Multi-Objective Optimization Algorithm Classification by Composing Black Box with Pareto-Reflecting Functions

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 invarianceproperties. This theoretical base, in turn, allows to derive a rigid set of construction rules. The related methodology bears two major advantages: It allows to classify and tailor MOO algorithms according to desired Pareto-front search attributes and, secondly, enables to significantly expand an MOO algorithm’s applicability area. Together with the mathematical framework we provide a git repository for the newly proposed methodology containing source code plus a variety of MOO operations and algorithms that cover a broad range of examples.

(Preprint)