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Efficiently Approximating High-Dimensional Pareto Frontiers for Tree-Structured Networks Using Expansion and Compression

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13884))

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Abstract

Real-world decision-making often involves working with many distinct objectives. However, as we consider a larger number of objectives, performance degrades rapidly and many instances become intractable. Our goal is to approximate higher-dimensional Pareto frontiers within a reasonable amount of time. Our work is motivated by a problem in computational sustainability that evaluates the tradeoffs between various ecological impacts of hydropower dam proliferation in the Amazon river basin. The current state-of-the-art algorithm finds a good approximation of the Pareto frontier within hours for three-objective problems, but a six-objective problem cannot be solved in a reasonable amount of time. To tackle this problem, we developed two different approaches: an expansion method, which assembles Pareto-frontiers optimized with respect to subsets of the original set of criteria, and a compression method, which assembles Pareto-frontiers optimized with respect to compressed criteria, which are a weighted sum of multiple original criteria. Our experimental results show that the aggregation of the different methods can reliably provide good approximations of the true Pareto-frontiers in practice. Source code and data are available at https://github.com/gomes-lab/Dam-Portfolio-Selection-Expansion-and-Compression-CPAIOR.

Y. Bai and Q. Shi—Equal contribution.

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Acknowledgments

We thank the reviewers for all the constructive feedback. This research is supported in part by grants from the National Science Foundation, Air Force Office of Scientific Research, and Cornell Atkinson Center for Sustainability.

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Authors and Affiliations

  1. Department of Computer Science, Cornell University, Ithaca, USA

    Yiwei Bai, Marc Grimson & Carla P. Gomes

  2. Center for Applied Mathematics, Cornell University, Ithaca, USA

    Qinru Shi

  3. Department of Ecology and Evolutionary Biology, Cornell University, Ithaca, USA

    Alexander Flecker

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  1. Yiwei Bai
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  2. Qinru Shi
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  4. Alexander Flecker
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  5. Carla P. Gomes
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Correspondence to Yiwei Bai .

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Editors and Affiliations

  1. Department of Management, University of Toronto Scarborough and Rotman School of Management, University of Toronto, Toronto, ON, Canada

    Andre A. Cire

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Bai, Y., Shi, Q., Grimson, M., Flecker, A., Gomes, C.P. (2023). Efficiently Approximating High-Dimensional Pareto Frontiers for Tree-Structured Networks Using Expansion and Compression. In: Cire, A.A. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2023. Lecture Notes in Computer Science, vol 13884. Springer, Cham. https://doi.org/10.1007/978-3-031-33271-5_1

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  • DOI: https://doi.org/10.1007/978-3-031-33271-5_1

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