9 citations · 9 across the 17 of their papers we have counts for
17 papers
The Prime Clockwork: A Dynamic Representation of Modular and Multiplicative Arithmetic
Michael T. M. Emmerich
The way numbers are represented strongly influences which arithmetic structures are easy to see. The \emph{prime clockwork} is a recursively growing discrete dynamical system: a li…
Riesz Energy Subset Selection in the Euclidean Plane is NP-Hard: A Reduction from the Ising Model on Planar Cubic Graphs
Michael Emmerich
We prove that minimum Riesz -energy subset selection in the Euclidean plane is NP-complete already for the fixed exponent . To our knowledge, this is the first Euclidean ha…
Computing the Integral R2 Indicator by Perspective Mapping and Box Decomposition
Michael T. M. Emmerich
The continuous integral R2 indicator is a Pareto-compliant refinement of the classical finite-weight-vector R2 indicator, used in performance assessment, bounded archiving for a-po…
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…
Exact and Fast Subset Selection Algorithms for the Bi-objective Integral R2 Indicator
Michael T. M. Emmerich
We study fixed-cardinality subset selection for the exact integral bi-objective indicator with a uniform continuum of weighted Tchebycheff scalarizing functions. The indicato…
Polynomial-Time Riesz-Energy Subset Selection for Ordered Point Sets on Lines and -Staircases
Michael T. M. Emmerich
We study efficient algorithms for one-dimensional fixed-cardinality minimum Riesz -energy subset selection on ordered real-line point sets and propose and test a polynomial-time…
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…
On the Complexity of Minimum Riesz s-Energy Subset Selection in Euclidean and Ultrametric Spaces
Michael T. M. Emmerich, Ksenia Pereverdieva, André Deutz
We study the computational complexity of exact cardinality-constrained minimum Riesz -energy subset selection in finite metric spaces: given points, select points of m…
Exact Dynamic Programming for Solow--Polasky Diversity Subset Selection on Lines and Staircases
Michael T. M. Emmerich
This paper studies exact fixed-cardinality Solow--Polasky diversity subset selection on ordered finite point sets, with monotone biobjective Pareto fronts and their higher…
Maximum Solow--Polasky Diversity Subset Selection Is NP-hard Even in the Euclidean Plane
Michael T. M. Emmerich, Ksenia Pereverdieva, André H. Deutz
We prove that, for every fixed , selecting a subset of prescribed cardinality that maximizes the Solow--Polasky diversity indicator is NP-hard for finite point sets in $\mat…
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…
Critical phase transitions in minimum-energy configurations for the exponential kernel family on the unit interval
Michael T. M. Emmerich
We study the optimal placement of ordered points on the unit interval for the bounded pair potential \[ K_q(d)=e^{-d^q}, \qquad q>0. \] The family interpolates between strongly…
Selecting a Maximum Solow-Polasky Diversity Subset in General Metric Spaces Is NP-hard
Michael T. M. Emmerich, Ksenia Pereverdieva, André H. Deutz
The Solow--Polasky diversity indicator (or magnitude) is a classical measure of diversity based on pairwise distances. It has applications in ecology, conservation planning, and, m…
Multicriteria Optimization and Decision Making: Principles, Algorithms and Case Studies
Michael Emmerich, André Deutz
Real-world decision and optimization problems, often involve constraints and conflicting criteria. For example, choosing a travel method must balance speed, cost, environmental foo…