use a built in class for choosing an item based on a list of relative probabilities.
DiscreteDistribution rwl = new DiscreteDistribution(probabilities);
// Probabilistically assign the required number of additional allocations.
// FIXME/ENHANCEMENT: We can improve the allocation fairness by updating the RouletteWheelLayout
// after each allocation (to reflect that allocation).
// targetSizeDeltaInt is negative, so flip the sign for code clarity.
targetSizeDeltaInt *= -1;
for (int i = 0; i < targetSizeDeltaInt; i++)
{
int specieIdx = DiscreteDistributionUtils.Sample(rwl, _rng);
specieStatsArr[specieIdx]._targetSizeInt++;
}
}
}
else if (targetSizeDeltaInt > 0)
{
// We have overshot the required populationSize. Adjust target sizes down to compensate.
// Determine each specie's relative probability of target size downward adjustment.
double[] probabilities = new double[specieCount];
for (int i = 0; i < specieCount; i++)
{
SpecieStats inst = specieStatsArr[i];
probabilities[i] = Math.Max(0.0, (double)inst._targetSizeInt - inst._targetSizeReal);
}
// Use a built in class for choosing an item based on a list of relative probabilities.
DiscreteDistribution rwl = new DiscreteDistribution(probabilities);
// Probabilistically decrement specie target sizes.
// ENHANCEMENT: We can improve the selection fairness by updating the RouletteWheelLayout
// after each decrement (to reflect that decrement).
for (int i = 0; i < targetSizeDeltaInt;)
{
int specieIdx = DiscreteDistributionUtils.Sample(rwl, _rng);
// Skip empty species. This can happen because the same species can be selected more than once.
if (0 != specieStatsArr[specieIdx]._targetSizeInt)
{
specieStatsArr[specieIdx]._targetSizeInt--;
i++;
}
}
}
// We now have Sum(_targetSizeInt) == _populationSize.
Debug.Assert(SumTargetSizeInt(specieStatsArr) == _populationSize);
// TODO: Better way of ensuring champ species has non-zero target size?
// However we need to check that the specie with the best genome has a non-zero targetSizeInt in order
// to ensure that the best genome is preserved. A zero size may have been allocated in some pathological cases.
if (0 == specieStatsArr[_bestSpecieIdx]._targetSizeInt)
{
specieStatsArr[_bestSpecieIdx]._targetSizeInt++;
// Adjust down the target size of one of the other species to compensate.
// Pick a specie at random (but not the champ specie). Note that this may result in a specie with a zero
// target size, this is OK at this stage. We handle allocations of zero in PerformOneGeneration().
int idx = DiscreteDistributionUtils.SampleUniformDistribution(specieCount - 1, _rng);
idx = idx == _bestSpecieIdx ? idx + 1 : idx;
if (specieStatsArr[idx]._targetSizeInt > 0)
{
specieStatsArr[idx]._targetSizeInt--;
}
else
{ // Scan forward from this specie to find a suitable one.
bool done = false;
idx++;
for (; idx < specieCount; idx++)
{
if (idx != _bestSpecieIdx && specieStatsArr[idx]._targetSizeInt > 0)
{
specieStatsArr[idx]._targetSizeInt--;
done = true;
break;
}
}
// Scan forward from start of species list.
if (!done)
{
for (int i = 0; i < specieCount; i++)
{
if (i != _bestSpecieIdx && specieStatsArr[i]._targetSizeInt > 0)
{
specieStatsArr[i]._targetSizeInt--;
done = true;
break;
}
}
if (!done)
{
throw new SharpNeatException("CalcSpecieStats(). Error adjusting target population size down. Is the population size less than or equal to the number of species?");
}
}
}
}
// Now determine the eliteSize for each specie. This is the number of genomes that will remain in a
// specie from the current generation and is a proportion of the specie's current size.
// Also here we calculate the total number of offspring that will need to be generated.
offspringCount = 0;
for (int i = 0; i < specieCount; i++)
{
// Special case - zero target size.
if (0 == specieStatsArr[i]._targetSizeInt)
{
specieStatsArr[i]._eliteSizeInt = 0;
continue;
}
// Discretize the real size with a probabilistic handling of the fractional part.
double eliteSizeReal = _specieList[i].GenomeList.Count * _eaParams.ElitismProportion;
int eliteSizeInt = (int)NumericsUtils.ProbabilisticRound(eliteSizeReal, _rng);
// Ensure eliteSizeInt is no larger than the current target size (remember it was calculated
// against the current size of the specie not its new target size).
SpecieStats inst = specieStatsArr[i];
inst._eliteSizeInt = Math.Min(eliteSizeInt, inst._targetSizeInt);
// Ensure the champ specie preserves the champ genome. We do this even if the target size is just 1
// - which means the champ genome will remain and no offspring will be produced from it, apart from
// the (usually small) chance of a cross-species mating.
if (i == _bestSpecieIdx && inst._eliteSizeInt == 0)
{
Debug.Assert(inst._targetSizeInt != 0, "Zero target size assigned to champ specie.");
inst._eliteSizeInt = 1;
}
// Now we can determine how many offspring to produce for the specie.
inst._offspringCount = inst._targetSizeInt - inst._eliteSizeInt;
offspringCount += inst._offspringCount;
// While we're here we determine the split between asexual and sexual reproduction. Again using
// some probabilistic logic to compensate for any rounding bias.
double offspringAsexualCountReal = (double)inst._offspringCount * _eaParams.OffspringAsexualProportion;
inst._offspringAsexualCount = (int)NumericsUtils.ProbabilisticRound(offspringAsexualCountReal, _rng);
inst._offspringSexualCount = inst._offspringCount - inst._offspringAsexualCount;
// Also while we're here we calculate the selectionSize. The number of the specie's fittest genomes
// that are selected from to create offspring. This should always be at least 1.
double selectionSizeReal = _specieList[i].GenomeList.Count * _eaParams.SelectionProportion;
inst._selectionSizeInt = Math.Max(1, (int)NumericsUtils.ProbabilisticRound(selectionSizeReal, _rng));
}
return(specieStatsArr);
}
/// <summary>
/// Randomly select a function based on each function's selection probability.
/// </summary>
public ActivationFunctionInfo GetRandomFunction(XorShiftRandom rng)
{
return(_functionList[DiscreteDistributionUtils.Sample(_rwl, rng)]);
}
/// <summary>
/// Gets one of the ConnectionMutationInfo items at random based upon the ActivationProbability
/// of the contained items.
/// </summary>
public ConnectionMutationInfo GetRandomItem(XorShiftRandom rng)
{
return(this[DiscreteDistributionUtils.Sample(_rouletteWheelLayout, rng)]);
}
