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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2015 Andres Hernandez
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
<https://www.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.
*/
#include <ql/experimental/math/fireflyalgorithm.hpp>
#include <ql/math/randomnumbers/sobolrsg.hpp>
#include <algorithm>
#include <cmath>
#include <utility>
namespace QuantLib {
FireflyAlgorithm::FireflyAlgorithm(Size M,
ext::shared_ptr<Intensity> intensity,
ext::shared_ptr<RandomWalk> randomWalk,
Size Mde,
Real mutation,
Real crossover,
unsigned long seed)
: mutation_(mutation), crossover_(crossover), M_(M), Mde_(Mde), Mfa_(M_ - Mde_),
intensity_(std::move(intensity)), randomWalk_(std::move(randomWalk)),
generator_(seed), distribution_(Mfa_, Mde > 0 ? M_ - 1 : M_),
rng_(seed) {
QL_REQUIRE(M_ >= Mde_,
"Differential Evolution subpopulation cannot be larger than total population");
}
void FireflyAlgorithm::startState(Problem &P, const EndCriteria &endCriteria) {
N_ = P.currentValue().size();
x_.reserve(M_);
xI_.reserve(M_);
xRW_.reserve(M_);
values_.reserve(M_);
uX_ = P.constraint().upperBound(P.currentValue());
lX_ = P.constraint().lowerBound(P.currentValue());
Array bounds = uX_ - lX_;
//Random initialization is done by Sobol sequence
SobolRsg sobol(N_);
//Prepare containers
for (Size i = 0; i < M_; i++) {
const SobolRsg::sample_type::value_type &sample = sobol.nextSequence().value;
x_.emplace_back(N_, 0.0);
xI_.emplace_back(N_, 0.0);
xRW_.emplace_back(N_, 0.0);
Array& x = x_.back();
for (Size j = 0; j < N_; j++) {
//Assign X=lb+(ub-lb)*random
x[j] = lX_[j] + bounds[j] * sample[j];
}
//Evaluate point
values_.emplace_back(P.value(x), i);
}
//init intensity & randomWalk
intensity_->init(this);
randomWalk_->init(this);
}
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;
//Variables for DE
Array z(N_, 0.0);
Size indexR1, indexR2;
decltype(distribution_)::param_type nParam(0, N_ - 1);
//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 = distribution_(generator_);
xBest = x_[indexBest];
}
do {
indexR1 = distribution_(generator_);
} while(indexR1 == indexBest);
do {
indexR2 = distribution_(generator_);
} while(indexR2 == indexBest || indexR2 == indexR1);
Size index = values_[i].second;
Array& x = x_[index];
Array& xR1 = x_[indexR1];
Array& xR2 = x_[indexR2];
Size rIndex = distribution_(generator_, nParam);
for (Size j = 0; j < N_; j++) {
if (j == rIndex || rng_.nextReal() <= crossover_) {
//Change x[j] according to crossover
z[j] = xBest[j] + mutation_*(xR1[j] - xR2[j]);
} else {
z[j] = x[j];
}
//Enforce bounds on positions
if (z[j] < lX_[j]) {
z[j] = lX_[j];
}
else if (z[j] > uX_[j]) {
z[j] = uX_[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
z[j] = x[j] + xI[j] + xRW[j];
//Enforce bounds on positions
if (z[j] < lX_[j]) {
z[j] = lX_[j];
}
else if (z[j] > uX_[j]) {
z[j] = uX_[j];
}
}
Real val = P.value(z);
if(!std::isnan(val))
{
//Accept new point
x = z;
values_[index].first = val;
//mark best
if (val < bestValue) {
bestValue = val;
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;
}
void FireflyAlgorithm::Intensity::findBrightest() {
//Brightest ignores all others
Array& xI = (*xI_)[(*values_)[0].second];
for (Size j = 0; j < N_; j++) {
xI[j] = 0.0;
}
for (Size i = 1; i < Mfa_; i++) {
//values_ is already sorted
Size index = (*values_)[i].second;
const Array& x = (*x_)[index];
Array& xI = (*xI_)[index];
for (Size j = 0; j < N_; j++) {
xI[j] = 0.0;
}
Real valueX = (*values_)[i].first;
for (Size k = 0; k < i - 1; k++){
const Array& y = (*x_)[(*values_)[k].second];
Real valueY = (*values_)[k].first;
Real intensity = intensityImpl(valueX, valueY, distance(x, y));
xI += intensity*(y - x);
}
}
}
}
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