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 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
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;
}