Approximation schemes for r-weighted Minimization Knapsack problems

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 probl...

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Bibliographic Details
Published in:Annals of operations research Vol. 279; no. 1-2; pp. 367 - 386
Main Authors: Elbassioni, Khaled, Karapetyan, Areg, Nguyen, Trung Thanh
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2019
Springer
Springer Nature B.V
Subjects:
Approximation
Approximation theory
Boolean algebra
Business and Management
Combinatorics
Computer simulation
Greedy algorithms
Knapsack problem
Linear programming
Mathematical research
Nonlinear theories
Operations research
Operations Research/Decision Theory
Optimization
Original Research
Polynomials
Smart grid
Theory of Computation
United Arab Emirates
Power generation planning
Economic dispatch control
Quasi polynomial-time approximation scheme
Weighted Minimization Knapsack
Polynomial-time approximation scheme
Smart grid
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary: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.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-018-3111-9