//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));
}
/**
* 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;
}