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Fast approximate bi-objective Pareto sets with quality bounds

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Abstract

We present and empirically characterize a general, parallel, heuristic algorithm for computing small \(\epsilon \)-Pareto sets. A primary feature of the algorithm is that it maintains and improves an upper bound on the \(\epsilon \) value throughout the algorithm. The algorithm can be used as part of a decision support tool for settings in which computing points in objective space is computationally expensive. We use the bi-objective TSP and graph clearing problems as benchmark examples. We characterize the performance of the algorithm through \(\epsilon \)-Pareto set size, upper bound on \(\epsilon \) value provided, true \(\epsilon \) value provided, and parallel speedup achieved. Our results show that the algorithm’s combination of small \(\epsilon \)-Pareto sets and parallel speedup is sufficient to be appealing in settings requiring manual review (i.e., those that have a human in the loop) or real-time solutions.

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Notes

  1. This work extends a short paper which appeared in the Proceedings of The 6th International Conference on Algorithmic Decision Theory [7].

  2. Recall that \([k]=\{1, 2, 3,\ldots ,k\}\).

  3. See, for instance, [27] in the multi-objective combinatorial optimization setting.

  4. We say discovered, because we assume that the set of feasible solutions is not available to us. In fact, computing one point in the set may require us to solve computationally complex problems, like NP-hard ILPs for the TSP or graph clearing problems.

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Acknowledgements

We thank the anonymous reviewers for their helpful input, and pointers to additional literature, including the work of Aneja and Nair [27].

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  1. Department of Computer Science, University of Kentucky, 329 Rose Street, Lexington, KY, 40508, USA

    William Bailey, Judy Goldsmith, Brent Harrison & Siyao Xu

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  1. William Bailey
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Bailey, W., Goldsmith, J., Harrison, B. et al. Fast approximate bi-objective Pareto sets with quality bounds. Auton Agent Multi-Agent Syst 37, 5 (2023). https://doi.org/10.1007/s10458-022-09588-0

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