Tag: hypervolume-indicator

• Exact Hypervolume Subset Selection in 3-D: Implementing a Galactic Algorithm

  Michael T. M. Emmerich, University of Jyväskylä, Finland, September 2026 In 2017 Karl Bringmann, Sergio Cabello and I showed that selecting the best out of points with respect to the hypervolume indicator is NP-hard already in three dimensions, that it can nevertheless be solved in time , and that it admits an efficient polynomial-time approximation…

  Michael Emmerich

  September 19, 2026

  Multicriteria Decision Analysis, Multiobjective Optimization

  hypervolume-indicator, math, mathematics, Multiobjective Optimization, science

• A Visualizer for 3-D Pareto Fronts Based on Anchored Boxes

  Michael Emmerich

  November 14, 2025

  Computational Science, Multiobjective Optimization, Small Python Math Examples, Uncategorized

  3-D Graphics, analysis, Attainment Surfaces, Computational Geometry, hypervolume-indicator, interactive plots, linear-algebra, math, mathematics, Multiobjective Optimization, Pareto front, plotly, python, Visualization