EndCriteria::Type DifferentialEvolution::minimize(Problem& p, const EndCriteria& endCriteria) {
EndCriteria::Type ecType;
upperBound_ = p.constraint().upperBound(p.currentValue());
lowerBound_ = p.constraint().lowerBound(p.currentValue());
currGenSizeWeights_ = Array(configuration().populationMembers,
configuration().stepsizeWeight);
currGenCrossover_ = Array(configuration().populationMembers,
configuration().crossoverProbability);
std::vector<Candidate> population(configuration().populationMembers,
Candidate(p.currentValue().size()));
fillInitialPopulation(population, p);
std::partial_sort(population.begin(), population.begin() + 1, population.end(),
sort_by_cost());
bestMemberEver_ = population.front();
Real fxOld = population.front().cost;
Size iteration = 0, stationaryPointIteration = 0;
// main loop - calculate consecutive emerging populations
while (!endCriteria.checkMaxIterations(iteration++, ecType)) {
calculateNextGeneration(population, p.costFunction());
std::partial_sort(population.begin(), population.begin() + 1, population.end(),
sort_by_cost());
if (population.front().cost < bestMemberEver_.cost)
bestMemberEver_ = population.front();
Real fxNew = population.front().cost;
if (endCriteria.checkStationaryFunctionValue(fxOld, fxNew, stationaryPointIteration,
ecType))
break;
fxOld = fxNew;
};
p.setCurrentValue(bestMemberEver_.values);
p.setFunctionValue(bestMemberEver_.cost);
return ecType;
}
Real GoldsteinLineSearch::operator()(Problem& P,
EndCriteria::Type& ecType,
const EndCriteria& endCriteria,
const Real t_ini)
{
Constraint& constraint = P.constraint();
succeed_=true;
bool maxIter = false;
Real /*qtold,*/ t = t_ini; // see below, this is never used ?
Size loopNumber = 0;
Real q0 = P.functionValue();
Real qp0 = P.gradientNormValue();
Real tl = 0.0;
Real tr = 0.0;
qt_ = q0;
qpt_ = (gradient_.empty()) ? qp0 : -DotProduct(gradient_,searchDirection_);
// Initialize gradient
gradient_ = Array(P.currentValue().size());
// Compute new point
xtd_ = P.currentValue();
t = update(xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value (xtd_);
while ((qt_ - q0) < -beta_*t*qpt_ || (qt_ - q0) > -alpha_*t*qpt_) {
if ((qt_ - q0) > -alpha_*t*qpt_)
tr = t;
else
tl = t;
++loopNumber;
// calculate the new step
if (close_enough(tr, 0.0))
t *= extrapolation_;
else
t = (tl + tr) / 2.0;
// Store old value of the function
// qtold = qt_; // this is never used ?
// New point value
xtd_ = P.currentValue();
t = update(xtd_, searchDirection_, t, constraint);
// Compute function value at the new point
qt_ = P.value (xtd_);
P.gradient (gradient_, xtd_);
// and it squared norm
maxIter = endCriteria.checkMaxIterations(loopNumber, ecType);
if (maxIter)
break;
}
if (maxIter)
succeed_ = false;
// Compute new gradient
P.gradient(gradient_, xtd_);
// and it squared norm
qpt_ = DotProduct(gradient_, gradient_);
// Return new step value
return t;
}
EndCriteria::Type LevenbergMarquardt::minimize(Problem& P,
const EndCriteria& endCriteria) {
EndCriteria::Type ecType = EndCriteria::None;
P.reset();
Array x_ = P.currentValue();
currentProblem_ = &P;
initCostValues_ = P.costFunction().values(x_);
int m = initCostValues_.size();
int n = x_.size();
boost::scoped_array<double> xx(new double[n]);
std::copy(x_.begin(), x_.end(), xx.get());
boost::scoped_array<double> fvec(new double[m]);
boost::scoped_array<double> diag(new double[n]);
int mode = 1;
double factor = 1;
int nprint = 0;
int info = 0;
int nfev =0;
boost::scoped_array<double> fjac(new double[m*n]);
int ldfjac = m;
boost::scoped_array<int> ipvt(new int[n]);
boost::scoped_array<double> qtf(new double[n]);
boost::scoped_array<double> wa1(new double[n]);
boost::scoped_array<double> wa2(new double[n]);
boost::scoped_array<double> wa3(new double[n]);
boost::scoped_array<double> wa4(new double[m]);
// requirements; check here to get more detailed error messages.
QL_REQUIRE(n > 0, "no variables given");
QL_REQUIRE(m >= n,
"less functions (" << m <<
") than available variables (" << n << ")");
QL_REQUIRE(endCriteria.functionEpsilon() >= 0.0,
"negative f tolerance");
QL_REQUIRE(xtol_ >= 0.0, "negative x tolerance");
QL_REQUIRE(gtol_ >= 0.0, "negative g tolerance");
QL_REQUIRE(endCriteria.maxIterations() > 0,
"null number of evaluations");
// call lmdif to minimize the sum of the squares of m functions
// in n variables by the Levenberg-Marquardt algorithm.
MINPACK::LmdifCostFunction lmdifCostFunction =
boost::bind(&LevenbergMarquardt::fcn, this, _1, _2, _3, _4, _5);
MINPACK::lmdif(m, n, xx.get(), fvec.get(),
static_cast<double>(endCriteria.functionEpsilon()),
static_cast<double>(xtol_),
static_cast<double>(gtol_),
static_cast<int>(endCriteria.maxIterations()),
static_cast<double>(epsfcn_),
diag.get(), mode, factor,
nprint, &info, &nfev, fjac.get(),
ldfjac, ipvt.get(), qtf.get(),
wa1.get(), wa2.get(), wa3.get(), wa4.get(),
lmdifCostFunction);
info_ = info;
// check requirements & endCriteria evaluation
QL_REQUIRE(info != 0, "MINPACK: improper input parameters");
//QL_REQUIRE(info != 6, "MINPACK: ftol is too small. no further "
// "reduction in the sum of squares "
// "is possible.");
if (info != 6) ecType = QuantLib::EndCriteria::StationaryFunctionValue;
//QL_REQUIRE(info != 5, "MINPACK: number of calls to fcn has "
// "reached or exceeded maxfev.");
endCriteria.checkMaxIterations(nfev, ecType);
QL_REQUIRE(info != 7, "MINPACK: xtol is too small. no further "
"improvement in the approximate "
"solution x is possible.");
QL_REQUIRE(info != 8, "MINPACK: gtol is too small. fvec is "
"orthogonal to the columns of the "
"jacobian to machine precision.");
// set problem
std::copy(xx.get(), xx.get()+n, x_.begin());
P.setCurrentValue(x_);
P.setFunctionValue(P.costFunction().value(x_));
return ecType;
}
EndCriteria::Type HybridSimulatedAnnealing<Sampler, Probability, Temperature, Reannealing>::minimize(Problem &P, const EndCriteria &endCriteria) {
EndCriteria::Type ecType = EndCriteria::None;
P.reset();
reannealing_.setProblem(P);
Array x = P.currentValue();
Size n = x.size();
Size k = 1;
Size kStationary = 1;
Size kReAnneal = 1;
Size kReset = 1;
Size maxK = endCriteria.maxIterations();
Size maxKStationary = endCriteria.maxStationaryStateIterations();
bool temperatureBreached = false;
Array currentTemperature(n, startTemperature_);
Array annealStep(n, 1.0);
Array bestPoint(x);
Array currentPoint(x);
Array startingPoint(x);
Array newPoint(x);
Real bestValue = P.value(bestPoint);
Real currentValue = bestValue;
Real startingValue = bestValue; //to reset to starting point if desired
while (k <= maxK && kStationary <= maxKStationary && !temperatureBreached)
{
//Draw a new sample point
sampler_(newPoint, currentPoint, currentTemperature);
//Evaluate new point
Real newValue = P.value(newPoint);
//Determine if new point is accepted
if (probability_(currentValue, newValue, currentTemperature)) {
if (optimizeScheme_ == EveryNewPoint) {
P.setCurrentValue(newPoint);
P.setFunctionValue(newValue);
localOptimizer_->minimize(P, endCriteria);
newPoint = P.currentValue();
newValue = P.functionValue();
}
currentPoint = newPoint;
currentValue = newValue;
}
//Check if we have a new best point
if (newValue < bestValue) {
if (optimizeScheme_ == EveryBestPoint) {
P.setCurrentValue(newPoint);
P.setFunctionValue(newValue);
localOptimizer_->minimize(P, endCriteria);
newPoint = P.currentValue();
newValue = P.functionValue();
}
kStationary = 0;
bestValue = newValue;
bestPoint = newPoint;
}
//Increase steps
k++;
kStationary++;
for (Size i = 0; i < annealStep.size(); i++)
annealStep[i]++;
//Reanneal if necessary
if (kReAnneal == reAnnealSteps_) {
kReAnneal = 0;
reannealing_(annealStep, currentPoint, currentValue, currentTemperature);
}
kReAnneal++;
//Reset if necessary
if (kReset == resetSteps_) {
kReset = 0;
switch (resetScheme_) {
case NoResetScheme:
break;
case ResetToBestPoint:
currentPoint = startingPoint;
currentValue = startingValue;
break;
case ResetToOrigin:
currentPoint = bestPoint;
currentValue = bestValue;
break;
}
}
kReset++;
//Update the current temperature according to current step
temperature_(currentTemperature, currentTemperature, annealStep);
//Check if temperature condition is breached
for (Size i = 0; i < n; i++)
temperatureBreached = temperatureBreached && currentTemperature[i] < endTemperature_;
}
//Change end criteria type if appropriate
if (k > maxK)
ecType = EndCriteria::MaxIterations;
else if (kStationary > maxKStationary)
ecType = EndCriteria::StationaryPoint;
//Set result to best point
P.setCurrentValue(bestPoint);
P.setFunctionValue(bestValue);
return ecType;
}
EndCriteria::Type Simplex::minimize(Problem& P,
const EndCriteria& endCriteria) {
// set up of the problem
//Real ftol = endCriteria.functionEpsilon(); // end criteria on f(x) (see Numerical Recipes in C++, p.410)
Real xtol = endCriteria.rootEpsilon(); // end criteria on x (see GSL v. 1.9, http://www.gnu.org/software/gsl/)
Size maxStationaryStateIterations_
= endCriteria.maxStationaryStateIterations();
EndCriteria::Type ecType = EndCriteria::None;
P.reset();
Array x_ = P.currentValue();
Integer iterationNumber_=0;
// Initialize vertices of the simplex
bool end = false;
Size n = x_.size(), i;
vertices_ = std::vector<Array>(n+1, x_);
for (i=0; i<n; i++) {
Array direction(n, 0.0);
direction[i] = 1.0;
P.constraint().update(vertices_[i+1], direction, lambda_);
}
// Initialize function values at the vertices of the simplex
values_ = Array(n+1, 0.0);
for (i=0; i<=n; i++)
values_[i] = P.value(vertices_[i]);
// Loop looking for minimum
do {
sum_ = Array(n, 0.0);
Size i;
for (i=0; i<=n; i++)
sum_ += vertices_[i];
// Determine the best (iLowest), worst (iHighest)
// and 2nd worst (iNextHighest) vertices
Size iLowest = 0;
Size iHighest, iNextHighest;
if (values_[0]<values_[1]) {
iHighest = 1;
iNextHighest = 0;
} else {
iHighest = 0;
iNextHighest = 1;
}
for (i=1;i<=n; i++) {
if (values_[i]>values_[iHighest]) {
iNextHighest = iHighest;
iHighest = i;
} else {
if ((values_[i]>values_[iNextHighest]) && i!=iHighest)
iNextHighest = i;
}
if (values_[i]<values_[iLowest])
iLowest = i;
}
// Now compute accuracy, update iteration number and check end criteria
//// Numerical Recipes exit strategy on fx (see NR in C++, p.410)
//Real low = values_[iLowest];
//Real high = values_[iHighest];
//Real rtol = 2.0*std::fabs(high - low)/
// (std::fabs(high) + std::fabs(low) + QL_EPSILON);
//++iterationNumber_;
//if (rtol < ftol ||
// endCriteria.checkMaxIterations(iterationNumber_, ecType)) {
// GSL exit strategy on x (see GSL v. 1.9, http://www.gnu.org/software/gsl
Real simplexSize = computeSimplexSize(vertices_);
++iterationNumber_;
if (simplexSize < xtol ||
endCriteria.checkMaxIterations(iterationNumber_, ecType)) {
endCriteria.checkStationaryPoint(0.0, 0.0,
maxStationaryStateIterations_, ecType); // PC this is probably not meant like this ? Use separate counter ?
endCriteria.checkMaxIterations(iterationNumber_, ecType);
x_ = vertices_[iLowest];
Real low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return ecType;
}
// If end criteria is not met, continue
Real factor = -1.0;
Real vTry = extrapolate(P, iHighest, factor);
if ((vTry <= values_[iLowest]) && (factor == -1.0)) {
factor = 2.0;
extrapolate(P, iHighest, factor);
} else if (std::fabs(factor) > QL_EPSILON) {
if (vTry >= values_[iNextHighest]) {
Real vSave = values_[iHighest];
factor = 0.5;
vTry = extrapolate(P, iHighest, factor);
if (vTry >= vSave && std::fabs(factor) > QL_EPSILON) {
for (Size i=0; i<=n; i++) {
if (i!=iLowest) {
#if defined(QL_ARRAY_EXPRESSIONS)
vertices_[i] =
0.5*(vertices_[i] + vertices_[iLowest]);
#else
vertices_[i] += vertices_[iLowest];
vertices_[i] *= 0.5;
#endif
values_[i] = P.value(vertices_[i]);
}
}
}
}
}
// If can't extrapolate given the constraints, exit
if (std::fabs(factor) <= QL_EPSILON) {
x_ = vertices_[iLowest];
Real low = values_[iLowest];
P.setFunctionValue(low);
P.setCurrentValue(x_);
return EndCriteria::StationaryFunctionValue;
}
} while (end == false);
QL_FAIL("optimization failed: unexpected behaviour");
}
EndCriteria::Type DifferentialEvolution::minimize(Problem& P,
const EndCriteria& endCriteria) {
EndCriteria::Type ecType = EndCriteria::MaxIterations;
QL_REQUIRE(P.currentValue().size() == nParam_,
"Number of parameters mismatch between problem and DE optimizer");
P.reset();
init();
Real bestCost = QL_MAX_REAL;
Size bestPop = 0;
for (Size p = 0; p < nPop_; ++p) {
Array tmp(currGen_[p].pop_);
try {
currGen_[p].cost_ = P.costFunction().value(tmp);
} catch (Error&) {
currGen_[p].cost_ = QL_MAX_REAL;
}
if (currGen_[p].cost_ < bestCost) {
bestPop = p;
bestCost = currGen_[p].cost_;
}
}
Size lastChange = 0;
Size lastParamChange = 0;
for(Size i=0; i<endCriteria.maxIterations(); ++i) {
Size newBestPop = bestPop;
Real newBestCost = bestCost;
for (Size p=0; p<nPop_; ++p) {
// Find 3 different populations randomly
Size r1;
do {
r1 = static_cast <Size> (uniformRng_.nextInt32() % nPop_);
}
while(r1 == p || r1 == bestPop);
Size r2;
do {
r2 = static_cast <Size> (uniformRng_.nextInt32() % nPop_);
}
while ( r2 == p || r2 == bestPop || r2 == r1);
Size r3;
do {
r3 = static_cast <Size> (uniformRng_.nextInt32() % nPop_);
} while ( r3 == p || r3 == bestPop || r3 == r1 || r3 == r2);
for(Size j=0; j<nParam_; ++j) {
nextGen_[p].pop_[j] = currGen_[p].pop_[j];
}
Size j = static_cast <Size> (uniformRng_.nextInt32() % nParam_);
Size L = 0;
do {
const double tmp =
currGen_[ p].pop_[j] * a0_
+ currGen_[ r1].pop_[j] * a1_
+ currGen_[ r2].pop_[j] * a2_
+ currGen_[ r3].pop_[j] * a3_
+ currGen_[bestPop].pop_[j] * aBest_;
nextGen_[p].pop_[j] =
std::min(maxParams_[j], std::max(minParams_[j], tmp));
j = (j+1)%nParam_;
++L;
} while ((uniformRng_.nextReal() < CR_) && (L < nParam_));
// Evaluate the new population
Array tmp(nextGen_[p].pop_);
try {
nextGen_[p].cost_ = P.costFunction().value(tmp);
} catch (Error&) {
nextGen_[p].cost_ = QL_MAX_REAL;
}
// Not better, discard it and keep the old one.
if (nextGen_[p].cost_ >= currGen_[p].cost_) {
nextGen_[p] = currGen_[p];
}
// Better, keep it.
else {
// New best?
if (nextGen_[p].cost_ < newBestCost) {
newBestPop = p;
newBestCost = nextGen_[p].cost_;
}
}
}
if(std::abs(newBestCost-bestCost) > endCriteria.functionEpsilon()) {
lastChange = i;
}
const Array absDiff = Abs(nextGen_[newBestPop].pop_-currGen_[bestPop].pop_);
if(*std::max_element(absDiff.begin(), absDiff.end()) > endCriteria.rootEpsilon()) {
lastParamChange = i;
}
bestPop = newBestPop;
bestCost = newBestCost;
currGen_ = nextGen_;
if(i-lastChange > endCriteria.maxStationaryStateIterations()) {
ecType = EndCriteria::StationaryFunctionValue;
break;
}
if(i-lastParamChange > endCriteria.maxStationaryStateIterations()) {
ecType = EndCriteria::StationaryPoint;
break;
}
if (adaptive_) adaptParameters();
}
const Array res(currGen_[bestPop].pop_);
P.setCurrentValue(res);
P.setFunctionValue(bestCost);
return ecType;
}
EndCriteria::Type
LineSearchBasedMethod::minimize(Problem& P,
const EndCriteria& endCriteria) {
// Initializations
Real ftol = endCriteria.functionEpsilon();
Size maxStationaryStateIterations_
= endCriteria.maxStationaryStateIterations();
EndCriteria::Type ecType = EndCriteria::None; // reset end criteria
P.reset(); // reset problem
Array x_ = P.currentValue(); // store the starting point
Size iterationNumber_ = 0;
// dimension line search
lineSearch_->searchDirection() = Array(x_.size());
bool done = false;
// function and squared norm of gradient values;
Real fnew, fold, gold2;
Real fdiff;
// classical initial value for line-search step
Real t = 1.0;
// Set gradient g at the size of the optimization problem
// search direction
Size sz = lineSearch_->searchDirection().size();
Array prevGradient(sz), d(sz), sddiff(sz), direction(sz);
// Initialize cost function, gradient prevGradient and search direction
P.setFunctionValue(P.valueAndGradient(prevGradient, x_));
P.setGradientNormValue(DotProduct(prevGradient, prevGradient));
lineSearch_->searchDirection() = -prevGradient;
bool first_time = true;
// Loop over iterations
do {
// Linesearch
if (!first_time)
prevGradient = lineSearch_->lastGradient();
t = (*lineSearch_)(P, ecType, endCriteria, t);
// don't throw: it can fail just because maxIterations exceeded
//QL_REQUIRE(lineSearch_->succeed(), "line-search failed!");
if (lineSearch_->succeed())
{
// Updates
// New point
x_ = lineSearch_->lastX();
// New function value
fold = P.functionValue();
P.setFunctionValue(lineSearch_->lastFunctionValue());
// New gradient and search direction vectors
// orthogonalization coef
gold2 = P.gradientNormValue();
P.setGradientNormValue(lineSearch_->lastGradientNorm2());
// conjugate gradient search direction
direction = getUpdatedDirection(P, gold2, prevGradient);
sddiff = direction - lineSearch_->searchDirection();
lineSearch_->searchDirection() = direction;
// Now compute accuracy and check end criteria
// Numerical Recipes exit strategy on fx (see NR in C++, p.423)
fnew = P.functionValue();
fdiff = 2.0*std::fabs(fnew-fold) /
(std::fabs(fnew) + std::fabs(fold) + QL_EPSILON);
if (fdiff < ftol ||
endCriteria.checkMaxIterations(iterationNumber_, ecType)) {
endCriteria.checkStationaryFunctionValue(0.0, 0.0,
maxStationaryStateIterations_, ecType);
endCriteria.checkMaxIterations(iterationNumber_, ecType);
return ecType;
}
P.setCurrentValue(x_); // update problem current value
++iterationNumber_; // Increase iteration number
first_time = false;
} else {
done = true;
}
} while (!done);
P.setCurrentValue(x_);
return ecType;
}
EndCriteria::Type FireflyAlgorithm::minimize(Problem &P, const EndCriteria &endCriteria) {
QL_REQUIRE(!P.constraint().empty(), "Firefly Algorithm is a constrained optimizer");
EndCriteria::Type ecType = EndCriteria::None;
P.reset();
Size iteration = 0;
Size iterationStat = 0;
Size maxIteration = endCriteria.maxIterations();
Size maxIStationary = endCriteria.maxStationaryStateIterations();
startState(P, endCriteria);
bool isFA = Mfa_ > 0 ? true : false;
//Variables for DE
Array z(N_, 0.0);
Size indexBest, indexR1, indexR2;
//Set best value & position
Real bestValue = values_[0].first;
Size bestPosition = 0;
for (Size i = 1; i < M_; i++) {
if (values_[i].first < bestValue) {
bestPosition = i;
bestValue = values_[i].first;
}
}
Array bestX = x_[bestPosition];
//Run optimization
do {
iteration++;
iterationStat++;
//Check if stopping criteria is met
if (iteration > maxIteration || iterationStat > maxIStationary)
break;
//Divide into two subpopulations
//First sort values
std::sort(values_.begin(), values_.end());
//Differential evolution
if(Mfa_ < M_){
Size indexBest = values_[0].second;
Array& xBest = x_[indexBest];
for (Size i = Mfa_; i < M_; i++) {
if (!isFA) {
//Pure DE requires random index
indexBest = drawIndex_();
xBest = x_[indexBest];
}
do {
indexR1 = drawIndex_();
} while(indexR1 == indexBest);
do {
indexR2 = drawIndex_();
} while(indexR2 == indexBest || indexR2 == indexR1);
Size index = values_[i].second;
Array& x = x_[index];
Array& xR1 = x_[indexR1];
Array& xR2 = x_[indexR2];
for (Size j = 0; j < N_; j++) {
if (rng_.nextReal() <= crossover_) {
//Change x[j] according to crossover
z[j] = xBest[j] + mutation_*(xR1[j] - xR2[j]);
} else {
z[j] = x[j];
}
}
Real val = P.value(z);
if (val < values_[index].first) {
//Accept new point
x = z;
values_[index].first = val;
//mark best
if (val < bestValue) {
bestValue = val;
bestX = x;
iterationStat = 0;
}
}
}
}
//Firefly algorithm
if(isFA){
//According to the intensity, determine best global position
intensity_->findBrightest();
//Prepare random walk
randomWalk_->walk();
//Loop over particles
for (Size i = 0; i < Mfa_; i++) {
Size index = values_[i].second;
Array& x = x_[index];
Array& xI = xI_[index];
Array& xRW = xRW_[index];
//Loop over dimensions
for (Size j = 0; j < N_; j++) {
//Update position
x[j] += xI[j] + xRW[j];
//Enforce bounds on positions
if (x[j] < lX_[j]) {
x[j] = lX_[j];
}
else if (x[j] > uX_[j]) {
x[j] = uX_[j];
}
}
//Evaluate x & mark best
values_[index].first = P.value(x);
if (values_[index].first < bestValue) {
bestValue = values_[index].first;
bestX = x;
iterationStat = 0;
}
}
}
} while (true);
if (iteration > maxIteration)
ecType = EndCriteria::MaxIterations;
else
ecType = EndCriteria::StationaryPoint;
//Set result to best point
P.setCurrentValue(bestX);
P.setFunctionValue(bestValue);
return ecType;
}
inline void setSize(Size M, Size N, Real c0, const EndCriteria &endCriteria) {
N_ = N;
c0_ = c0;
iteration_ = 0;
maxIterations_ = endCriteria.maxIterations();
}