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Boosting Efficiency for Computing the Pareto Frontier on Tree Structured Networks

  • Jonathan M. Gomes-Selman
  • Qinru Shi
  • Yexiang Xue
  • Roosevelt García-Villacorta
  • Alexander S. Flecker
  • Carla P. Gomes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10848)

Abstract

Multi-objective optimization plays a key role in the study of real-world problems, as they often involve multiple criteria. In multi-objective optimization it is important to identify the so-called Pareto frontier, which characterizes the trade-offs between the objectives of different solutions. We show how a divide-and-conquer approach, combined with batched processing and pruning, significantly boosts the performance of an exact and approximation dynamic programming (DP) algorithm for computing the Pareto frontier on tree-structured networks, proposed in [18]. We also show how exploiting restarts and a new instance selection strategy boosts the performance and accuracy of a mixed integer programming (MIP) approach for approximating the Pareto frontier. We provide empirical results demonstrating that our DP and MIP approaches have complementary strengths and outperform previous algorithms in efficiency and accuracy. Our work is motivated by a problem in computational sustainability concerning the evaluation of trade-offs in ecosystem services due to the proliferation of hydropower dams throughout the Amazon basin. Our approaches are general and can be applied to computing the Pareto frontier of a variety of multi-objective problems on tree-structured networks.

Keywords

Multi-objective optimization Pareto frontier Approximation algorithms Dynamic programming Mixed-integer programming 

Notes

Acknowledgments

This work was supported by NSF Expedition awards for Computational Sustainability (CCF-1522054 and CNS-0832782), NSF CRI (CNS-1059284) and Cornell University’s Atkinson Center for a Sustainable Future.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Jonathan M. Gomes-Selman
    • 1
  • Qinru Shi
    • 2
  • Yexiang Xue
    • 3
  • Roosevelt García-Villacorta
    • 4
  • Alexander S. Flecker
    • 4
  • Carla P. Gomes
    • 3
  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA
  2. 2.Center for Applied MathematicsCornell UniversityIthacaUSA
  3. 3.Department of Computer ScienceCornell UniversityIthacaUSA
  4. 4.Department of Ecology and Evolutionary BiologyCornell UniversityIthacaUSA

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