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An approach to generate comprehensive piecewise linear interpolation of pareto outcomes to aid decision making

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Abstract

Multiple criteria decision making is a well established field encompassing aspects of search for solutions and selection of solutions in presence of more than one conflicting objectives. In this paper, we discuss an approach aimed towards the latter. The decision maker is presented with a limited number of Pareto optimal outcomes and is required to identify regions of interest for further investigation. The inherent sparsity of the given Pareto optimal outcomes in high dimensional space makes it an arduous task for the decision maker. To address this problem, an existing line of thought in literature is to generate a set of approximated Pareto optimal outcomes using piecewise linear interpolation. We present an approach within this paradigm, but one that delivers a comprehensive linearly interpolated set as opposed to its subset delivered by existing methods. We illustrate the advantage in doing so in comparison to stricter non-dominance conditions imposed in existing PAreto INTerpolation method. The interpolated set of outcomes delivered by the proposed approach are non-dominated with respect to the given Pareto optimal outcomes, and additionally the interpolated outcomes along uniformly distributed reference directions are presented to the decision maker. The errors in the given interpolations are also estimated in order to further aid decision making by establishing confidence in achieving true Pareto outcomes in their vicinity. The proposed approach for interpolation is computationally less demanding (for higher number of objectives) and also further amenable to parallelization. We illustrate the performance of the approach using six well established tri-objective test problems and two real-life examples. The problems span different types of fronts, such as convex, concave, mixed, degenerate, highlighting the wide applicability of the approach.

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Notes

  1. In [11], the first two rules are covered as a single rule R1, but we differentiate them as R1.1 and R1.2.

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Acknowledgments

The third author would like to acknowledge the support from Australian Research Council (ARC) Future Fellowship. Thanks also to Markus Hartikainen for discussions regarding PAINT.

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  1. School of Engineering and Information Technology, The University of New South Wales, Canberra, ACT 2600, Australia

    Kalyan Shankar Bhattacharjee, Hemant Kumar Singh & Tapabrata Ray

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  1. Kalyan Shankar Bhattacharjee
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  2. Hemant Kumar Singh
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  3. Tapabrata Ray
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Correspondence to Hemant Kumar Singh.

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Bhattacharjee, K.S., Singh, H.K. & Ray, T. An approach to generate comprehensive piecewise linear interpolation of pareto outcomes to aid decision making. J Glob Optim 68, 71–93 (2017). https://doi.org/10.1007/s10898-016-0454-0

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