An algebra of Pareto points

Abstract

Multicriteria optimisation problems occur naturally in engineering practices. Pareto analysis has proven to be a powerful tool to characterise potentially interesting realisations of a particular engineering problem for design-space exploration. Depending on the optimisation goals, one of the Pareto-optimal alternatives is the optimal realisation. It occurs however, that partial design decisions have to be taken, leaving other aspects of the optimisation problem to be decided at a later stage, and that Pareto-optimal configurations have to be composed (dynamically) from Pareto-optimal configurations of components. Both aspects are not supported by current analysis methods. This paper introduces a novel, algebraic approach to Pareto analysis. It allows for describing incremental design decisions and composing sets of Pareto-optimal configurations. The algebra can be used to study the operations on Pareto sets and the efficient computation of Pareto sets and their compositions.