9 citations · 9 across the 17 of their papers we have counts for
7 papers · 1 filter
Three-Objective Integral R2 Subset Selection: NP-Hardness and Submodular Approximation
Michael T. M. Emmerich
Selecting a fixed number of representative points from a finite Pareto-front approximation is a fundamental post-processing task in multiobjective optimization. This paper studies…
Optimizing Explicit Unit-Distance Lower-Bound Certificates
Michael T. M. Emmerich
The 2026 disproof of Erdős's unit-distance conjecture and Sawin's quantitative refinement show that the maximum number of unit distances among planar points can exceed $…
Preference-Shaped Expected Hypervolume and R2 Improvement: Exact Computation and Monotonicity
Michael T. M. Emmerich
This paper studies preference-shaped expected improvement criteria for Bayesian multiobjective optimization. We consider two indicator families which are often used for similar alg…
Exact Uniform L1 Spacing for Solow-Polasky Diversity on Lines and Ordered Pareto Fronts
Michael T. M. Emmerich, Mahboubeh Nezhadmoghaddam, Jesús Guillermo Falcón Cardona
We study fixed-cardinality maximization of the inverse-matrix Solow--Polasky diversity, equivalently finite metric magnitude for the exponential kernel, on one-dimensional and orde…
Nonsmooth Set-Gradient Ascent to the Pareto Front via Layered Hypervolume and Magnitude Indicators
Michael T. M. Emmerich
A nonsmooth set-gradient ascent method is developed for moving finite approximation sets toward the Pareto front in multiobjective optimization. The method optimizes layered set in…
The Magnitude of Dominated Sets: A Pareto Compliant Indicator Grounded in Metric Geometry
Michael T. M. Emmerich
We investigate \emph{magnitude} as a new unary and strictly Pareto-compliant quality indicator for finite approximation sets to the Pareto front in multiobjective optimization. Mag…