Category: Multiobjective Optimization
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A Tree-Free Path to Efficiently Compute the Hypervolume Indicator in Three Dimensions
In many algorithmic settings, the use of balanced trees, heaps, or other dynamic data structures is the standard way to achieve good asymptotic complexity. However, these structures can introduce memory fragmentation, unpredictable allocation patterns, garbage collection overhead, and branch-heavy execution — all undesirable in systems where performance must be deterministic and low-level behavior is important.…
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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…
