bool is_eq(const fitness_vector & f1, const fitness_vector & f2, double eps){
if(f1.size() != f2.size()) return false;
for(unsigned int i = 0; i < f1.size(); i++){
if(fabs(f1[i]-f2[i])>eps) return false;
}
return true;
}
/**
* This method should be used both as a solution to 3D cases, and as a general termination method for algorithms that reduce D-dimensional problem to 3-dimensional one.
*
* This is the implementation of the algorithm for computing hypervolume as it was presented by Nicola Beume et al.
* The implementation uses std::multiset (which is based on red-black tree data structure) as a container for the sweeping front.
* Original implementation by Beume et. al uses AVL-tree.
* The difference is insiginificant as the important characteristics (maintaining order when traversing, self-balancing) of both structures and the asymptotic times (O(log n) updates) are guaranteed.
* Computational complexity: O(n*log(n))
*
* @param[in] points vector of points containing the 3-dimensional points for which we compute the hypervolume
* @param[in] r_point reference point for the points
*
* @return hypervolume.
*/
double hv3d::compute(std::vector<fitness_vector> &points, const fitness_vector &r_point) const
{
if (m_initial_sorting) {
sort(points.begin(), points.end(), fitness_vector_cmp(2,'<'));
}
double V = 0.0; // hypervolume
double A = 0.0; // area of the sweeping plane
std::multiset<fitness_vector, fitness_vector_cmp> T(fitness_vector_cmp(0, '>'));
// sentinel points (r_point[0], -INF, r_point[2]) and (-INF, r_point[1], r_point[2])
const double INF = std::numeric_limits<double>::max();
fitness_vector sA(r_point.begin(), r_point.end()); sA[1] = -INF;
fitness_vector sB(r_point.begin(), r_point.end()); sB[0] = -INF;
T.insert(sA);
T.insert(sB);
double z3 = points[0][2];
T.insert(points[0]);
A = fabs((points[0][0] - r_point[0]) * (points[0][1] - r_point[1]));
std::multiset<fitness_vector>::iterator p;
std::multiset<fitness_vector>::iterator q;
for(std::vector<fitness_vector>::size_type idx = 1 ; idx < points.size() ; ++idx) {
p = T.insert(points[idx]);
q = (p);
++q; //setup q to be a successor of p
if ( (*q)[1] <= (*p)[1] ) { // current point is dominated
T.erase(p); // disregard the point from further calculation
} else {
V += A * fabs(z3 - (*p)[2]);
z3 = (*p)[2];
std::multiset<fitness_vector>::reverse_iterator rev_it(q);
++rev_it;
std::multiset<fitness_vector>::reverse_iterator erase_begin (rev_it);
std::multiset<fitness_vector>::reverse_iterator rev_it_pred;
while((*rev_it)[1] >= (*p)[1] ) {
rev_it_pred = rev_it;
++rev_it_pred;
A -= fabs(((*rev_it)[0] - (*rev_it_pred)[0])*((*rev_it)[1] - (*q)[1]));
++rev_it;
}
A += fabs(((*p)[0] - (*(rev_it))[0])*((*p)[1] - (*q)[1]));
T.erase(rev_it.base(),erase_begin.base());
}
}
V += A * fabs(z3 - r_point[2]);
return V;
}
/**
* Verifies whether reference point and the hypervolume method meet certain criteria.
*
* @param[in] r_point fitness vector describing the reference point
*
* @throws value_error if reference point's and point set dimension do not agree
*/
void hypervolume::verify_before_compute(const fitness_vector &r_point, hv_algorithm::base_ptr hv_algorithm) const
{
if ( m_points[0].size() != r_point.size() ) {
pagmo_throw(value_error, "Point set dimensions and reference point dimension must be equal.");
}
hv_algorithm->verify_before_compute(m_points, r_point);
}
/**
* Verifies whether given algorithm suits the requested data.
*
* @param[in] points vector of points containing the d dimensional points for which we compute the hypervolume
* @param[in] r_point reference point for the vector of points
*
* @throws value_error when trying to compute the hypervolume for the dimension other than 3 or non-maximal reference point
*/
void hv3d::verify_before_compute(const std::vector<fitness_vector> &points, const fitness_vector &r_point) const
{
if (r_point.size() != 3) {
pagmo_throw(value_error, "Algorithm hv3d works only for 3-dimensional cases");
}
base::assert_minimisation(points, r_point);
}
/**
* Computes the original fitness of the multi-objective problem. It also updates the ideal point in case
* m_adapt_ideal is true
*
* @param[out] f non-decomposed fitness vector
* @param[in] x chromosome
*/
void decompose::compute_original_fitness(fitness_vector &f, const decision_vector &x) const {
m_original_problem->objfun(f,x);
if (m_adapt_ideal) {
for (fitness_vector::size_type i=0; i<f.size(); ++i) {
if (f[i] < m_z[i]) m_z[i] = f[i];
}
}
}
/// Implementation of the objective function.
/// Add noises to the computed fitness vector.
void noisy::objfun_impl(fitness_vector &f, const decision_vector &x) const
{
//1 - Initialize a temporary fitness vector storing one trial result
//and we use it also to init the return value
fitness_vector tmp(f.size(),0.0);
f=tmp;
//2 - We set the seed
m_drng.seed(m_seed+m_decision_vector_hash(x));
//3 - We average upon multiple runs
for (unsigned int j=0; j< m_trials; ++j) {
m_original_problem->objfun(tmp, x);
inject_noise_f(tmp);
for (fitness_vector::size_type i=0; i<f.size();++i) {
f[i] = f[i] + tmp[i] / (double)m_trials;
}
}
}
/// Implementation of the objective function.
/// Add noises to the decision vector before calling the actual objective function.
void robust::objfun_impl(fitness_vector &f, const decision_vector &x) const
{
// Temporary storage used for averaging
fitness_vector tmp(f.size(),0.0);
f = tmp;
// Set the seed
m_drng.seed(m_seed);
// Perturb decision vector and evaluate
decision_vector x_perturbed(x);
for(unsigned int i = 0; i < m_trials; ++i){
inject_noise_x(x_perturbed);
m_original_problem->objfun(tmp, x_perturbed);
for(fitness_vector::size_type j = 0; j < f.size(); ++j){
f[j] += tmp[j] / (double)m_trials;
}
}
}
/// Apply noise on a fitness vector
void noisy::inject_noise_f(fitness_vector& f) const
{
for(f_size_type i = 0; i < f.size(); i++){
if(m_noise_type == NORMAL){
f[i] += m_normal_dist(m_drng)*m_param_second+m_param_first;
}
else if(m_noise_type == UNIFORM){
f[i] += m_uniform_dist(m_drng)*(m_param_second-m_param_first)+m_param_first;
}
}
}
/// Implementation of the objective function.
void dejong::objfun_impl(fitness_vector &f, const decision_vector &x) const
{
pagmo_assert(f.size() == 1);
decision_vector::size_type n = x.size();
double retval = 0.0;
for (decision_vector::size_type i=0; i<n; i++){
retval += x[i]*x[i];
}
f[0] = retval;
}
/// Implementation of the objective function.
void schwefel::objfun_impl(fitness_vector &f, const decision_vector &x) const
{
pagmo_assert(f.size() == 1);
std::vector<double>::size_type n = x.size();
double value=0;
for (std::vector<double>::size_type i=0; i<n; i++){
value += x[i] * sin(sqrt(fabs(x[i])));
}
f[0] = 418.9828872724338 * n - value;
}
/// Implementation of the objective function.
void rastrigin::objfun_impl(fitness_vector &f, const decision_vector &x) const
{
pagmo_assert(f.size() == 1);
const double omega = 2.0 * boost::math::constants::pi<double>();
f[0] = 0;
const decision_vector::size_type n = x.size();
for (decision_vector::size_type i = 0; i < n; ++i) {
f[0] += x[i] * x[i] - 10.0 * std::cos(omega * x[i]);
}
f[0] += 10.0 * n;
}
/// Implementation of the objective function.
void michalewicz::objfun_impl(fitness_vector &f, const decision_vector &x) const
{
pagmo_assert(f.size() == 1);
decision_vector::size_type n = x.size();
double retval = 0.0;
for (decision_vector::size_type i=0; i<n; i++){
retval -= sin(x[i]) * pow(sin((i+1)*x[i]*x[i]/boost::math::constants::pi<double>()) , 2*m_m);
}
f[0] = retval;
}
/**
* Computes the decomposed fitness from the original multi-objective one and a weight vector
*
* @param[out] f decomposed fitness vector
* @param[in] original_fit original multi-objective fitness vector
* @param[in] weights weights vector
*/
void decompose::compute_decomposed_fitness(fitness_vector &f, const fitness_vector &original_fit, const fitness_vector &weights) const
{
if ( (m_weights.size() != weights.size()) || (original_fit.size() != m_weights.size()) ) {
pagmo_throw(value_error,"Check the sizes of input weights and fitness vector");
}
if(m_method == WEIGHTED) {
f[0] = 0.0;
for(base::f_size_type i = 0; i < m_original_problem->get_f_dimension(); ++i) {
f[0]+= weights[i]*original_fit[i];
}
} else if (m_method == TCHEBYCHEFF) {
f[0] = 0.0;
double tmp,weight;
for(base::f_size_type i = 0; i < m_original_problem->get_f_dimension(); ++i) {
(weights[i]==0) ? (weight = 1e-4) : (weight = weights[i]); //fixes the numerical problem of 0 weights
tmp = weight * fabs(original_fit[i] - m_z[i]);
if(tmp > f[0]) {
f[0] = tmp;
}
}
} else { //BI method
const double THETA = 5.0;
double d1 = 0.0;
double weight_norm = 0.0;
for(base::f_size_type i = 0; i < m_original_problem->get_f_dimension(); ++i) {
d1 += (original_fit[i] - m_z[i]) * weights[i];
weight_norm += pow(weights[i],2);
}
weight_norm = sqrt(weight_norm);
d1 = fabs(d1)/weight_norm;
double d2 = 0.0;
for(base::f_size_type i = 0; i < m_original_problem->get_f_dimension(); ++i) {
d2 += pow(original_fit[i] - (m_z[i] + d1*weights[i]/weight_norm), 2);
}
d2 = sqrt(d2);
f[0] = d1 + THETA * d2;
}
}
hv_algorithm::base_ptr hypervolume::get_best_contributions(const fitness_vector &r_point) const
{
switch(r_point.size()) {
case 2:
return hv_algorithm::base_ptr(new hv_algorithm::hv2d());
break;
case 3:
return hv_algorithm::base_ptr(new hv_algorithm::hv3d());
break;
default:
return hv_algorithm::base_ptr(new hv_algorithm::wfg());
}
}
/// Implementation of the objective function.
void zdt2::objfun_impl(fitness_vector &f, const decision_vector &x) const
{
pagmo_assert(f.size() == 2);
pagmo_assert(x.size() == 30);
double g = 0;
f[0] = x[0];
for(problem::base::size_type i = 2; i < 30; ++i) {
g += x[i];
}
g = 1 + (9 * g) / 29;
f[1] = g * ( 1 - (x[0]/g)*(x[0]/g));
}
/// Implementation of the objective function.
void zdt6::objfun_impl(fitness_vector &f, const decision_vector &x) const
{
pagmo_assert(f.size() == 2);
pagmo_assert(x.size() == 10);
double g = 0;
f[0] = 1 - exp(-4*x[0])*pow(sin(6*m_pi*x[0]),6);
for(problem::base::size_type i = 2; i < 10; ++i) {
g += x[i];
}
g = 1 + (9 * g) / 9;
f[1] = g * ( 1 - (f[0]/g)*(f[0]/g));
}
//Generate a random weights vector whose sum of all elements is equal to 1
void generate_weights(fitness_vector & weights)
{
rng_double drng = rng_generator::get<rng_double>();
//generate n random numbers between 0 and 1 and store in weights where n = weights.size()
std::generate(weights.begin(), weights.end(), std::bind(fRand, drng));
//caculate the sum of all elements of weights vector
double sum = std::accumulate(weights.begin(), weights.end(), 0.0);
//divide each element of weights vector by the calculated sum to make the sum of all elements equal to 1
std::transform(weights.begin(), weights.end(), weights.begin(),
std::bind1st(std::multiplies<double>(),1/sum));
}
/// Implementation of the objective function.
void levy5::objfun_impl(fitness_vector &f, const decision_vector &x) const
{
pagmo_assert(f.size() == 1);
decision_vector::size_type n = x.size();
double isum = 0.0;
double jsum = 0.0;
f[0] = 0;
for ( decision_vector::size_type j=0; j<n; j+=2 ) {
for ( int i=1; i<=5; i++ ) {
isum += (double)(i) * cos((double)(i-1)*x[j] + (double)(i));
jsum += (double)(i) * cos((double)(i+1)*x[j+1] + (double)(i));
}
}
f[0] = isum*jsum;
for ( decision_vector::size_type j=0; j<n; j+=2 )
f[0] += pow(x[j] + 1.42513,2) + pow(x[j+1] + 0.80032,2);
}
/// Implementation of the objective function.
void sch::objfun_impl(fitness_vector &f, const decision_vector &x) const
{
pagmo_assert(f.size() == 2 && x.size() == 1);
f[0] = x[0]*x[0];
f[1] = (x[0]-2) * (x[0]-2);
}
/// Implementation of the objective functions.
/// (Wraps over the original implementation)
void con2mo::objfun_impl(fitness_vector &f, const decision_vector &x) const
{
constraint_vector c(m_original_problem->get_c_dimension(),0.);
m_original_problem->compute_constraints(c,x);
decision_vector original_f(m_original_problem->get_f_dimension(),0.);
m_original_problem->objfun(original_f,x);
f_size_type original_nbr_obj = original_f.size();
c_size_type number_of_constraints = c.size();
c_size_type number_of_eq_constraints = number_of_constraints - m_original_problem->get_ic_dimension();
c_size_type number_of_violated_constraints = 0;
// computes the number of satisfied constraints
if(m_method==OBJ_CSTRS){
for(c_size_type i=0; i<number_of_constraints; i++){
if(!m_original_problem->test_constraint(c,i))
number_of_violated_constraints += 1;
}
}
// modify equality constraints to behave as inequality constraints:
const std::vector<double> &c_tol = m_original_problem->get_c_tol();
for(c_size_type i=0; i<number_of_constraints; i++) {
if(i<number_of_eq_constraints){
c[i] = std::abs(c[i]) - c_tol.at(i);
}
else{
c[i] = c[i] - c_tol.at(i);
}
}
// clean the fitness vector
for(f_size_type i=0; i<f.size(); i++) {
f[i] = 0.;
}
// in all cases, the first objectives holds the initial objectives
for(f_size_type i=0; i<original_nbr_obj; i++) {
f[i] = original_f.at(i);
}
switch(m_method)
{
case OBJ_CSTRS:
{
for(c_size_type i=0; i<number_of_constraints; i++) {
if(c.at(i) > 0.) {
f[original_nbr_obj+i] = c.at(i);
} else if(number_of_violated_constraints != 0) {
f[original_nbr_obj+i] = number_of_violated_constraints;
} else {
f[original_nbr_obj+i] = 0.;
for(f_size_type j=0; j<original_nbr_obj; j++) {
f[original_nbr_obj+i] += original_f.at(j);
}
}
}
break;
}
case OBJ_CSTRSVIO:
{
for(c_size_type i=0; i<number_of_constraints; i++) {
if(c.at(i) > 0.) {
f[original_nbr_obj] += c.at(i);
}
}
break;
}
case OBJ_EQVIO_INEQVIO:
{
// treating equality constraints
for(c_size_type i=0; i<number_of_eq_constraints; i++) {
if(c.at(i) > 0.) {
f[original_nbr_obj] += c.at(i);
}
}
for(c_size_type i=number_of_eq_constraints; i<number_of_constraints; i++) {
if(c.at(i) > 0.) {
f[original_nbr_obj+1] += c.at(i);
}
}
break;
}
default:
pagmo_throw(value_error, "Error: There are only 3 methods for the constrained to multi-objective!");
break;
}
}