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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Vydáno v:Annals of operations research Ročník 279; číslo 1-2; s. 367 - 386
Hlavní autoři: Elbassioni, Khaled, Karapetyan, Areg, Nguyen, Trung Thanh
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.08.2019
Springer
Springer Nature B.V
Témata:
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
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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.
AbstractList 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.
Audience Academic
Author Karapetyan, Areg
Elbassioni, Khaled
Nguyen, Trung Thanh
Author_xml – sequence: 1
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  surname: Elbassioni
  fullname: Elbassioni, Khaled
  organization: Masdar Institute, Khalifa University of Science and Technology
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  givenname: Areg
  surname: Karapetyan
  fullname: Karapetyan, Areg
  organization: Masdar Institute, Khalifa University of Science and Technology
– sequence: 3
  givenname: Trung Thanh
  surname: Nguyen
  fullname: Nguyen, Trung Thanh
  email: ttnguyen.cs@gmail.com
  organization: Hai Phong University
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crossref_primary_10_1007_s10479_022_05054_y
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Cites_doi 10.1145/2955089
10.1016/j.dam.2017.06.020
10.1109/TSG.2016.2616945
10.1145/320211.320240
10.1007/s10288-011-0180-x
10.1016/S0167-6377(02)00122-0
10.1287/ijoc.12.1.57.11901
10.1016/0304-3975(76)90048-7
10.1007/978-3-540-24777-7
10.1137/0221060
10.1016/S0377-2217(01)00179-5
10.1007/s00453-008-9248-1
ContentType Journal Article
Copyright Springer Science+Business Media, LLC, part of Springer Nature 2018
COPYRIGHT 2019 Springer
Annals of Operations Research is a copyright of Springer, (2018). All Rights Reserved.
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Issue 1-2
Keywords Power generation planning
Economic dispatch control
Quasi polynomial-time approximation scheme
Weighted Minimization Knapsack
Polynomial-time approximation scheme
Smart grid
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Snippet Stimulated by salient applications arising from power systems, this paper studies a class of non-linear Knapsack problems with non-separable quadratic...
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SubjectTerms 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
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Title Approximation schemes for r-weighted Minimization Knapsack problems
URI https://link.springer.com/article/10.1007/s10479-018-3111-9
https://www.proquest.com/docview/2150941517
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