15 papers
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 ErdÅs'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…