public CMAESCandidate(double[] weightIN, sbyte[][] trainingDataIN, sbyte[] targetsIN, PUFObjectiveFunction functionIN)
{
//WeightVector = (double[])weightIN.Clone();
//TrainingData = (double[][])trainingDataIN.Clone();
//Targets = (double[][])targetsIN.Clone();
WeightVector = weightIN;
TrainingData = trainingDataIN;
Targets = targetsIN;
FunctionP = functionIN;
ObjFunctionValue = FunctionP.ObjFunValue(WeightVector, TrainingData, Targets);
}
//standard CMA-ES with maximum parallelization
public static CMAESCandidate ComputeCMAESBecker(int dimensionNumber, PUFObjectiveFunction pFunction, sbyte[][] trainingData, sbyte[] targets, double[] initialWeightVector, Random randomGenerator)
{
int n = dimensionNumber + 1; //number of weights + epsilon
Matrix <double> xMean = Matrix <double> .Build.Dense(n, 1);
CMAESCandidate c11 = new CMAESCandidate(initialWeightVector, trainingData, targets, pFunction);
Console.Out.WriteLine("Starting Point Accuracy");
Console.Out.WriteLine(c11.GetObjectiveFunctionValue().ToString());
CMAESCandidate globalBestCandidate = null;
double sigma = 0.5;
//double stopfitness = 1e-10;
//double stopfitness = 0.99;
double stopfitness = double.MaxValue;
int stopeval = AppConstants.MaxIterationNumberCMAES;
//double stopeval = AppConstants.MaxEvaluations
//Strategy parameter setting: Selection
int lambdaVal = (int)(4.0 + Math.Floor(3.0 * Math.Log(n))); //population size, note lambda keyword reserved by python so lambda->lambdaVal
//lambdaVal = AppConstants.PopulationSizeCMAES #change by KRM cause I think we need more sampling
double mu = lambdaVal / 2.0;
Matrix <double> weights = Matrix <double> .Build.Dense((int)mu, 1); //weights = numpy.matrix(weightsPrime, dtype = float).reshape(mu, 1)
for (int i = 0; i < (int)mu; i++)
{
weights[i, 0] = Math.Log(mu + 0.5) - Math.Log(i + 1); //weights[i, 0] = math.log(mu + 0.5) - math.log((i + 1))#use i+1 instead of i in this case to match matlab indexing
}
mu = Math.Floor(mu);
double sumWeights = 0.0;
for (int i = 0; i < weights.RowCount; i++)
{
sumWeights = sumWeights + weights[i, 0];
}
//Divide by the sum
for (int i = 0; i < weights.RowCount; i++)
{
weights[i, 0] = weights[i, 0] / sumWeights;
}
//Computation for the mueff variable
double mueffNum = 0.0;
double mueffDem = 0.0;
for (int i = 0; i < weights.RowCount; i++)
{
mueffNum = weights[i, 0] + mueffNum;
mueffDem = weights[i, 0] * weights[i, 0] + mueffDem;
}
mueffNum = mueffNum * mueffNum;
double mueff = mueffNum / mueffDem;
// Strategy parameter setting: Adaptation
double cc = (4.0 + mueff / n) / (n + 4.0 + 2.0 * mueff / n); //#time constant for cumulation for C
double cs = (mueff + 2.0) / (n + mueff + 5.0); //#t-const for cumulation for sigma control
double c1 = 2.0 / ((n + 1.3) * (n + 1.3) + mueff); //#learning rate for rank-one update of C
double cmu = Math.Min(1.0 - c1, 2.0 * (mueff - 2.0 + 1.0 / mueff) / ((n + 2) * (n + 2) + mueff)); //# and for rank-mu update
double damps = 1.0 + 2.0 * Math.Max(0, Math.Sqrt((mueff - 1) / (n + 1)) - 1) + cs; //# damping for sigma
//Initialize dynamic (internal) strategy parameters and constants
//evolution paths for C and sigma
Matrix <double> pc = Matrix <double> .Build.Dense(n, 1);
Matrix <double> ps = Matrix <double> .Build.Dense(n, 1);
Matrix <double> D = Matrix <double> .Build.Dense(n, 1);
for (int i = 0; i < n; i++)
{
pc[i, 0] = 0;
ps[i, 0] = 0;
D[i, 0] = 1.0;
}
//Create B Matrix
Matrix <double> B = Matrix <double> .Build.Dense(n, n);
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
if (i == j)
{
B[i, j] = 1.0;
}
else
{
B[i, j] = 0.0;
}
}
}
//Create C Matrix
Matrix <double> dSquare = Matrix <double> .Build.Dense(n, 1);
for (int i = 0; i < n; i++)
{
dSquare[i, 0] = D[i, 0] * D[i, 0];
}
Matrix <double> C = B * Diagonalize1DMatrix(dSquare) * B.Transpose(); //C = B * self.diag(DSquare) * numpy.transpose(B)
//Create invertsqrtC Matrix
Matrix <double> oneOverD = Matrix <double> .Build.Dense(n, 1);
for (int i = 0; i < n; i++)
{
oneOverD[i, 0] = 1.0 / D[i, 0];
}
Matrix <double> invsqrtC = B * Diagonalize1DMatrix(oneOverD) * B.Transpose();
double eigeneval = 0; //track update of B and D
double chiN = Math.Pow(n, 0.5) * (1.0 - 1.0 / (4.0 * n) + 1.0 / (21.0 * Math.Pow(n, 2.0)));
int counteval = 0;
//the next 40 lines contain the 20 lines of interesting code
//CMAESCandidate[] candidateArray = new CMAESCandidate[lambdaVal];
List <CMAESCandidate> candidateArray = new List <CMAESCandidate>();
for (int i = 0; i < lambdaVal; i++)
{
candidateArray.Add(new CMAESCandidate());
}
while (counteval < stopeval)
{
Matrix <double> arx = Matrix <double> .Build.Dense(n, lambdaVal);
//fill in the initial solutions
for (int i = 0; i < lambdaVal; i++)
{
Matrix <double> randD = Matrix <double> .Build.Dense(n, 1);
for (int j = 0; j < n; j++)
{
randD[j, 0] = D[j, 0] * GenerateRandomNormalVariableForCMAES(randomGenerator, 0, 1.0);
}
Matrix <double> inputVector = xMean + sigma * B * randD;
double[] tempWeightVector = new double[inputVector.RowCount];
for (int k = 0; k < inputVector.RowCount; k++)
{
tempWeightVector[k] = inputVector[k, 0];
}
candidateArray[i] = new CMAESCandidate(tempWeightVector, trainingData, targets, pFunction);
counteval = counteval + 1;
}
candidateArray.Sort(); //This maybe problematic, not sure about sorting in C#
candidateArray.Reverse();
Matrix <double> xOld = xMean.Clone();
//Get the new mean value
Matrix <double> arxSubset = Matrix <double> .Build.Dense(n, (int)mu); //in Maltab this variable would be "arx(:,arindex(1:mu))
//This replaces line arxSubset[:, i] = CandidateList[i].InputVector
for (int i = 0; i < mu; i++)
{
for (int j = 0; j < n; j++)
{
arxSubset[j, i] = candidateArray[i].GetWeightVector()[j];
}
}
xMean = arxSubset * weights; //Line 76 Matlab
//Cumulation: Update evolution paths
ps = (1 - cs) * ps + Math.Sqrt(cs * (2.0 - cs) * mueff) * invsqrtC * (xMean - xOld) / sigma;
//Compute ps.^2 equivalent
double psSquare = 0;
for (int i = 0; i < ps.RowCount; i++)
{
psSquare = psSquare + ps[i, 0] * ps[i, 0];
}
//Compute hsig
double hSig = 0.0;
double term1ForHsig = psSquare / (1.0 - Math.Pow(1.0 - cs, 2.0 * counteval / lambdaVal)) / n;
double term2ForHsig = 2.0 + 4.0 / (n + 1.0);
if (term1ForHsig < term2ForHsig)
{
hSig = 1.0;
}
//Compute pc, Line 82 Matlab
pc = (1.0 - cc) * pc + hSig * Math.Sqrt(cc * (2.0 - cc) * mueff) * (xMean - xOld) / sigma;
//Adapt covariance matrix C
Matrix <double> repmatMatrix = Tile((int)mu, xOld); //NOT SURE IF THIS IS RIGHT IN C# FIX repmatMatrix = numpy.tile(xold, mu)
Matrix <double> artmp = (1.0 / sigma) * (arxSubset - repmatMatrix);
// C = (1-c1-cmu) * C + c1 * (pc * pc' + (1-hsig) * cc*(2-cc) * C) + cmu * artmp * diag(weights) * artmp' #This is the original Matlab line for reference
C = (1.0 - c1 - cmu) * C + c1 * (pc * pc.Transpose() + (1 - hSig) * cc * (2.0 - cc) * C) + cmu * artmp * Diagonalize1DMatrix(weights) * artmp.Transpose();
//Adapt step size sigma
//sigma = sigma * Math.Exp((cs / damps) * (numpy.linalg.norm(ps) / chiN - 1))
sigma = sigma * Math.Exp((cs / damps) * (ps.L2Norm() / chiN - 1)); //NOT SURE IF THIS IS RIGHT FIX IN C#
//Update B and D from C
if ((counteval - eigeneval) > (lambdaVal / (c1 + cmu) / n / 10.0))
{
eigeneval = counteval;
//C = numpy.triu(C) + numpy.transpose(numpy.triu(C, 1)) #enforce symmetry
C = C.UpperTriangle() + C.StrictlyUpperTriangle().Transpose(); //NOT SURE IF THIS IS RIGHT FIX IN C#
//eigen decomposition
Evd <double> eigen = C.Evd();
B = eigen.EigenVectors;
Vector <System.Numerics.Complex> vectorEigenValues = eigen.EigenValues;
for (int i = 0; i < vectorEigenValues.Count; i++)
{
D[i, 0] = vectorEigenValues[i].Real;
}
//take sqrt of D
for (int i = 0; i < vectorEigenValues.Count; i++)
{
D[i, 0] = Math.Sqrt(D[i, 0]);
}
for (int i = 0; i < n; i++)
{
oneOverD[i, 0] = 1.0 / D[i, 0];
}
Matrix <double> middleTerm = Diagonalize1DMatrix(oneOverD); //#Built in Numpy function doesn't create the right size matrix in this case (ex: Numpy gives 1x1 but should be 5x5)
invsqrtC = B * middleTerm * B.Transpose();
}
globalBestCandidate = candidateArray[0];
//Termination Conditions
//bestCandidate = candidateArray[0]; //Array index 0 has the smallest objective function value
//if (bestCandidate.GetObjectiveFunctionValue() < currentBestValue)
//{
// currentBestValue = bestCandidate.GetObjectiveFunctionValue();
// globalBestCandidate = (CMAESCandidate)bestCandidate.Clone();
//}
//if (bestCandidate.GetObjectiveFunctionValue() >= stopfitness)
//{
// return globalBestCandidate;
//}
//Add in extra termination conditions
//if (bestCandidate.GetObjectiveFunctionValue() == currentBestValue)
//{
// repeatCount = repeatCount + 1;
//}
//else
//{
// repeatCount = 0;
//}
////we have repeated too many times
//if (repeatCount > 10)
//{
// Console.Out.WriteLine("CMA-ES terminated to due to repeated best.");
// return globalBestCandidate;
//}
Console.Out.WriteLine("Iteration #" + counteval.ToString());
//Console.Out.WriteLine("Best Value=" + (1.0 - currentBestValue).ToString());
Console.Out.WriteLine("Current Value=" + (candidateArray[candidateArray.Count - 1].GetObjectiveFunctionValue()).ToString());
}//end while loop
return(globalBestCandidate); //just in case everything terminates
}
//Run the CMA-ES from a recovered file
public static CMAESCandidate RecoveredCMAES(Random randomGenerator, int coreNumberForSaving, PUFObjectiveFunction pFunction, InvariantData invData, VariantData varData)
{
double stopFitness = 0.98;
//non-specific variables (used by each core)
int stopeval = invData.GetMaxEval();
sbyte[][] trainingData = invData.GetTrainingData();
sbyte[] targets = invData.GetTrainingResponseForPUF(coreNumberForSaving);
//core specific variables (specific to each run of CMA-ES)
int counteval = varData.GetCurrentEval();
int n = varData.GetDimensionNum();
int lambdaVal = varData.GetLambda();
Matrix <double> xMean = varData.GetXMean();
Matrix <double> D = varData.GetD();
Matrix <double> B = varData.GetB();
double sigma = varData.GetSigma();
Matrix <double> weights = varData.GetWeights();
Matrix <double> ps = varData.GetPS();
double cs = varData.GetCS();
double mueff = varData.GetMueff();
double cc = varData.GetCC();
Matrix <double> pc = varData.GetPC();
Matrix <double> invsqrtC = varData.GetInvSqrtC();
Matrix <double> C = varData.GetMatrixC();
double mu = varData.GetMu();
double c1 = varData.GetC1();
double cmu = varData.GetCmu();
double damps = varData.GetDamps();
double chiN = varData.GetChiN();
double eigeneval = varData.GetEigenVal();
CMAESCandidate globalBestCandidate = varData.GetGlobalBest();
Matrix <double> oneOverD = Matrix <double> .Build.Dense(n, 1); //Don't need to copy this because we get it from D
//just a sanity check
if (varData.coreNumber != coreNumberForSaving)
{
throw new Exception("The saved core number and current core number don't match.");
}
//the next 40 lines contain the 20 lines of interesting code
//CMAESCandidate[] candidateArray = new CMAESCandidate[lambdaVal];
List <CMAESCandidate> candidateArray = new List <CMAESCandidate>();
for (int i = 0; i < lambdaVal; i++)
{
candidateArray.Add(new CMAESCandidate());
}
while (counteval < stopeval)
{
Matrix <double> arx = Matrix <double> .Build.Dense(n, lambdaVal);
//fill in the initial solutions
for (int i = 0; i < lambdaVal; i++)
{
Matrix <double> randD = Matrix <double> .Build.Dense(n, 1);
for (int j = 0; j < n; j++)
{
randD[j, 0] = D[j, 0] * GenerateRandomNormalVariableForCMAES(randomGenerator, 0, 1.0);
}
Matrix <double> inputVector = xMean + sigma * B * randD;
double[] tempWeightVector = new double[inputVector.RowCount];
for (int k = 0; k < inputVector.RowCount; k++)
{
tempWeightVector[k] = inputVector[k, 0];
}
candidateArray[i] = new CMAESCandidate(tempWeightVector, trainingData, targets, pFunction);
counteval = counteval + 1;
}
candidateArray.Sort(); //This maybe problematic, not sure about sorting in C#
candidateArray.Reverse();
Matrix <double> xOld = xMean.Clone();
//Get the new mean value
Matrix <double> arxSubset = Matrix <double> .Build.Dense(n, (int)mu); //in Maltab this variable would be "arx(:,arindex(1:mu))
//This replaces line arxSubset[:, i] = CandidateList[i].InputVector
for (int i = 0; i < mu; i++)
{
for (int j = 0; j < n; j++)
{
arxSubset[j, i] = candidateArray[i].GetWeightVector()[j];
}
}
xMean = arxSubset * weights; //Line 76 Matlab
//Cumulation: Update evolution paths
ps = (1 - cs) * ps + Math.Sqrt(cs * (2.0 - cs) * mueff) * invsqrtC * (xMean - xOld) / sigma;
//Compute ps.^2 equivalent
double psSquare = 0;
for (int i = 0; i < ps.RowCount; i++)
{
psSquare = psSquare + ps[i, 0] * ps[i, 0];
}
//Compute hsig
double hSig = 0.0;
double term1ForHsig = psSquare / (1.0 - Math.Pow(1.0 - cs, 2.0 * counteval / lambdaVal)) / n;
double term2ForHsig = 2.0 + 4.0 / (n + 1.0);
if (term1ForHsig < term2ForHsig)
{
hSig = 1.0;
}
//Compute pc, Line 82 Matlab
pc = (1.0 - cc) * pc + hSig * Math.Sqrt(cc * (2.0 - cc) * mueff) * (xMean - xOld) / sigma;
//Adapt covariance matrix C
Matrix <double> repmatMatrix = Tile((int)mu, xOld); //NOT SURE IF THIS IS RIGHT IN C# FIX repmatMatrix = numpy.tile(xold, mu)
Matrix <double> artmp = (1.0 / sigma) * (arxSubset - repmatMatrix);
// C = (1-c1-cmu) * C + c1 * (pc * pc' + (1-hsig) * cc*(2-cc) * C) + cmu * artmp * diag(weights) * artmp' #This is the original Matlab line for reference
C = (1.0 - c1 - cmu) * C + c1 * (pc * pc.Transpose() + (1 - hSig) * cc * (2.0 - cc) * C) + cmu * artmp * Diagonalize1DMatrix(weights) * artmp.Transpose();
//Adapt step size sigma
//sigma = sigma * Math.Exp((cs / damps) * (numpy.linalg.norm(ps) / chiN - 1))
sigma = sigma * Math.Exp((cs / damps) * (ps.L2Norm() / chiN - 1)); //NOT SURE IF THIS IS RIGHT FIX IN C#
//Update B and D from C
if ((counteval - eigeneval) > (lambdaVal / (c1 + cmu) / n / 10.0))
{
eigeneval = counteval;
//C = numpy.triu(C) + numpy.transpose(numpy.triu(C, 1)) #enforce symmetry
C = C.UpperTriangle() + C.StrictlyUpperTriangle().Transpose(); //NOT SURE IF THIS IS RIGHT FIX IN C#
//eigen decomposition
Evd <double> eigen = C.Evd();
B = eigen.EigenVectors;
Vector <System.Numerics.Complex> vectorEigenValues = eigen.EigenValues;
for (int i = 0; i < vectorEigenValues.Count; i++)
{
D[i, 0] = vectorEigenValues[i].Real;
}
//take sqrt of D
for (int i = 0; i < vectorEigenValues.Count; i++)
{
D[i, 0] = Math.Sqrt(D[i, 0]);
}
for (int i = 0; i < n; i++)
{
oneOverD[i, 0] = 1.0 / D[i, 0];
}
Matrix <double> middleTerm = Diagonalize1DMatrix(oneOverD); //#Built in Numpy function doesn't create the right size matrix in this case (ex: Numpy gives 1x1 but should be 5x5)
invsqrtC = B * middleTerm * B.Transpose();
}
globalBestCandidate = candidateArray[0];
//Stopping condition
if (globalBestCandidate.GetObjectiveFunctionValue() > stopFitness)
{
return(globalBestCandidate);
}
//Time to save the state
VariantData varDataUpdated = new VariantData(coreNumberForSaving, counteval, n, lambdaVal, xMean, D, B, sigma, weights, ps, cs, mueff, cc, invsqrtC, C, mu, pc, c1, cmu, damps, chiN, eigeneval, globalBestCandidate);
string fname = AppConstants.SaveDir + counteval.ToString() + "VariantData" + coreNumberForSaving.ToString();
FileInfo fi = new FileInfo(fname);
Stream str = fi.Open(FileMode.OpenOrCreate, FileAccess.Write);
BinaryFormatter bf = new BinaryFormatter();
bf.Serialize(str, varDataUpdated);
str.Close();
Console.Out.WriteLine("Iteration #" + counteval.ToString());
Console.Out.WriteLine("Current Value=" + (candidateArray[candidateArray.Count - 1].GetObjectiveFunctionValue()).ToString());
}//end while loop
return(globalBestCandidate); //just in case everything terminates
}