An Algebra of Pareto Points
Multi-criteria optimisation problems occur naturally in many engineering practices. Pareto analysis has proven to be a powerful tool to characterise potentially interesting realisations of a particular engineering problem. It is therefore used frequently for design-space exploration problems. Depending on the optimisation goals, one of the Pareto-optimal alternatives will be the optimal realisation. It often happens 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. These aspects are not supported by current analysis methods. This paper introduces a novel, algebraic approach to Pareto analysis. The approach is particularly designed to allow 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 algebra is illustrated with a case-study based on transmitting an MPEG-4 video stream from a server to a hand-held device.
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