Approximation schemes for r-weighted Minimization Knapsack problems

Khaled Elbassioni, Areg Karapetyan, Trung Thanh Nguyen

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageBritish English
Pages (from-to)367-386
Number of pages20
JournalAnnals of Operations Research
Issue number1-2
StatePublished - 15 Aug 2019


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


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