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PROBLEM-TAILORED MULTI-OBJECTIVE OPTIMIZATION ALGORITHM CONSTRUCTION by PARETO REFLECTIONS

MCML Authors

Abstract

Multi-criteria decision-making requires knowledge about trade-offs between conflicting targets. Multi-objective optimization (MOO) strives to provide this information in terms of the set of Pareto optimal solutions. From an application point of view, a taxonomic scheme for selecting or constructing appropriate MOO algorithms under the constraint of individually selectable solution attributes for a given black box problem is of outstanding benefit. In this context, we introduce a mathematical framework to construct MOO algorithms tailored to individual needs. The approach is based on the composition of black-box functions with tailor-made support functions. The composition must exhibit a basic property, which we call Pareto reflective, to preserve Pareto points when support functions are concatenated with a black-box function. Mathematically, we prove some of the support functions’ fundamental structures and, thereby, class inducing invariance properties. This theoretical base, in turn, allows to derive a rigid set of construction rules such as edge point identification or equidistant grid scanning of the Pareto front. The related methodology bears two major advantages: it allows to classify and tailor MOO algorithms according to desired Pareto front search attributes, and secondly, it enables to significantly expand a MOO algorithm’s applicability area.

article

Journal of Mathematical Sciences

Jul. 2025.

Authors

N. Palm • H. Palm

Links

DOI

Research Area

 A1 | Statistical Foundations & Explainability

BibTeXKey: PP25

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