/usr/include/ql/math/optimization/simulatedannealing.hpp is in libquantlib0-dev 1.7.1-1.
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/*
Copyright (C) 2013 Peter Caspers
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
/*! \file simulatedannealing.hpp
\brief Numerical Recipes in C (second edition), Chapter 10.9,
with the original exit criterion in f(x) replaced by one
in x (see simplex.cpp for a reference to GSL concerning this)
*/
#ifndef quantlib_optimization_simulatedannealing_hpp
#define quantlib_optimization_simulatedannealing_hpp
#include <ql/math/randomnumbers/mt19937uniformrng.hpp>
#include <ql/math/optimization/problem.hpp>
#include <ql/math/optimization/constraint.hpp>
#include <boost/math/special_functions/fpclassify.hpp>
namespace QuantLib {
/*! Class RNG must implement the following interface:
\code
RNG::sample_type RNG::next() const;
\endcode
\ingroup optimizers
*/
template <class RNG = MersenneTwisterUniformRng>
class SimulatedAnnealing : public OptimizationMethod {
public:
enum Scheme {
ConstantFactor,
ConstantBudget
};
/*! reduce temperature T by a factor of \f$ (1-\epsilon) \f$ after m moves */
SimulatedAnnealing(const Real lambda, const Real T0,
const Real epsilon, const Size m,
const RNG &rng = RNG())
: scheme_(ConstantFactor), lambda_(lambda), T0_(T0),
epsilon_(epsilon), alpha_(0.0), K_(0), rng_(rng), m_(m) {}
/*! budget a total of K moves, set temperature T to the initial
temperature times \f$ ( 1 - k/K )^\alpha \f$ with k being the total number
of moves so far. After K moves the temperature is guaranteed to be
zero, after that the optimization runs like a deterministic simplex
algorithm.
*/
SimulatedAnnealing(const Real lambda, const Real T0, const Size K,
const Real alpha, const RNG &rng = RNG())
: scheme_(ConstantBudget), lambda_(lambda), T0_(T0), epsilon_(0.0),
alpha_(alpha), K_(K), rng_(rng) {}
EndCriteria::Type minimize(Problem &P, const EndCriteria &ec);
private:
const Scheme scheme_;
const Real lambda_, T0_, epsilon_, alpha_;
const Size K_;
const RNG rng_;
Real simplexSize();
void amotsa(Problem &, Real);
Real T_;
std::vector<Array> vertices_;
Array values_, sum_;
Integer i_, ihi_, ilo_, j_, m_, n_;
Real fac1_, fac2_, yflu_;
Real rtol_, swap_, yhi_, ylo_, ynhi_, ysave_, yt_, ytry_, yb_, tt_;
Array pb_, ptry_;
Size iteration_, iterationT_;
};
template <class RNG>
Real SimulatedAnnealing<RNG>::simplexSize() { // this is taken from
// simplex.cpp
Array center(vertices_.front().size(), 0);
for (Size i = 0; i < vertices_.size(); ++i)
center += vertices_[i];
center *= 1 / Real(vertices_.size());
Real result = 0;
for (Size i = 0; i < vertices_.size(); ++i) {
Array temp = vertices_[i] - center;
result += std::sqrt(DotProduct(temp, temp));
}
return result / Real(vertices_.size());
}
template <class RNG>
void SimulatedAnnealing<RNG>::amotsa(Problem &P, Real fac) {
fac1_ = (1.0 - fac) / ((Real)n_);
fac2_ = fac1_ - fac;
for (j_ = 0; j_ < n_; j_++) {
ptry_[j_] = sum_[j_] * fac1_ - vertices_[ihi_][j_] * fac2_;
}
if (!P.constraint().test(ptry_))
ytry_ = QL_MAX_REAL;
else
ytry_ = P.value(ptry_);
if (boost::math::isnan(ytry_)) {
ytry_ = QL_MAX_REAL;
}
if (ytry_ <= yb_) {
yb_ = ytry_;
pb_ = ptry_;
}
yflu_ = ytry_ - tt_ * std::log(rng_.next().value);
if (yflu_ < yhi_) {
values_[ihi_] = ytry_;
yhi_ = yflu_;
for (j_ = 0; j_ < n_; j_++) {
sum_[j_] += ptry_[j_] - vertices_[ihi_][j_];
vertices_[ihi_][j_] = ptry_[j_];
}
}
ytry_ = yflu_;
return;
}
template <class RNG>
EndCriteria::Type SimulatedAnnealing<RNG>::minimize(Problem &P,
const EndCriteria &ec) {
Size stationaryStateIterations_ = 0;
EndCriteria::Type ecType = EndCriteria::None;
P.reset();
Array x = P.currentValue();
iteration_ = 0;
n_ = x.size();
ptry_ = Array(n_, 0.0);
// build vertices
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_);
}
values_ = Array(n_ + 1, 0.0);
for (i_ = 0; i_ <= n_; i_++) {
if (!P.constraint().test(vertices_[i_]))
values_[i_] = QL_MAX_REAL;
else
values_[i_] = P.value(vertices_[i_]);
if (boost::math::isnan(ytry_)) { // handle NAN
values_[i_] = QL_MAX_REAL;
}
}
// minimize
T_ = T0_;
yb_ = QL_MAX_REAL;
pb_ = Array(n_, 0.0);
do {
iterationT_ = iteration_;
do {
sum_ = Array(n_, 0.0);
for (i_ = 0; i_ <= n_; i_++)
sum_ += vertices_[i_];
tt_ = -T_;
ilo_ = 0;
ihi_ = 1;
ynhi_ = values_[0] + tt_ * std::log(rng_.next().value);
ylo_ = ynhi_;
yhi_ = values_[1] + tt_ * std::log(rng_.next().value);
if (ylo_ > yhi_) {
ihi_ = 0;
ilo_ = 1;
ynhi_ = yhi_;
yhi_ = ylo_;
ylo_ = ynhi_;
}
for (i_ = 2; i_ < n_ + 1; i_++) {
yt_ = values_[i_] + tt_ * std::log(rng_.next().value);
if (yt_ <= ylo_) {
ilo_ = i_;
ylo_ = yt_;
}
if (yt_ > yhi_) {
ynhi_ = yhi_;
ihi_ = i_;
yhi_ = yt_;
} else {
if (yt_ > ynhi_) {
ynhi_ = yt_;
}
}
}
// rtol_ = 2.0 * std::fabs(yhi_ - ylo_) /
// (std::fabs(yhi_) + std::fabs(ylo_));
// check rtol against some ftol... // NR end criterion in f(x)
// GSL end criterion in x (cf. above)
if (ec.checkStationaryPoint(simplexSize(), 0.0,
stationaryStateIterations_,
ecType) ||
ec.checkMaxIterations(iteration_, ecType)) {
// no matter what, we return the best ever point !
P.setCurrentValue(pb_);
P.setFunctionValue(yb_);
return ecType;
}
iteration_ += 2;
amotsa(P, -1.0);
if (ytry_ <= ylo_) {
amotsa(P, 2.0);
} else {
if (ytry_ >= ynhi_) {
ysave_ = yhi_;
amotsa(P, 0.5);
if (ytry_ >= ysave_) {
for (i_ = 0; i_ < n_ + 1; i_++) {
if (i_ != ilo_) {
for (j_ = 0; j_ < n_; j_++) {
sum_[j_] = 0.5 * (vertices_[i_][j_] +
vertices_[ilo_][j_]);
vertices_[i_][j_] = sum_[j_];
}
values_[i_] = P.value(sum_);
}
}
iteration_ += n_;
for (i_ = 0; i_ < n_; i_++)
sum_[i_] = 0.0;
for (i_ = 0; i_ <= n_; i_++)
sum_ += vertices_[i_];
}
} else {
iteration_ += 1;
}
}
} while (iteration_ <
iterationT_ + (scheme_ == ConstantFactor ? m_ : 1));
switch (scheme_) {
case ConstantFactor:
T_ *= (1.0 - epsilon_);
break;
case ConstantBudget:
if (iteration_ <= K_)
T_ = T0_ *
std::pow(1.0 - (Real)iteration_ / (Real)K_, alpha_);
else
T_ = 0.0;
break;
}
} while (true);
}
}
#endif
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