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Convergence

Method
FrontContainer
Convergence Indicators
double gd(const front &reference) const
double igd(const front &reference) const
double igd_plus(const front &reference) const
double hausdorff(const front &reference) const
Standard deviation of Convergence Indicators
double std_gd(const front &reference) const
double std_igd(const front &reference) const
double std_igd_plus(const front &reference) const

Parameters

  • reference - Target front. An estimate of the best front possible for the problem.

Return value

  • How far the current front is from the reference front

Complexity

O(mnlog⁡n)

Notes

Convergence indicators measure the distance from a front approximation to the exact Pareto front, or at least a better approximation of the exact front.

Example

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front<double, 3, unsigned> pf_star({min, max, min});
for (const auto &[p,v] : pf) {
    pf_star(p[0] - 1.0, p[1] + 1.0, p[2] - 1.0) = v;
}
std::cout << "GD: " << pf.gd(pf_star) << std::endl;
std::cout << "STDGD: " << pf.std_gd(pf_star) << std::endl;
std::cout << "IGD: " << pf.igd(pf_star) << std::endl;
std::cout << "STDGD: " << pf.std_igd(pf_star) << std::endl;
std::cout << "Hausdorff: " << pf.hausdorff(pf_star) << std::endl;
std::cout << "IGD+: " << pf.igd_plus(pf_star) << std::endl;
std::cout << "STDIGD+: " << pf.std_igd_plus(pf_star) << std::endl;

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pf_star = pareto.front(['min', 'max', 'min'])
for [p, v] in pf:
    pf_star[p[0] - 1.0, p[1] + 1.0, p[2] - 1.0] = v

print('GD:', pf.gd(pf_star))
print('STDGD:', pf.std_gd(pf_star))
print('IGD:', pf.igd(pf_star))
print('STDGD:', pf.std_igd(pf_star))
print('Hausdorff:', pf.hausdorff(pf_star))
print('IGD+:', pf.igd_plus(pf_star))
print('STDIGD+:', pf.std_igd_plus(pf_star))

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GD: 1.54786
STDGD: 0.0465649
IGD: 1.52137
STDGD: 0.0472864
Hausdorff: 1.54786
IGD+: 1.48592
STDIGD+: 0.0522492