An Algebra of Pareto Points

Multi-criteria 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.

(The pdf version of the complete paper. ES Report ESR-2005-02 provides an extended version including all proofs. The most recent and most complete treatment of the material, including proofs, can be found in the Fundamenta Informaticae journal version.)

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