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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2012 Ralph Schreyer
Copyright (C) 2012 Mateusz Kapturski
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.
*/
#include <ql/math/optimization/differentialevolution.hpp>
#include <algorithm>
#include <cmath>
namespace QuantLib {
namespace {
struct sort_by_cost {
bool operator()(const DifferentialEvolution::Candidate& left,
const DifferentialEvolution::Candidate& right) {
return left.cost < right.cost;
}
};
template <class I>
void randomize(I begin, I end,
const MersenneTwisterUniformRng& rng) {
Size n = static_cast<Size>(end-begin);
for (Size i=n-1; i>0; --i) {
std::swap(begin[i], begin[rng.nextInt32() % (i+1)]);
}
}
}
EndCriteria::Type DifferentialEvolution::minimize(Problem& p, const EndCriteria& endCriteria) {
EndCriteria::Type ecType;
p.reset();
if (configuration().upperBound.empty()) {
upperBound_ = p.constraint().upperBound(p.currentValue());
} else {
QL_REQUIRE(configuration().upperBound.size() == p.currentValue().size(),
"wrong upper bound size in differential evolution configuration");
upperBound_ = configuration().upperBound;
}
if (configuration().lowerBound.empty()) {
lowerBound_ = p.constraint().lowerBound(p.currentValue());
} else {
QL_REQUIRE(configuration().lowerBound.size() == p.currentValue().size(),
"wrong lower bound size in differential evolution configuration");
lowerBound_ = configuration().lowerBound;
}
currGenSizeWeights_ =
Array(configuration().populationMembers, configuration().stepsizeWeight);
currGenCrossover_ = Array(configuration().populationMembers,
configuration().crossoverProbability);
std::vector<Candidate> population;
if (!configuration().initialPopulation.empty()) {
population.resize(configuration().initialPopulation.size());
for (Size i = 0; i < population.size(); ++i) {
population[i].values = configuration().initialPopulation[i];
QL_REQUIRE(population[i].values.size() == p.currentValue().size(),
"wrong values size in initial population");
population[i].cost = p.costFunction().value(population[i].values);
}
} else {
population = std::vector<Candidate>(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);
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;
}
void DifferentialEvolution::calculateNextGeneration(
std::vector<Candidate>& population,
Problem& p) const {
std::vector<Candidate> mirrorPopulation;
std::vector<Candidate> oldPopulation = population;
switch (configuration().strategy) {
case Rand1Standard: {
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop1 = population;
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop2 = population;
randomize(population.begin(), population.end(), rng_);
mirrorPopulation = shuffledPop1;
for (Size popIter = 0; popIter < population.size(); popIter++) {
population[popIter].values = population[popIter].values
+ configuration().stepsizeWeight
* (shuffledPop1[popIter].values - shuffledPop2[popIter].values);
}
}
break;
case BestMemberWithJitter: {
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop1 = population;
randomize(population.begin(), population.end(), rng_);
Array jitter(population[0].values.size(), 0.0);
for (Size popIter = 0; popIter < population.size(); popIter++) {
for (Real& jitterIter : jitter) {
jitterIter = rng_.nextReal();
}
population[popIter].values = bestMemberEver_.values
+ (shuffledPop1[popIter].values - population[popIter].values)
* (0.0001 * jitter + configuration().stepsizeWeight);
}
mirrorPopulation = std::vector<Candidate>(population.size(),
bestMemberEver_);
}
break;
case CurrentToBest2Diffs: {
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop1 = population;
randomize(population.begin(), population.end(), rng_);
for (Size popIter = 0; popIter < population.size(); popIter++) {
population[popIter].values = oldPopulation[popIter].values
+ configuration().stepsizeWeight
* (bestMemberEver_.values - oldPopulation[popIter].values)
+ configuration().stepsizeWeight
* (population[popIter].values - shuffledPop1[popIter].values);
}
mirrorPopulation = shuffledPop1;
}
break;
case Rand1DiffWithPerVectorDither: {
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop1 = population;
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop2 = population;
randomize(population.begin(), population.end(), rng_);
mirrorPopulation = shuffledPop1;
Array FWeight = Array(population.front().values.size(), 0.0);
for (Real& fwIter : FWeight)
fwIter = (1.0 - configuration().stepsizeWeight) * rng_.nextReal() +
configuration().stepsizeWeight;
for (Size popIter = 0; popIter < population.size(); popIter++) {
population[popIter].values = population[popIter].values
+ FWeight * (shuffledPop1[popIter].values - shuffledPop2[popIter].values);
}
}
break;
case Rand1DiffWithDither: {
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop1 = population;
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop2 = population;
randomize(population.begin(), population.end(), rng_);
mirrorPopulation = shuffledPop1;
Real FWeight = (1.0 - configuration().stepsizeWeight) * rng_.nextReal()
+ configuration().stepsizeWeight;
for (Size popIter = 0; popIter < population.size(); popIter++) {
population[popIter].values = population[popIter].values
+ FWeight * (shuffledPop1[popIter].values - shuffledPop2[popIter].values);
}
}
break;
case EitherOrWithOptimalRecombination: {
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop1 = population;
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop2 = population;
randomize(population.begin(), population.end(), rng_);
mirrorPopulation = shuffledPop1;
Real probFWeight = 0.5;
if (rng_.nextReal() < probFWeight) {
for (Size popIter = 0; popIter < population.size(); popIter++) {
population[popIter].values = oldPopulation[popIter].values
+ configuration().stepsizeWeight
* (shuffledPop1[popIter].values - shuffledPop2[popIter].values);
}
} else {
Real K = 0.5 * (configuration().stepsizeWeight + 1); // invariant with respect to probFWeight used
for (Size popIter = 0; popIter < population.size(); popIter++) {
population[popIter].values = oldPopulation[popIter].values
+ K
* (shuffledPop1[popIter].values - shuffledPop2[popIter].values
- 2.0 * population[popIter].values);
}
}
}
break;
case Rand1SelfadaptiveWithRotation: {
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop1 = population;
randomize(population.begin(), population.end(), rng_);
std::vector<Candidate> shuffledPop2 = population;
randomize(population.begin(), population.end(), rng_);
mirrorPopulation = shuffledPop1;
adaptSizeWeights();
for (Size popIter = 0; popIter < population.size(); popIter++) {
if (rng_.nextReal() < 0.1){
population[popIter].values = rotateArray(bestMemberEver_.values);
}else {
population[popIter].values = bestMemberEver_.values
+ currGenSizeWeights_[popIter]
* (shuffledPop1[popIter].values - shuffledPop2[popIter].values);
}
}
}
break;
default:
QL_FAIL("Unknown strategy ("
<< Integer(configuration().strategy) << ")");
}
// in order to avoid unnecessary copying we use the same population object for mutants
crossover(oldPopulation, population, population, mirrorPopulation, p);
}
void DifferentialEvolution::crossover(
const std::vector<Candidate>& oldPopulation,
std::vector<Candidate>& population,
const std::vector<Candidate>& mutantPopulation,
const std::vector<Candidate>& mirrorPopulation,
Problem& p) const {
if (configuration().crossoverIsAdaptive) {
adaptCrossover();
}
Array mutationProbabilities = getMutationProbabilities(population);
std::vector<Array> crossoverMask(population.size(),
Array(population.front().values.size(), 1.0));
std::vector<Array> invCrossoverMask = crossoverMask;
getCrossoverMask(crossoverMask, invCrossoverMask, mutationProbabilities);
// crossover of the old and mutant population
for (Size popIter = 0; popIter < population.size(); popIter++) {
population[popIter].values = oldPopulation[popIter].values * invCrossoverMask[popIter]
+ mutantPopulation[popIter].values * crossoverMask[popIter];
// immediately apply bounds if specified
if (configuration().applyBounds) {
for (Size memIter = 0; memIter < population[popIter].values.size(); memIter++) {
if (population[popIter].values[memIter] > upperBound_[memIter])
population[popIter].values[memIter] = upperBound_[memIter]
+ rng_.nextReal()
* (mirrorPopulation[popIter].values[memIter]
- upperBound_[memIter]);
if (population[popIter].values[memIter] < lowerBound_[memIter])
population[popIter].values[memIter] = lowerBound_[memIter]
+ rng_.nextReal()
* (mirrorPopulation[popIter].values[memIter]
- lowerBound_[memIter]);
}
}
// evaluate objective function as soon as possible to avoid unnecessary loops
try {
population[popIter].cost = p.value(population[popIter].values);
} catch (Error&) {
population[popIter].cost = QL_MAX_REAL;
}
if (!std::isfinite(population[popIter].cost))
population[popIter].cost = QL_MAX_REAL;
}
}
void DifferentialEvolution::getCrossoverMask(
std::vector<Array> & crossoverMask,
std::vector<Array> & invCrossoverMask,
const Array & mutationProbabilities) const {
for (Size cmIter = 0; cmIter < crossoverMask.size(); cmIter++) {
for (Size memIter = 0; memIter < crossoverMask[cmIter].size(); memIter++) {
if (rng_.nextReal() < mutationProbabilities[cmIter]) {
invCrossoverMask[cmIter][memIter] = 0.0;
} else {
crossoverMask[cmIter][memIter] = 0.0;
}
}
}
}
Array DifferentialEvolution::getMutationProbabilities(
const std::vector<Candidate> & population) const {
Array mutationProbabilities = currGenCrossover_;
switch (configuration().crossoverType) {
case Normal:
break;
case Binomial:
mutationProbabilities = currGenCrossover_
* (1.0 - 1.0 / population.front().values.size())
+ 1.0 / population.front().values.size();
break;
case Exponential:
for (Size coIter = 0;coIter< currGenCrossover_.size(); coIter++){
mutationProbabilities[coIter] =
(1.0 - std::pow(currGenCrossover_[coIter],
(int) population.front().values.size()))
/ (population.front().values.size()
* (1.0 - currGenCrossover_[coIter]));
}
break;
default:
QL_FAIL("Unknown crossover type ("
<< Integer(configuration().crossoverType) << ")");
break;
}
return mutationProbabilities;
}
Array DifferentialEvolution::rotateArray(Array a) const {
randomize(a.begin(), a.end(), rng_);
return a;
}
void DifferentialEvolution::adaptSizeWeights() const {
// [=Fl & =Fu] respectively see Brest, J. et al., 2006,
// "Self-Adapting Control Parameters in Differential
// Evolution"
Real sizeWeightLowerBound = 0.1, sizeWeightUpperBound = 0.9;
// [=tau1] A Comparative Study on Numerical Benchmark
// Problems." page 649 for reference
Real sizeWeightChangeProb = 0.1;
for (Real& currGenSizeWeight : currGenSizeWeights_) {
if (rng_.nextReal() < sizeWeightChangeProb)
currGenSizeWeight = sizeWeightLowerBound + rng_.nextReal() * sizeWeightUpperBound;
}
}
void DifferentialEvolution::adaptCrossover() const {
Real crossoverChangeProb = 0.1; // [=tau2]
for (Real& coIter : currGenCrossover_) {
if (rng_.nextReal() < crossoverChangeProb)
coIter = rng_.nextReal();
}
}
void DifferentialEvolution::fillInitialPopulation(
std::vector<Candidate> & population,
const Problem& p) const {
// use initial values provided by the user
population.front().values = p.currentValue();
population.front().cost = p.costFunction().value(population.front().values);
// rest of the initial population is random
for (Size j = 1; j < population.size(); ++j) {
for (Size i = 0; i < p.currentValue().size(); ++i) {
Real l = lowerBound_[i], u = upperBound_[i];
population[j].values[i] = l + (u-l)*rng_.nextReal();
}
population[j].cost = p.costFunction().value(population[j].values);
if (!std::isfinite(population[j].cost))
population[j].cost = QL_MAX_REAL;
}
}
}
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