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Correlation

Method
FrontContainer
Conflict / Harmony
dimension_type direct_conflict(const size_t a, const size_t b) const
[[nodiscard]] double maxmin_conflict(const size_t a, const size_t b) const
[[nodiscard]] double conflict(const size_t a, const size_t b) const
Normalized Conflict / Harmony
[[nodiscard]] double normalized_direct_conflict(const size_t a, const size_t b) const
[[nodiscard]] double normalized_maxmin_conflict(const size_t a, const size_t b) const
[[nodiscard]] double normalized_conflict(const size_t a, const size_t b) const

Parameters

  • a, b - dimension indices

Return value

  • The direct, max-min, or non-parametric conflict between two objectives.
  • The normalized indicators divide the results by the maximum value possible for that correlation indicator.

Complexity

  • Direct: \(O(n)\)
  • Max-min: \(O(n)\)
  • Non-parametric: \(O(n \log n)\)

Notes

Correlation indicators can measure the relationship between objectives in a front. The more conflict between a pair of objectives, the more important it is to focus on these objectives. Objectives with little conflict are good candidates to be latter aggregated into a simpler objective function.

Example

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std::cout << "Direct conflict(0,1): " << pf.direct_conflict(0,1) << std::endl;
std::cout << "Normalized direct conflict(0,1): " << pf.normalized_direct_conflict(0,1) << std::endl;
std::cout << "Maxmin conflict(0,1): " << pf.maxmin_conflict(0,1) << std::endl;
std::cout << "Normalized maxmin conflict(0,1): " << pf.normalized_maxmin_conflict(0,1) << std::endl;
std::cout << "Non-parametric conflict(0,1): " << pf.conflict(0,1) << std::endl;
std::cout << "Normalized conflict(0,1): " << pf.normalized_conflict(0,1) << std::endl;

std::cout << "Direct conflict(1,2): " << pf.direct_conflict(1,2) << std::endl;
std::cout << "Normalized direct conflict(1,2): " << pf.normalized_direct_conflict(1,2) << std::endl;
std::cout << "Maxmin conflict(1,2): " << pf.maxmin_conflict(1,2) << std::endl;
std::cout << "Normalized maxmin conflict(1,2): " << pf.normalized_maxmin_conflict(1,2) << std::endl;
std::cout << "Non-parametric conflict(1,2): " << pf.conflict(1,2) << std::endl;
std::cout << "Normalized conflict(1,2): " << pf.normalized_conflict(1,2) << std::endl;

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print('Direct conflict(0,1):', pf.direct_conflict(0, 1))
print('Normalized direct conflict(0,1):', pf.normalized_direct_conflict(0, 1))
print('Maxmin conflict(0,1):', pf.maxmin_conflict(0, 1))
print('Normalized maxmin conflict(0,1):', pf.normalized_maxmin_conflict(0, 1))
print('Non-parametric conflict(0,1):', pf.conflict(0, 1))
print('Normalized conflict(0,1):', pf.normalized_conflict(0, 1))

print('Direct conflict(1,2):', pf.direct_conflict(1, 2))
print('Normalized direct conflict(1,2):', pf.normalized_direct_conflict(1, 2))
print('Maxmin conflict(1,2):', pf.maxmin_conflict(1, 2))
print('Normalized maxmin conflict(1,2):', pf.normalized_maxmin_conflict(1, 2))
print('Non-parametric conflict(1,2):', pf.conflict(1, 2))
print('Normalized conflict(1,2):', pf.normalized_conflict(1, 2))

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Direct conflict(0,1): 34.3539
Normalized direct conflict(0,1): 0.360795
Maxmin conflict(0,1): 7.77615
Normalized maxmin conflict(0,1): 0.388808
Non-parametric conflict(0,1): 184
Normalized conflict(0,1): 0.92
Direct conflict(1,2): 32.0107
Normalized direct conflict(1,2): 0.280515
Maxmin conflict(1,2): 5.85805
Normalized maxmin conflict(1,2): 0.292903
Non-parametric conflict(1,2): 146
Normalized conflict(1,2): 0.73