Approximation schemes for r-weighted Minimization Knapsack problems

Khaled Elbassioni (), Areg Karapetyan () and Trung Thanh Nguyen ()
Additional contact information
Khaled Elbassioni: Masdar Institute, Khalifa University of Science and Technology
Areg Karapetyan: Masdar Institute, Khalifa University of Science and Technology
Trung Thanh Nguyen: Hai Phong University

Annals of Operations Research, 2019, vol. 279, issue 1, No 14, 367-386

Abstract: 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 (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10479-018-3111-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:annopr:v:279:y:2019:i:1:d:10.1007_s10479-018-3111-9

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-018-3111-9

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().