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Dominance Relationships

Method
FrontContainer
Archive-Point Dominance
bool dominates(const key_type &p)
bool strongly_dominates(const key_type &p) const
bool is_partially_dominated_by(const key_type &p) const
bool is_completely_dominated_by(const key_type &p) const
bool non_dominates(const key_type &p) const
Archive-Front Dominance
bool dominates(const front &P) const
bool strongly_dominates(const front &P) const
bool is_partially_dominated_by(const front &P) const
bool is_completely_dominated_by(const front &P) const
bool non_dominates(const front &P) const
Archive-Archive Dominance
bool dominates(const archive &A) const
bool strongly_dominates(const archive &A) const
bool is_partially_dominated_by(const archive &A) const
bool is_completely_dominated_by(const archive &A) const
bool non_dominates(const archive &A) const

Parameters

  • p - point we are checking for dominance
  • P - front we are checking for dominance
  • A - archive we are checking for dominance

Return value

  • bool- true if and only if the point p (or front P, or archive A) is dominated, is strongly dominated, partially dominates, completely dominates, or non-dominantes *this

Complexity

  • is_completely_dominated_by: \(O(1)\) for points and \(O(n)\) for fronts
  • All others: \(O(m \log n)\) for points and \(O(m n \log n)\) for fronts

Notes

The dominance between archives is defined in terms of the first front in the archive.

Note

See the section fronts / dominance relationships for more details

Example

Continuing from the previous example:

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// Point-point dominance
using point_type = archive<double, 3, unsigned>::key_type;
point_type p1({0, 0, 0});
point_type p2({1, 1, 1});
std::vector<bool> is_minimization = {true, false, true};
std::cout << (p1.dominates(p2, is_minimization) ? "p1 dominates p2" : "p1 does not dominate p2") << std::endl;
std::cout << (p1.strongly_dominates(p2, is_minimization) ? "p1 strongly dominates p2" : "p1 does not strongly dominate p2") << std::endl;
std::cout << (p1.non_dominates(p2, is_minimization) ? "p1 non-dominates p2" : "p1 does not non-dominate p2") << std::endl;

// Archive-point dominance
std::cout << (ar.dominates(p2) ? "ar dominates p2" : "ar does not dominate p2") << std::endl;
std::cout << (ar.strongly_dominates(p2) ? "ar strongly dominates p2" : "ar does not strongly dominate p2") << std::endl;
std::cout << (ar.non_dominates(p2) ? "ar non-dominates p2" : "ar does not non-dominate p2") << std::endl;
std::cout << (ar.is_partially_dominated_by(p2) ? "ar is partially dominated by p2" : "ar is not is partially dominated by p2") << std::endl;
std::cout << (ar.is_completely_dominated_by(p2) ? "ar is completely dominated by p2" : "ar is not is completely dominated by p2") << std::endl;

// Archive-archive dominance
archive<double, 3, unsigned> ar2({min, max, min});
for (const auto& [p,v]: ar) {
    ar2[point_type({p[0] - 1, p[1] + 1, p[2] - 1})] = v;
}
std::cout << (ar.dominates(ar2) ? "ar dominates ar2" : "ar does not dominate ar2") << std::endl;
std::cout << (ar.strongly_dominates(ar2) ? "ar strongly dominates ar2" : "ar does not strongly dominate ar2") << std::endl;
std::cout << (ar.non_dominates(ar2) ? "ar non-dominates ar2" : "ar does not non-dominate ar2") << std::endl;
std::cout << (ar.is_partially_dominated_by(ar2) ? "ar is partially dominated by ar2" : "ar is not is partially dominated by ar2") << std::endl;
std::cout << (ar.is_completely_dominated_by(ar2) ? "ar is completely dominated by ar2" : "ar is not is completely dominated by ar2") << std::endl;

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# Point-point dominance
p1 = pareto.point([0, 0, 0])
p2 = pareto.point([1, 1, 1])
is_minimization = [True, False, True]
print('p1 dominates p2' if p1.dominates(p2, is_minimization) else 'p1 does not dominate p2')
print('p1 strongly dominates p2' if p1.strongly_dominates(p2, is_minimization) else 'p1 does not strongly dominate p2')
print('p1 non-dominates p2' if p1.non_dominates(p2, is_minimization) else 'p1 does not non-dominate p2')

# Archive-point dominance
print('ar dominates p2' if ar.dominates(p2) else 'ar does not dominate p2')
print('ar strongly dominates p2' if ar.strongly_dominates(p2) else 'ar does not strongly dominate p2')
print('ar non-dominates p2' if ar.non_dominates(p2) else 'ar does not non-dominate p2')
print('ar is partially dominated by p2' if ar.is_partially_dominated_by(p2) else 'ar is not is partially dominated by p2')
print('ar is completely dominated by p2' if ar.is_completely_dominated_by(p2) else 'ar is not is completely dominated by p2')

# Archive-archive dominance
ar2 = pareto.archive(['min', 'max', 'min'])
for [p, v] in ar:
    ar2[pareto.point([p[0] - 1, p[1] + 1, p[2] - 1])] = v

print('ar dominates ar2' if ar.dominates(ar2) else 'ar does not dominate ar2')
print('ar strongly dominates ar2' if ar.strongly_dominates(ar2) else 'ar does not strongly dominate ar2')
print('ar non-dominates ar2' if ar.non_dominates(ar2) else 'ar does not non-dominate ar2')
print('ar is partially dominated by ar2' if ar.is_partially_dominated_by(ar2) else 'ar is not is partially dominated by ar2')
print('ar is completely dominated by ar2' if ar.is_completely_dominated_by(ar2) else 'ar is not is completely dominated by ar2')

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p1 does not dominate p2
p1 does not strongly dominate p2
p1 non-dominates p2
ar dominates p2
ar strongly dominates p2
ar does not non-dominate p2
ar is not is partially dominated by p2
ar is not is completely dominated by p2
ar does not dominate ar2
ar does not strongly dominate ar2
ar does not non-dominate ar2
ar is partially dominated by ar2
ar is completely dominated by ar2