Category: Multiobjective Optimization
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Multiobjective Heatmaps: Landscape Visualization via ε-Dominance
Michael Emmerich, January 16th, 2025(inspired by a discussion of an application problem with Jonas Schwaab, ETH Zurich) In single-objective optimization, it is easy to visualize a function that depends on only two continuous or integer input variables by means of a heatmap plot, where the lightness indicates the achievement in the objective function, say F(x1,…
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2-D Hypervolume Subset Selection in Python
Hypervolume Subset Selection Problem (HSSP) is a dynamic programming algorithm used to select a subset of points from a non-dominated 2D Pareto front. This subset maximizes the hypervolume (or dominated area in 2-D) covered with respect to a reference point that bounds this area from above to make it finite. Originally proposed by Auger et…
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Uniformly Lighting the Christmas Tree: Riesz s-Energy in Action
Uniformly Lighting the Christmas Trees: Riesz -Energy in Action Michael Emmerich, December 25th, 2024 Did you ever have the problem of how to distribute candles uniformly across your Christmas Tree? Well, here is a solution from the mathematical sciences! Using the concept of Riesz -Energy, we can optimize the placement of stars or candles on…
Michael Emmerich 