bool multiset_test()
{
#if ( ! (__GNUC__==4 && __GNUC_MINOR__==6) )
data_buffer buffer;
buffer.buffer().open("./test2_.bin");
buffer.buffer().reserve(TEST_COUNT*sizeof(data)+TEST_COUNT);
buffer.buffer().clear();
index123_type index123( (cmp123(buffer)) );
index123.clear();
return
init(buffer, index123)
&& check(buffer, index123)
&& stress(buffer, index123, 10000)
&& check(buffer, index123)
&& clear(buffer, index123)
&& init(buffer, index123)
&& erase_begin(buffer, index123)
&& check(buffer, index123);
#else
return true;
#endif
}
/**
* 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;
}
