/*-----------------------------------------------------------*/
void NOMAD::LH_Search::values_for_var_i ( int p ,
const NOMAD::Double & delta ,
const NOMAD::Double & delta_max ,
const NOMAD::bb_input_type & bbit ,
const NOMAD::Double & lb ,
const NOMAD::Double & ub ,
NOMAD::Point & x ) const
{
// categorical variables have already been treated as fixed variables:
if ( bbit == NOMAD::CATEGORICAL )
return;
int i;
NOMAD::Double v;
NOMAD::Random_Pickup rp (p);
bool rounding = ( bbit != NOMAD::CONTINUOUS );
bool lb_def = lb.is_defined();
bool ub_def = ub.is_defined();
double w = ( ( lb_def && ub_def ) ?
ub.value()-lb.value() : 1.0 ) / p;
// main loop:
for ( i = 0 ; i < p ; ++i )
{
// both bounds exist:
if ( lb_def && ub_def )
v = lb + ( i + NOMAD::RNG::rand()/NOMAD::D_INT_MAX ) * w;
// one of the bounds does not exist:
else
{
// lb exists, and ub not: mapping [0;1] --> [lb;+INF[
if ( lb_def )
v = lb + 10 * delta_max * sqrt ( - log ( NOMAD::DEFAULT_EPSILON +
( i + NOMAD::RNG::rand()/NOMAD::D_INT_MAX ) * w ) );
// lb does not exist:
else
{
// ub exists, and lb not: mapping [0;1] --> ]-INF;ub]
if ( ub_def )
v = ub - delta_max * 10 *
sqrt ( -log ( NOMAD::DEFAULT_EPSILON +
( i +NOMAD::RNG::rand()/NOMAD::D_INT_MAX ) * w ) );
// there are no bounds: mapping [0;1] --> ]-INF;+INF[
else
v = (NOMAD::RNG::rand()%2 ? -1.0 : 1.0) * delta_max * 10 *
sqrt ( - log ( NOMAD::DEFAULT_EPSILON +
( i + NOMAD::RNG::rand()/NOMAD::D_INT_MAX ) * w ) );
}
}
// rounding:
if ( rounding )
v = v.round();
// projection to mesh (with ref=0):
v.project_to_mesh ( 0.0 , delta , lb , ub );
// affectation + permutation:
x[rp.pickup()] = v;
}
}
/*---------------------------------------------------------*/
void NOMAD::Directions::compute ( std::list<NOMAD::Direction> & dirs ,
NOMAD::poll_type poll ,
const NOMAD::Point & poll_center ,
int mesh_index ,
int halton_index ,
const NOMAD::Direction & feas_success_dir ,
const NOMAD::Direction & infeas_success_dir )
{
dirs.clear();
// categorical variables: do nothing:
if ( _is_categorical )
return;
// binary variables: we use special directions:
if ( _is_binary )
{
compute_binary_directions ( dirs );
return;
}
NOMAD::Double pow_gps , cst;
const NOMAD::Direction * bl;
NOMAD::Direction * pd;
int i , j , k , hat_i;
std::list<NOMAD::Direction>::const_iterator it2 , end2;
/*-----------------------------------*/
/* loop on the types of directions */
/*-----------------------------------*/
const std::set<NOMAD::direction_type> & dir_types =
(poll == NOMAD::PRIMARY) ? _direction_types : _sec_poll_dir_types;
std::set<NOMAD::direction_type>::const_iterator it , end = dir_types.end() ;
for ( it = dir_types.begin() ; it != end ; ++it )
{
if ( *it == NOMAD::UNDEFINED_DIRECTION ||
*it == NOMAD::NO_DIRECTION ||
*it == NOMAD::MODEL_SEARCH_DIR )
continue;
/*--------------*/
/* Ortho-MADS */
/*--------------*/
if ( NOMAD::dir_is_orthomads (*it) )
{
// Ortho-MADS initializations:
if ( !_primes )
ortho_mads_init ( _halton_seed );
// halton index:
if ( halton_index < 0 )
{
int max_halton_index = NOMAD::Mesh::get_max_halton_index();
// mesh_index+ _halton_seed -> used to make sure that the sequence of strictly increasing mesh_index produces a non biased sequence of halton_index
halton_index = ( mesh_index >= NOMAD::Mesh::get_max_mesh_index() ) ? mesh_index + _halton_seed : max_halton_index + 1;
if ( halton_index > max_halton_index )
NOMAD::Mesh::set_max_halton_index ( halton_index );
}
NOMAD::Direction halton_dir ( _nc , 0.0 , *it );
NOMAD::Double alpha_t_l;
if ( compute_halton_dir ( halton_index ,
mesh_index ,
alpha_t_l ,
halton_dir ) )
{
#ifdef DEBUG
_out << std::endl
<< NOMAD::open_block ( "compute Ortho-MADS directions with" )
<< "type = " << *it << std::endl
<< "Halton index (tk) = " << halton_index << std::endl
<< "mesh index (lk) = " << mesh_index << std::endl
<< "alpha (tk,lk) = " << alpha_t_l << std::endl
<< "Halton direction = ( ";
halton_dir.NOMAD::Point::display ( _out , " " , -1 , -1 );
_out << " )" << std::endl << NOMAD::close_block();
#endif
// Ortho-MADS 2n and n+1:
// ----------------------
if ( *it == NOMAD::ORTHO_2N || *it == NOMAD::ORTHO_NP1_QUAD || *it == NOMAD::ORTHO_NP1_NEG )
{
// creation of the 2n directions:
// For ORTHO_NP1 the reduction from 2N to N+1 is done in MADS::POLL
NOMAD::Direction ** H = new NOMAD::Direction * [2*_nc];
// Ordering D_k alternates Hk and -Hk instead of [H_k -H_k]
for ( i = 0 ; i < _nc ; ++i )
{
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , *it ) );
H[i ] = &(*(--dirs.end()));
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , *it ) );
H[i+_nc] = &(*(--dirs.end()));
}
// Householder transformations on the 2n directions:
householder ( halton_dir ,
true , // complete_to_2n = true
H );
delete [] H;
}
// Ortho-MADS 1 or Ortho-MADS 2:
// -----------------------------
else
{
dirs.push_back ( halton_dir );
if ( *it == NOMAD::ORTHO_2 )
dirs.push_back ( -halton_dir );
}
}
}
/*-----------*/
/* LT-MADS */
/*-----------*/
else if ( NOMAD::dir_is_ltmads (*it) ) {
if ( !_lt_initialized)
lt_mads_init();
bl = get_bl ( mesh_index , *it , hat_i );
// LT-MADS 1 or LT-MADS 2: -b(l) and/or b(l):
// ------------------------------------------
if ( *it == NOMAD::LT_1 || *it == NOMAD::LT_2 ) {
dirs.push_back ( - *bl );
if ( *it == NOMAD::LT_2 )
dirs.push_back ( *bl );
}
// LT-MADS 2n or LT-MADS n+1:
// --------------------------
else {
// row permutation vector:
int * row_permutation_vector = new int [_nc];
row_permutation_vector[hat_i] = hat_i;
NOMAD::Random_Pickup rp ( _nc );
for ( i = 0 ; i < _nc ; ++i )
if ( i != hat_i ) {
j = rp.pickup();
if ( j == hat_i )
j = rp.pickup();
row_permutation_vector[i] = j;
}
rp.reset();
for ( j = 0 ; j < _nc ; ++j ) {
i = rp.pickup();
if ( i != hat_i ) {
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , *it ) );
pd = &(*(--dirs.end()));
create_lt_direction ( mesh_index , *it , i , hat_i , pd );
permute_coords ( *pd , row_permutation_vector );
}
else
dirs.push_back ( *bl );
// completion to maximal basis:
if ( *it == NOMAD::LT_2N )
dirs.push_back ( NOMAD::Direction ( - *(--dirs.end()) , NOMAD::LT_2N ) );
}
delete [] row_permutation_vector;
// completion to minimal basis:
if ( *it == NOMAD::LT_NP1 ) {
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::LT_NP1 ) );
pd = &(*(--dirs.end()));
end2 = --dirs.end();
for ( it2 = dirs.begin() ; it2 != end2 ; ++it2 ) {
for ( i = 0 ; i < _nc ; ++i )
(*pd)[i] -= (*it2)[i];
}
}
}
}
/*-------*/
/* GPS */
/*-------*/
else {
// GPS for binary variables: should'nt be here:
if ( *it == NOMAD::GPS_BINARY ) {
#ifdef DEBUG
_out << std::endl << "Warning (" << "Directions.cpp" << ", " << __LINE__
<< "): tried to generate binary directions at the wrong place)"
<< std::endl << std::endl;
#endif
dirs.clear();
return;
}
// this value represents the non-zero values in GPS directions
// (it is tau^{|ell_k|/2}, and it is such that Delta^m_k * pow_gps = Delta^p_k):
if ( !pow_gps.is_defined() )
pow_gps = pow ( NOMAD::Mesh::get_mesh_update_basis() , abs(mesh_index) / 2.0 );
// GPS 2n, static:
// ---------------
if ( *it == NOMAD::GPS_2N_STATIC ) {
for ( i = 0 ; i < _nc ; ++i ) {
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::GPS_2N_STATIC ) );
pd = &(*(--dirs.end()));
(*pd)[i] = pow_gps;
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::GPS_2N_STATIC ) );
pd = &(*(--dirs.end()));
(*pd)[i] = -pow_gps;
}
}
// GPS 2n, random:
// ---------------
else if ( *it == NOMAD::GPS_2N_RAND ) {
int v , cnt;
std::list <int>::const_iterator end3;
std::list <int>::iterator it3;
std::list <int> rem_cols;
std::vector<int> rem_col_by_row ( _nc );
// creation of the 2n directions:
std::vector<NOMAD::Direction *> pdirs ( 2 * _nc );
for ( i = 0 ; i < _nc ; ++i ) {
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::GPS_2N_RAND ) );
pdirs[i] = &(*(--dirs.end()));
(*pdirs[i])[i] = pow_gps;
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::GPS_2N_RAND ) );
pdirs[i+_nc] = &(*(--dirs.end()));
(*pdirs[i+_nc])[i] = -pow_gps;
rem_cols.push_back(i);
rem_col_by_row[i] = i;
}
// random perturbations:
for ( i = 1 ; i < _nc ; ++i ) {
if ( rem_col_by_row[i] > 0 ) {
v = NOMAD::RNG::rand()%3 - 1; // v in { -1 , 0 , 1 }
if ( v ) {
// we decide a (i,j) couple:
k = NOMAD::RNG::rand()%(rem_col_by_row[i]);
cnt = 0;
end3 = rem_cols.end();
it3 = rem_cols.begin();
while ( cnt != k ) {
++it3;
++cnt;
}
j = *it3;
// the perturbation:
(*pdirs[i])[j] = (*pdirs[j+_nc])[i] = -v * pow_gps;
(*pdirs[j])[i] = (*pdirs[i+_nc])[j] = v * pow_gps;
// updates:
rem_cols.erase(it3);
it3 = rem_cols.begin();
while ( *it3 != i )
++it3;
rem_cols.erase(it3);
for ( k = i+1 ; k < _nc ; ++k )
rem_col_by_row[k] -= j<k ? 2 : 1;
}
}
}
}
// GPS n+1, static:
// ----------------
else if ( *it == NOMAD::GPS_NP1_STATIC ) {
// (n+1)^st direction:
dirs.push_back ( NOMAD::Direction ( _nc , -pow_gps , NOMAD::GPS_NP1_STATIC ) );
// first n directions:
for ( i = 0 ; i < _nc ; ++i ) {
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::GPS_NP1_STATIC ) );
pd = &(*(--dirs.end()));
(*pd)[i] = pow_gps;
}
}
// GPS n+1, random:
// ----------------
else if ( *it == NOMAD::GPS_NP1_RAND )
{
// (n+1)^st direction:
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::GPS_NP1_RAND ) );
NOMAD::Direction * pd1 = &(*(--dirs.end()));
NOMAD::Double d;
// first n directions:
for ( i = 0 ; i < _nc ; ++i )
{
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::GPS_NP1_RAND ) );
pd = &(*(--dirs.end()));
d = NOMAD::RNG::rand()%2 ? -pow_gps : pow_gps;
(*pd )[i] = d;
(*pd1)[i] = -d;
}
}
// GPS n+1, static, uniform angles:
// --------------------------------
else if ( *it == NOMAD::GPS_NP1_STATIC_UNIFORM )
{
cst = pow_gps * sqrt(static_cast<double>(_nc)*(_nc+1))/_nc;
// n first directions:
for ( j = _nc-1 ; j >= 0 ; --j )
{
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::GPS_NP1_STATIC_UNIFORM ) );
pd = &(*(--dirs.end()));
k = _nc-j-1;
for ( i = 0 ; i < k ; ++i )
(*pd)[i] = -cst / sqrt(static_cast<double>(_nc-i)*(_nc-i+1));
(*pd)[k] = (cst * (j+1)) / sqrt(static_cast<double>(j+1)*(j+2));
}
// (n+1)^st direction:
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::GPS_NP1_STATIC_UNIFORM ) );
pd = &(*(--dirs.end()));
for ( i = 0 ; i < _nc ; ++i )
(*pd)[i] = -cst / sqrt(static_cast<double>(_nc-i)*(_nc-i+1));
}
// GPS n+1, random, uniform angles:
// --------------------------------
// (we apply the procedure defined in
// "Pattern Search Methods for user-provided points:
// application to molecular geometry problems",
// by Alberto, Nogueira, Rocha and Vicente,
// SIOPT 14-4, 1216-1236, 2004, doi:10.1137/S1052623400377955)
else if ( *it == NOMAD::GPS_NP1_RAND_UNIFORM )
{
cst = pow_gps * sqrt(static_cast<double>(_nc)*(_nc+1))/_nc;
// n first directions:
for ( j = _nc-1 ; j >= 0 ; --j )
{
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::GPS_NP1_STATIC_UNIFORM ) );
pd = &(*(--dirs.end()));
k = _nc-j-1;
for ( i = 0 ; i < k ; ++i )
(*pd)[i] = -cst / sqrt(static_cast<double>(_nc-i)*(_nc-i+1));
(*pd)[k] = (cst * (j+1)) / sqrt(static_cast<double>(j+1)*(j+2));
}
// (n+1)^st direction:
dirs.push_back ( NOMAD::Direction ( _nc , 0.0 , NOMAD::GPS_NP1_STATIC_UNIFORM ) );
pd = &(*(--dirs.end()));
for ( i = 0 ; i < _nc ; ++i )
(*pd)[i] = -cst / sqrt(static_cast<double>(_nc-i)*(_nc-i+1));
// random perturbations:
NOMAD::Random_Pickup rp ( _nc );
std::vector<bool> done ( _nc );
bool chg_sgn;
std::list<NOMAD::Direction>::iterator it;
NOMAD::Double tmp;
end2 = dirs.end();
for ( i = 0 ; i < _nc ; ++i )
done[i] = false;
for ( i = 0 ; i < _nc ; ++i )
{
k = rp.pickup();
if ( i != k && !done[i] )
{
chg_sgn = ( NOMAD::RNG::rand()%2 != 0 );
for ( it = dirs.begin() ; it != end2 ; ++it )
{
tmp = (*it)[i];
(*it)[i] = ( chg_sgn ? -1.0 : 1.0 ) * (*it)[k];
(*it)[k] = tmp;
}
done[i] = done[k] = true;
}
else
if ( NOMAD::RNG::rand()%2 )
for ( it = dirs.begin() ; it != end2 ; ++it )
(*it)[i] = -(*it)[i];
}
}
}
} // end of loop on the types of directions
}