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// CppNumericalSolver
#ifndef CMAES_H_
#define CMAES_H_
#include <random>
#include <Eigen/Dense>
#include "isolver.h"
namespace cppoptlib {
/**
* @brief Covariance Matrix Adaptation
*/
template<typename TProblem>
class CMAesSolver : public ISolver<TProblem, 1> {
public:
using Super = ISolver<TProblem, 1>;
using typename Super::Scalar;
using typename Super::TVector;
using typename Super::THessian;
using typename Super::TCriteria;
using TMatrix = Eigen::Matrix<Scalar, TProblem::Dim, Eigen::Dynamic>;
using TVarVector = Eigen::Matrix<Scalar, Eigen::Dynamic, 1>;
protected:
std::mt19937 gen;
Scalar m_stepSize;
/*
* @brief Create a vector sampled from a normal distribution
*
*/
TVector normDist(const int n) {
TVector sample = TVector::Zero(n);
std::normal_distribution<Scalar> d(0, 1);
for (int i = 0; i < n; ++i) {
sample[i] = d(gen);
}
return sample;
}
std::vector<size_t> index_partial_sort(const TVarVector &x, Eigen::ArrayXd::Index N)
{
eigen_assert(x.size() >= N);
std::vector<size_t> allIndices(x.size()), indices(N);
for(size_t i = 0; i < allIndices.size(); i++) {
allIndices[i] = i;
}
partial_sort(allIndices.begin(), allIndices.begin() + N, allIndices.end(), [&x](size_t i1, size_t i2) { return x[i1] < x[i2]; });
//std::cout << "SORTED: ";
for (Eigen::ArrayXd::Index i = 0; i < N; i++) {
indices[i] = allIndices[i];
//std::cout << indices[i] << ",";
}
//std::cout << std::endl;
return indices;
}
public:
CMAesSolver() : gen((std::random_device())()) {
m_stepSize = 0.5;
// Set some sensible defaults for the stop criteria
Super::m_stop.iterations = 1e5;
Super::m_stop.gradNorm = 0; // Switch this off
Super::m_stop.condition = 1e14;
Super::m_stop.xDelta = 1e-7;
Super::m_stop.fDelta = 1e-9;
}
void minimize(TProblem &objFunc, TVector &x0) {
TVector var0 = TVector::Ones(x0.rows());
this->minimize(objFunc, x0, var0);
}
/**
* @brief minimize
* @details [long description]
*
* @param objFunc [description]
*/
void minimize(TProblem &objFunc, TVector &x0, const TVector &var0) {
const int n = x0.rows();
eigen_assert(x0.rows() == var0.rows());
int la = ceil(4 + round(3 * log(n)));
const int mu = floor(la / 2);
TVarVector w = TVarVector::Zero(mu);
for (int i = 0; i < mu; ++i) {
w[i] = log(mu+1/2)-log(i+1);
}
w /= w.sum();
const Scalar mu_eff = (w.sum()*w.sum()) / w.dot(w);
la = std::max<int>(16, la); // Increase to 16 samples for very small populations, but AFTER calcaulting mu_eff
const Scalar cc = (4. + mu_eff / n) / (n + 4. + 2.*mu_eff/n);
const Scalar cs = (mu_eff + 2.) / (n + mu_eff + 5.);
const Scalar c1 = 2. / (pow(n + 1.3, 2.) + mu_eff);
const Scalar cmu = std::min(1. - c1, 2.*(mu_eff - 2. + 1./mu_eff) / (pow(n+2, 2.) + mu_eff));
const Scalar ds = 1. + cs + 2.*std::max(0., sqrt((mu_eff - 1.) / (n + 1.)) - 1.);
const Scalar chi = sqrt(n) * (1. - 1./(4.*n) + 1./(21.*n*n));
const Scalar hsig_thr = (1.4 + 2 / (n + 1.)) * chi;
TVector pc = TVector::Zero(n);
TVector ps = TVector::Zero(n);
THessian B = THessian::Identity();
THessian D = THessian::Identity();
THessian C = B*D*(B*D).transpose();
Scalar sigma = m_stepSize;
TVector xmean = x0;
TVector zmean = TVector::Zero(n);
TMatrix arz(n, la);
TMatrix arx(n, la);
TVarVector costs(la);
Scalar prevCost = objFunc.value(x0);
// CMA-ES Main Loop
int eigen_last_eval = 0;
int eigen_next_eval = std::max<Scalar>(1, 1/(10*n*(c1+cmu)));
this->m_current.reset();
if (Super::m_debug >= DebugLevel::Low) {
std::cout << "CMA-ES Initial Config" << std::endl;
std::cout << "n " << n << " la " << la << " mu " << mu << " mu_eff " << mu_eff << " sigma " << sigma << std::endl;
std::cout << "cs " << cs << " ds " << ds << " chi " << chi << " cc " << cc << " c1 " << c1 << " cmu " << cmu
<< " hsig_thr " << hsig_thr << std::endl;
std::cout << "C" << std::endl << C << std::endl;
std::cout << "Hessian will be updated every " << eigen_next_eval << " iterations." << std::endl;
std::cout << "Iteration: " << this->m_current.iterations << " best cost " << prevCost << " sigma " << sigma
<< " cond " << this->m_current.condition << " xmean " << x0.transpose() << std::endl;
}
do {
for (int k = 0; k < la; ++k) {
arz.col(k) = normDist(n);
arx.col(k) = xmean + sigma * B*D*arz.col(k);
costs[k] = objFunc(arx.col(k));
}
if (Super::m_debug >= DebugLevel::High) {
std::cout << "arz" << std::endl << arz << std::endl;
std::cout << "arx" << std::endl << arx << std::endl;
std::cout << "costs " << costs.transpose() << std::endl;
}
std::vector<size_t> indices = index_partial_sort(costs, mu);
xmean = TVector::Zero(n);
zmean = TVector::Zero(n);
for (int k = 0; k < mu; k++) {
zmean += w[k]*arz.col(indices[k]);
xmean += w[k]*arx.col(indices[k]);
}
// Update evolution paths
ps = (1. - cs)*ps + sqrt(cs*(2. - cs)*mu_eff) * B*zmean;
Scalar hsig = (ps.norm()/sqrt(pow(1 - (1. - cs), (2 * (this->m_current.iterations + 1)))) < hsig_thr) ? 1.0 : 0.0;
pc = (1. - cc)*pc + hsig*sqrt(cc*(2. - cc)*mu_eff)*(B*D*zmean);
// Adapt covariance matrix
C = (1 - c1 - cmu)*C
+ c1*(pc*pc.transpose() + (1 - hsig)*cc*(2 - cc)*C);
for (int k = 0; k < mu; ++k) {
TVector temp = B*D*arz.col(k);
C += cmu*w(k)*temp*temp.transpose();
}
sigma = sigma * exp((cs/ds) * ((ps).norm()/chi - 1.));
++Super::m_current.iterations;
if ((Super::m_current.iterations - eigen_last_eval) == eigen_next_eval) {
// Update B and D
eigen_last_eval = Super::m_current.iterations;
Eigen::SelfAdjointEigenSolver<THessian> eigenSolver(C);
B = eigenSolver.eigenvectors();
D.diagonal() = eigenSolver.eigenvalues().array().sqrt();
if (Super::m_debug >= DebugLevel::High) {
std::cout << "Updated hessian." << std::endl;
std::cout << "C" << std::endl << C << std::endl;
std::cout << "B" << std::endl << B << std::endl;
std::cout << "D" << std::endl << D << std::endl;
}
}
Super::m_current.condition = D.diagonal().maxCoeff() / D.diagonal().minCoeff();
Super::m_current.xDelta = (xmean - x0).norm();
x0 = xmean;
Super::m_current.fDelta = fabs(costs[indices[0]] - prevCost);
prevCost = costs[indices[0]];
if (Super::m_debug >= DebugLevel::Low) {
std::cout << "Iteration: " << this->m_current.iterations << " best cost " << costs[indices[0]] << " sigma " << sigma
<< " cond " << this->m_current.condition << " xmean " << xmean.transpose() << std::endl;
}
if (fabs(costs[indices[0]] - costs[indices[mu-1]]) < 1e-6) {
sigma = sigma * exp(0.2+cs/ds);
if (Super::m_debug >= DebugLevel::Low) {
std::cout << "Flat fitness " << costs[indices[0]] << " " << costs[indices[mu-1]] << std::endl;
}
}
Super::m_status = checkConvergence(this->m_stop, this->m_current);
} while (objFunc.callback(this->m_current, x0) && (this->m_status == Status::Continue));
// Return the best evaluated solution
x0 = xmean;
m_stepSize = sigma;
if (Super::m_debug >= DebugLevel::Low) {
std::cout << "Stop" << std::endl;
this->m_stop.print(std::cout);
std::cout << "Current" << std::endl;
this->m_current.print(std::cout);
std::cout << "Reason: " << Super::m_status << std::endl;
}
}
};
} /* namespace cppoptlib */
#endif /* CMAES_H_ */
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