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Cardinality

Method
FrontContainer
double coverage(const front &rhs) const
double coverage_ratio(const front &rhs) const

Parameters

  • rhs - front being compared

Return value

  • C-metric indicator

Complexity

\[ O(m n \log n) \]

Notes

Cardinality indicators compare two fronts and indicate how many points in one front are non-dominated by points in the other front. The coverage ratio compares which front dominates more points in the other with lhs.coverage(rhs) / rhs.coverage(lhs).

Example

Continuing from the previous example:

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std::cout << "C-metric: " << pf.coverage(pf2) << std::endl;
std::cout << "Coverage ratio: " << pf.coverage_ratio(pf2) << std::endl;
std::cout << "C-metric: " << pf2.coverage(pf) << std::endl;
std::cout << "Coverage ratio: " << pf2.coverage_ratio(pf) << std::endl;

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print('C-metric:', pf.coverage(pf2))
print('Coverage ratio:', pf.coverage_ratio(pf2))
print('C-metric:', pf2.coverage(pf))
print('Coverage ratio:', pf2.coverage_ratio(pf))

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C-metric: 0
Coverage ratio: 0
C-metric: 1
Coverage ratio: inf