Alternating control tree search for knapsack/covering problems
Abstract The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating C...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Hvattum, Lars Magnus [verfasserIn] |
|---|
| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2008 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC 2008 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of heuristics - Springer US, 1995, 16(2008), 3 vom: 26. Nov., Seite 239-258 |
|---|---|
| Übergeordnetes Werk: |
volume:16 ; year:2008 ; number:3 ; day:26 ; month:11 ; pages:239-258 |
| Links: |
|---|
| DOI / URN: |
10.1007/s10732-008-9100-4 |
|---|
| Katalog-ID: |
OLC2039387226 |
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| 520 | |a Abstract The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the following three components: (1) ACT-1, a process that solves an LP relaxation of the current form of the KCP. (2) ACT-2, a method that partitions the variables according to 0, 1, and fractional values to create sub-problems that can be solved with relatively high efficiency. (3) ACT-3, an updating procedure that adjoins inequalities to produce successively more constrained versions of KCP, and in conjunction with the solution processes of ACT-1 and ACT-2, ensures finite convergence to optimality. The ACT method can also be used as a heuristic approach using early termination rules. Computational results show that the ACT-framework successfully enhances the performance of three widely different heuristics for the KCP. Our ACT-method involving scatter search performs better than any other known method on a large set of KCP-instances from the literature. The ACT-based methods are also found to be highly effective on the MKP. | ||
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10.1007/s10732-008-9100-4 doi (DE-627)OLC2039387226 (DE-He213)s10732-008-9100-4-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 24 ssgn Hvattum, Lars Magnus verfasserin aut Alternating control tree search for knapsack/covering problems 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2008 Abstract The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the following three components: (1) ACT-1, a process that solves an LP relaxation of the current form of the KCP. (2) ACT-2, a method that partitions the variables according to 0, 1, and fractional values to create sub-problems that can be solved with relatively high efficiency. (3) ACT-3, an updating procedure that adjoins inequalities to produce successively more constrained versions of KCP, and in conjunction with the solution processes of ACT-1 and ACT-2, ensures finite convergence to optimality. The ACT method can also be used as a heuristic approach using early termination rules. Computational results show that the ACT-framework successfully enhances the performance of three widely different heuristics for the KCP. Our ACT-method involving scatter search performs better than any other known method on a large set of KCP-instances from the literature. The ACT-based methods are also found to be highly effective on the MKP. Knapsack Covering Tree search Heuristic Arntzen, Halvard aut Løkketangen, Arne aut Glover, Fred aut Enthalten in Journal of heuristics Springer US, 1995 16(2008), 3 vom: 26. Nov., Seite 239-258 (DE-627)215140281 (DE-600)1333974-6 (DE-576)063244721 1381-1231 nnns volume:16 year:2008 number:3 day:26 month:11 pages:239-258 https://doi.org/10.1007/s10732-008-9100-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 GBV_ILN_4012 GBV_ILN_4029 AR 16 2008 3 26 11 239-258 |
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10.1007/s10732-008-9100-4 doi (DE-627)OLC2039387226 (DE-He213)s10732-008-9100-4-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 24 ssgn Hvattum, Lars Magnus verfasserin aut Alternating control tree search for knapsack/covering problems 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2008 Abstract The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the following three components: (1) ACT-1, a process that solves an LP relaxation of the current form of the KCP. (2) ACT-2, a method that partitions the variables according to 0, 1, and fractional values to create sub-problems that can be solved with relatively high efficiency. (3) ACT-3, an updating procedure that adjoins inequalities to produce successively more constrained versions of KCP, and in conjunction with the solution processes of ACT-1 and ACT-2, ensures finite convergence to optimality. The ACT method can also be used as a heuristic approach using early termination rules. Computational results show that the ACT-framework successfully enhances the performance of three widely different heuristics for the KCP. Our ACT-method involving scatter search performs better than any other known method on a large set of KCP-instances from the literature. The ACT-based methods are also found to be highly effective on the MKP. Knapsack Covering Tree search Heuristic Arntzen, Halvard aut Løkketangen, Arne aut Glover, Fred aut Enthalten in Journal of heuristics Springer US, 1995 16(2008), 3 vom: 26. Nov., Seite 239-258 (DE-627)215140281 (DE-600)1333974-6 (DE-576)063244721 1381-1231 nnns volume:16 year:2008 number:3 day:26 month:11 pages:239-258 https://doi.org/10.1007/s10732-008-9100-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 GBV_ILN_4012 GBV_ILN_4029 AR 16 2008 3 26 11 239-258 |
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10.1007/s10732-008-9100-4 doi (DE-627)OLC2039387226 (DE-He213)s10732-008-9100-4-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 24 ssgn Hvattum, Lars Magnus verfasserin aut Alternating control tree search for knapsack/covering problems 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2008 Abstract The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the following three components: (1) ACT-1, a process that solves an LP relaxation of the current form of the KCP. (2) ACT-2, a method that partitions the variables according to 0, 1, and fractional values to create sub-problems that can be solved with relatively high efficiency. (3) ACT-3, an updating procedure that adjoins inequalities to produce successively more constrained versions of KCP, and in conjunction with the solution processes of ACT-1 and ACT-2, ensures finite convergence to optimality. The ACT method can also be used as a heuristic approach using early termination rules. Computational results show that the ACT-framework successfully enhances the performance of three widely different heuristics for the KCP. Our ACT-method involving scatter search performs better than any other known method on a large set of KCP-instances from the literature. The ACT-based methods are also found to be highly effective on the MKP. Knapsack Covering Tree search Heuristic Arntzen, Halvard aut Løkketangen, Arne aut Glover, Fred aut Enthalten in Journal of heuristics Springer US, 1995 16(2008), 3 vom: 26. Nov., Seite 239-258 (DE-627)215140281 (DE-600)1333974-6 (DE-576)063244721 1381-1231 nnns volume:16 year:2008 number:3 day:26 month:11 pages:239-258 https://doi.org/10.1007/s10732-008-9100-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 GBV_ILN_4012 GBV_ILN_4029 AR 16 2008 3 26 11 239-258 |
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10.1007/s10732-008-9100-4 doi (DE-627)OLC2039387226 (DE-He213)s10732-008-9100-4-p DE-627 ger DE-627 rakwb eng 510 VZ 3,2 24 ssgn Hvattum, Lars Magnus verfasserin aut Alternating control tree search for knapsack/covering problems 2008 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC 2008 Abstract The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the following three components: (1) ACT-1, a process that solves an LP relaxation of the current form of the KCP. (2) ACT-2, a method that partitions the variables according to 0, 1, and fractional values to create sub-problems that can be solved with relatively high efficiency. (3) ACT-3, an updating procedure that adjoins inequalities to produce successively more constrained versions of KCP, and in conjunction with the solution processes of ACT-1 and ACT-2, ensures finite convergence to optimality. The ACT method can also be used as a heuristic approach using early termination rules. Computational results show that the ACT-framework successfully enhances the performance of three widely different heuristics for the KCP. Our ACT-method involving scatter search performs better than any other known method on a large set of KCP-instances from the literature. The ACT-based methods are also found to be highly effective on the MKP. Knapsack Covering Tree search Heuristic Arntzen, Halvard aut Løkketangen, Arne aut Glover, Fred aut Enthalten in Journal of heuristics Springer US, 1995 16(2008), 3 vom: 26. Nov., Seite 239-258 (DE-627)215140281 (DE-600)1333974-6 (DE-576)063244721 1381-1231 nnns volume:16 year:2008 number:3 day:26 month:11 pages:239-258 https://doi.org/10.1007/s10732-008-9100-4 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-WIW SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_26 GBV_ILN_70 GBV_ILN_2108 GBV_ILN_4012 GBV_ILN_4029 AR 16 2008 3 26 11 239-258 |
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Hvattum, Lars Magnus Arntzen, Halvard Løkketangen, Arne Glover, Fred |
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alternating control tree search for knapsack/covering problems |
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Alternating control tree search for knapsack/covering problems |
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Abstract The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the following three components: (1) ACT-1, a process that solves an LP relaxation of the current form of the KCP. (2) ACT-2, a method that partitions the variables according to 0, 1, and fractional values to create sub-problems that can be solved with relatively high efficiency. (3) ACT-3, an updating procedure that adjoins inequalities to produce successively more constrained versions of KCP, and in conjunction with the solution processes of ACT-1 and ACT-2, ensures finite convergence to optimality. The ACT method can also be used as a heuristic approach using early termination rules. Computational results show that the ACT-framework successfully enhances the performance of three widely different heuristics for the KCP. Our ACT-method involving scatter search performs better than any other known method on a large set of KCP-instances from the literature. The ACT-based methods are also found to be highly effective on the MKP. © Springer Science+Business Media, LLC 2008 |
| abstractGer |
Abstract The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the following three components: (1) ACT-1, a process that solves an LP relaxation of the current form of the KCP. (2) ACT-2, a method that partitions the variables according to 0, 1, and fractional values to create sub-problems that can be solved with relatively high efficiency. (3) ACT-3, an updating procedure that adjoins inequalities to produce successively more constrained versions of KCP, and in conjunction with the solution processes of ACT-1 and ACT-2, ensures finite convergence to optimality. The ACT method can also be used as a heuristic approach using early termination rules. Computational results show that the ACT-framework successfully enhances the performance of three widely different heuristics for the KCP. Our ACT-method involving scatter search performs better than any other known method on a large set of KCP-instances from the literature. The ACT-based methods are also found to be highly effective on the MKP. © Springer Science+Business Media, LLC 2008 |
| abstract_unstemmed |
Abstract The Multidimensional Knapsack/Covering Problem (KCP) is a 0–1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the following three components: (1) ACT-1, a process that solves an LP relaxation of the current form of the KCP. (2) ACT-2, a method that partitions the variables according to 0, 1, and fractional values to create sub-problems that can be solved with relatively high efficiency. (3) ACT-3, an updating procedure that adjoins inequalities to produce successively more constrained versions of KCP, and in conjunction with the solution processes of ACT-1 and ACT-2, ensures finite convergence to optimality. The ACT method can also be used as a heuristic approach using early termination rules. Computational results show that the ACT-framework successfully enhances the performance of three widely different heuristics for the KCP. Our ACT-method involving scatter search performs better than any other known method on a large set of KCP-instances from the literature. The ACT-based methods are also found to be highly effective on the MKP. © Springer Science+Business Media, LLC 2008 |
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Alternating control tree search for knapsack/covering problems |
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