Module indicators 

Performance indicators for multi-objective optimization

Provides metrics to evaluate the quality of Pareto fronts:

• Hypervolume (exact 2D sweep, Monte Carlo for higher dimensions)
• Inverted Generational Distance (IGD)
• Generational Distance (GD)
• Additive epsilon indicator
• Spread / diversity indicator
• Domination utilities and non-dominated sorting

References

• Zitzler, Thiele (1998). Multiobjective Optimization Using Evolutionary Algorithms — A Comparative Case Study.
• Deb et al. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II.
• Van Veldhuizen & Lamont (1998). Evolutionary Computation and Convergence to a Pareto Front.

Enums

R2Utility

Scalarizing utility function type for the R2 indicator.

Functions

additive_epsilon_indicator

Additive epsilon indicator (I_ε+).

delta_metric

Delta metric (Δ) — Deb’s modified spread measure.

dominates

Returns true if vector a Pareto-dominates vector b.

generational_distance

Generational Distance (GD).

hypervolume_2d

Exact 2-D hypervolume indicator.

hypervolume_contribution

Hypervolume contribution of each point in a Pareto front.

hypervolume_mc

Monte-Carlo hypervolume approximation for arbitrary number of objectives.

igd

Inverted Generational Distance (IGD).

igd_plus

Inverted Generational Distance Plus (IGD+).

non_dominated_sort

Fast non-dominated sorting.

r2_indicator

R2 quality indicator.

spacing_metric

Spacing metric (SP).

spread

Spread / diversity indicator (Δ, Delta).