How is Hypervolume calculated?
How is Hypervolume calculated?
The hypervolume of a set of points is calculated as a sum of exclusive hypervolumes, and each exclusive hypervolume is calculated by limiting the underlying set with the contributing point p, and subtracting the hypervolume of the modified set from the inclusive hypervolume of p.
What does hypervolume measure?
A measure that has been the subject of much recent study in evolutionary multi-objective optimization is the hypervolume indicator. It measures the volume of the dominated portion of the objective space and is of exceptional interest as it possesses the highly desirable feature of strict Pareto compliance.
How to specify a reference point in hypervolume calculation for fair performance comparison?
A general guideline for the reference point specification is to use a slightly worse point than the nadir point so that the reference point is dominated by all Pareto optimal solutions (i.e., so that all Pareto optimal solutions in a solution set have positive hypervolume contributions).
What is emo algorithm?
The hypervolume measure is one of the most frequently applied measures for comparing the results of evolutionary multiobjective optimization algorithms (EMOA). The algorithm computes a well distributed set of solutions with bounded size thereby focussing on interesting regions of the Pareto front(s).
What is Pareto spread?
Spread — The spread is a measure of the movement of the Pareto set. To calculate the spread, the gamultiobj algorithm first evaluates σ, the standard deviation of the crowding distance measure of points that are on the Pareto front with finite distance.
What is N-dimensional Hypervolume?
The Hutchinsonian niche is an “n-dimensional hypervolume”, where the dimensions are environmental conditions and resources, that define the requirements of an individual or a species to practice its way of life, more particularly, for its population to persist.
What is Hypervolume in geometry?
We formally define the hypervolume, z, as a set of points within an n-dimensional real-valued continuous space that encloses a set of m observations, w.
