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Approximation schemes for r-weighted Minimization Knapsack problems

  • Khaled Elbassioni
  • Areg Karapetyan
  • Trung Thanh Nguyen
Original Research
  • 11 Downloads

Abstract

Stimulated by salient applications arising from power systems, this paper studies a class of non-linear Knapsack problems with non-separable quadratic constrains, formulated in either binary or integer form. These problems resemble the duals of the corresponding variants of 2-weighted Knapsack problem (a.k.a., complex-demand Knapsack problem) which has been studied in the extant literature under the paradigm of smart grids. Nevertheless, the employed techniques resulting in a polynomial-time approximation scheme (PTAS) for the 2-weighted Knapsack problem are not amenable to its minimization version. We instead propose a greedy geometry-based approach that arrives at a quasi PTAS (QPTAS) for the minimization variant with boolean variables. As for the integer formulation, a linear programming-based method is developed that obtains a PTAS. In view of the curse of dimensionality, fast greedy heuristic algorithms are presented, additionally to QPTAS. Their performance is corroborated extensively by empirical simulations under diverse settings and scenarios.

Keywords

Weighted Minimization Knapsack Quasi polynomial-time approximation scheme Polynomial-time approximation scheme Power generation planning Smart grid Economic dispatch control 

Notes

Acknowledgements

We would like to thank the Editor and anonymous reviewers for their careful reading of our manuscript and their helpful comments that improved the presentation of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Khaled Elbassioni
    • 1
  • Areg Karapetyan
    • 1
  • Trung Thanh Nguyen
    • 2
  1. 1.Masdar Institute, Khalifa University of Science and TechnologyAbu DhabiUAE
  2. 2.Hai Phong UniversityHaiphongVietnam

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