What is Hypervolume multi-objective optimization?
The hypervolume indicator was first proposed as a method for assessing multiobjective op- timization algorithms [85]. It evaluates the optimizer outcome by simultaneously taking into account the proximity of the points to the Pareto front, diversity, and spread.
What is Hypervolume optimization?
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.
What is multi-objective optimization method?
Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective …
What is multi-objective evolutionary optimization?
A multiobjective optimization problem involves several conflicting objectives and has a set of Pareto optimal solutions. By evolving a population of solutions, multiobjective evolutionary algorithms (MOEAs) are able to approximate the Pareto optimal set in a single run.
What is the Hypervolume?
A hypervolume function can be defined as a function h(x) mapping from an n-dimensional Euclidean space to a 1-dimensional Euclidean space, as . The domain of this function may be restricted to a finite region , and corresponds to the possible values of axis combinations.
What is Hypervolume niche?
The “hypervolume” defines the multi-dimensional space of resources (e.g., light, nutrients, structure, etc.) available to (and specifically used by) organisms, and “all species other than those under consideration are regarded as part of the coordinate system.” The niche concept was popularized by the zoologist G.
What is many objective optimization?
Multi-objective optimization refers to the simultaneous optimization of multiple conflicting objectives. It gives rise to a set of optimal solutions (known as the Pareto-optimal solutions), instead of a single optimal solution [1].
What is single objective and multi-objective optimization?
In single objective optimisation problems, the Pareto optimal solution is unique as the focus is on the decision variable space. The multi-objective optimisation process extends the optimisation theory by allowing single objectives to be optimised simultaneously.
What is the difference between single-objective and multi-objective optimization?
In the single-objective optimization, the superiority of a solution over other solutions was easily determined by comparing their objective function values. However, in the multi-objective optimization problem, the goodness of a solution was determined by the dominance.
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 Pareto compliance?
Pareto compliance is a critical property of quality indicators (QIs) focused on measuring convergence to the Pareto front. This property allows a QI not to contradict the order imposed by the Pareto dominance relation.