Approximating single- and multi-objective nonlinear sum and product knapsack problems

We present a fully polynomial-time approximation scheme (FPTAS) for a very general version of the well-known knapsack problem. This generalization covers, with few exceptions, all versions of knapsack problems that have been studied in the literature so far and allows for an objective function consi...
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Autor*in:	Boeckmann, Jan [verfasserIn] Thielen, Clemens [verfasserIn] Pferschy, Ulrich [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Nonlinear knapsack problem Approximation scheme Product knapsack problem Multi-objective knapsack problem

Übergeordnetes Werk:	Enthalten in: Discrete optimization - New York, NY [u.a.] : Elsevier, 2004, 48
Übergeordnetes Werk:	volume:48

DOI / URN:	10.1016/j.disopt.2023.100771

Katalog-ID:	ELV010037411

Internformat


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024	7		\|a 10.1016/j.disopt.2023.100771 \|2 doi
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084			\|a 31.80 \|2 bkl
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100	1		\|a Boeckmann, Jan \|e verfasserin \|0 (orcid)0000-0001-5909-8354 \|4 aut
245	1	0	\|a Approximating single- and multi-objective nonlinear sum and product knapsack problems
264		1	\|c 2023
336			\|a nicht spezifiziert \|b zzz \|2 rdacontent
337			\|a Computermedien \|b c \|2 rdamedia
338			\|a Online-Ressource \|b cr \|2 rdacarrier
520			\|a We present a fully polynomial-time approximation scheme (FPTAS) for a very general version of the well-known knapsack problem. This generalization covers, with few exceptions, all versions of knapsack problems that have been studied in the literature so far and allows for an objective function consisting of sums or products of possibly nonlinear, separable item profits, while the knapsack constraint states an upper bound on the sum of possibly nonlinear, separable item weights. Moreover, we extend our FPTAS to a multi-objective fully polynomial-time approximation scheme (MFPTAS) for the multi-objective version of the problem.
650		4	\|a Nonlinear knapsack problem
650		4	\|a Approximation scheme
650		4	\|a Product knapsack problem
650		4	\|a Multi-objective knapsack problem
700	1		\|a Thielen, Clemens \|e verfasserin \|4 aut
700	1		\|a Pferschy, Ulrich \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Discrete optimization \|d New York, NY [u.a.] : Elsevier, 2004 \|g 48 \|h Online-Ressource \|w (DE-627)389458953 \|w (DE-600)2148551-3 \|w (DE-576)267762356 \|7 nnns
773	1	8	\|g volume:48
912			\|a GBV_USEFLAG_U
912			\|a SYSFLAG_U
912			\|a GBV_ELV
912			\|a SSG-OPC-MAT
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
936	b	k	\|a 31.80 \|j Angewandte Mathematik \|q VZ
936	b	k	\|a 31.12 \|j Kombinatorik \|j Graphentheorie \|q VZ
951			\|a AR
952			\|d 48

Indexfelder

author_variant	j b jb c t ct u p up
matchkey_str	boeckmannjanthielenclemenspferschyulrich:2023----:prxmtnsnladutojcieolnasmnpo
hierarchy_sort_str	2023
bklnumber	31.80 31.12
publishDate	2023
allfields	10.1016/j.disopt.2023.100771 doi (DE-627)ELV010037411 (ELSEVIER)S1572-5286(23)00013-0 DE-627 ger DE-627 rda eng 510 330 VZ 31.80 bkl 31.12 bkl Boeckmann, Jan verfasserin (orcid)0000-0001-5909-8354 aut Approximating single- and multi-objective nonlinear sum and product knapsack problems 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We present a fully polynomial-time approximation scheme (FPTAS) for a very general version of the well-known knapsack problem. This generalization covers, with few exceptions, all versions of knapsack problems that have been studied in the literature so far and allows for an objective function consisting of sums or products of possibly nonlinear, separable item profits, while the knapsack constraint states an upper bound on the sum of possibly nonlinear, separable item weights. Moreover, we extend our FPTAS to a multi-objective fully polynomial-time approximation scheme (MFPTAS) for the multi-objective version of the problem. Nonlinear knapsack problem Approximation scheme Product knapsack problem Multi-objective knapsack problem Thielen, Clemens verfasserin aut Pferschy, Ulrich verfasserin aut Enthalten in Discrete optimization New York, NY [u.a.] : Elsevier, 2004 48 Online-Ressource (DE-627)389458953 (DE-600)2148551-3 (DE-576)267762356 nnns volume:48 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik VZ 31.12 Kombinatorik Graphentheorie VZ AR 48
spelling	10.1016/j.disopt.2023.100771 doi (DE-627)ELV010037411 (ELSEVIER)S1572-5286(23)00013-0 DE-627 ger DE-627 rda eng 510 330 VZ 31.80 bkl 31.12 bkl Boeckmann, Jan verfasserin (orcid)0000-0001-5909-8354 aut Approximating single- and multi-objective nonlinear sum and product knapsack problems 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We present a fully polynomial-time approximation scheme (FPTAS) for a very general version of the well-known knapsack problem. This generalization covers, with few exceptions, all versions of knapsack problems that have been studied in the literature so far and allows for an objective function consisting of sums or products of possibly nonlinear, separable item profits, while the knapsack constraint states an upper bound on the sum of possibly nonlinear, separable item weights. Moreover, we extend our FPTAS to a multi-objective fully polynomial-time approximation scheme (MFPTAS) for the multi-objective version of the problem. Nonlinear knapsack problem Approximation scheme Product knapsack problem Multi-objective knapsack problem Thielen, Clemens verfasserin aut Pferschy, Ulrich verfasserin aut Enthalten in Discrete optimization New York, NY [u.a.] : Elsevier, 2004 48 Online-Ressource (DE-627)389458953 (DE-600)2148551-3 (DE-576)267762356 nnns volume:48 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik VZ 31.12 Kombinatorik Graphentheorie VZ AR 48
allfields_unstemmed	10.1016/j.disopt.2023.100771 doi (DE-627)ELV010037411 (ELSEVIER)S1572-5286(23)00013-0 DE-627 ger DE-627 rda eng 510 330 VZ 31.80 bkl 31.12 bkl Boeckmann, Jan verfasserin (orcid)0000-0001-5909-8354 aut Approximating single- and multi-objective nonlinear sum and product knapsack problems 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We present a fully polynomial-time approximation scheme (FPTAS) for a very general version of the well-known knapsack problem. This generalization covers, with few exceptions, all versions of knapsack problems that have been studied in the literature so far and allows for an objective function consisting of sums or products of possibly nonlinear, separable item profits, while the knapsack constraint states an upper bound on the sum of possibly nonlinear, separable item weights. Moreover, we extend our FPTAS to a multi-objective fully polynomial-time approximation scheme (MFPTAS) for the multi-objective version of the problem. Nonlinear knapsack problem Approximation scheme Product knapsack problem Multi-objective knapsack problem Thielen, Clemens verfasserin aut Pferschy, Ulrich verfasserin aut Enthalten in Discrete optimization New York, NY [u.a.] : Elsevier, 2004 48 Online-Ressource (DE-627)389458953 (DE-600)2148551-3 (DE-576)267762356 nnns volume:48 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik VZ 31.12 Kombinatorik Graphentheorie VZ AR 48
allfieldsGer	10.1016/j.disopt.2023.100771 doi (DE-627)ELV010037411 (ELSEVIER)S1572-5286(23)00013-0 DE-627 ger DE-627 rda eng 510 330 VZ 31.80 bkl 31.12 bkl Boeckmann, Jan verfasserin (orcid)0000-0001-5909-8354 aut Approximating single- and multi-objective nonlinear sum and product knapsack problems 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We present a fully polynomial-time approximation scheme (FPTAS) for a very general version of the well-known knapsack problem. This generalization covers, with few exceptions, all versions of knapsack problems that have been studied in the literature so far and allows for an objective function consisting of sums or products of possibly nonlinear, separable item profits, while the knapsack constraint states an upper bound on the sum of possibly nonlinear, separable item weights. Moreover, we extend our FPTAS to a multi-objective fully polynomial-time approximation scheme (MFPTAS) for the multi-objective version of the problem. Nonlinear knapsack problem Approximation scheme Product knapsack problem Multi-objective knapsack problem Thielen, Clemens verfasserin aut Pferschy, Ulrich verfasserin aut Enthalten in Discrete optimization New York, NY [u.a.] : Elsevier, 2004 48 Online-Ressource (DE-627)389458953 (DE-600)2148551-3 (DE-576)267762356 nnns volume:48 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik VZ 31.12 Kombinatorik Graphentheorie VZ AR 48
allfieldsSound	10.1016/j.disopt.2023.100771 doi (DE-627)ELV010037411 (ELSEVIER)S1572-5286(23)00013-0 DE-627 ger DE-627 rda eng 510 330 VZ 31.80 bkl 31.12 bkl Boeckmann, Jan verfasserin (orcid)0000-0001-5909-8354 aut Approximating single- and multi-objective nonlinear sum and product knapsack problems 2023 nicht spezifiziert zzz rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier We present a fully polynomial-time approximation scheme (FPTAS) for a very general version of the well-known knapsack problem. This generalization covers, with few exceptions, all versions of knapsack problems that have been studied in the literature so far and allows for an objective function consisting of sums or products of possibly nonlinear, separable item profits, while the knapsack constraint states an upper bound on the sum of possibly nonlinear, separable item weights. Moreover, we extend our FPTAS to a multi-objective fully polynomial-time approximation scheme (MFPTAS) for the multi-objective version of the problem. Nonlinear knapsack problem Approximation scheme Product knapsack problem Multi-objective knapsack problem Thielen, Clemens verfasserin aut Pferschy, Ulrich verfasserin aut Enthalten in Discrete optimization New York, NY [u.a.] : Elsevier, 2004 48 Online-Ressource (DE-627)389458953 (DE-600)2148551-3 (DE-576)267762356 nnns volume:48 GBV_USEFLAG_U SYSFLAG_U GBV_ELV SSG-OPC-MAT GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_151 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2106 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 31.80 Angewandte Mathematik VZ 31.12 Kombinatorik Graphentheorie VZ AR 48
language	English
source	Enthalten in Discrete optimization 48 volume:48
sourceStr	Enthalten in Discrete optimization 48 volume:48
format_phy_str_mv	Article
bklname	Angewandte Mathematik Kombinatorik Graphentheorie
institution	findex.gbv.de
topic_facet	Nonlinear knapsack problem Approximation scheme Product knapsack problem Multi-objective knapsack problem
dewey-raw	510
isfreeaccess_bool	false
container_title	Discrete optimization
authorswithroles_txt_mv	Boeckmann, Jan @@aut@@ Thielen, Clemens @@aut@@ Pferschy, Ulrich @@aut@@
publishDateDaySort_date	2023-01-01T00:00:00Z
hierarchy_top_id	389458953
dewey-sort	3510
id	ELV010037411
language_de	englisch
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author	Boeckmann, Jan
spellingShingle	Boeckmann, Jan ddc 510 bkl 31.80 bkl 31.12 misc Nonlinear knapsack problem misc Approximation scheme misc Product knapsack problem misc Multi-objective knapsack problem Approximating single- and multi-objective nonlinear sum and product knapsack problems
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topic_title	510 330 VZ 31.80 bkl 31.12 bkl Approximating single- and multi-objective nonlinear sum and product knapsack problems Nonlinear knapsack problem Approximation scheme Product knapsack problem Multi-objective knapsack problem
topic	ddc 510 bkl 31.80 bkl 31.12 misc Nonlinear knapsack problem misc Approximation scheme misc Product knapsack problem misc Multi-objective knapsack problem
topic_unstemmed	ddc 510 bkl 31.80 bkl 31.12 misc Nonlinear knapsack problem misc Approximation scheme misc Product knapsack problem misc Multi-objective knapsack problem
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title	Approximating single- and multi-objective nonlinear sum and product knapsack problems
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title_full	Approximating single- and multi-objective nonlinear sum and product knapsack problems
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author_browse	Boeckmann, Jan Thielen, Clemens Pferschy, Ulrich
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title_sort	approximating single- and multi-objective nonlinear sum and product knapsack problems
title_auth	Approximating single- and multi-objective nonlinear sum and product knapsack problems
abstract	We present a fully polynomial-time approximation scheme (FPTAS) for a very general version of the well-known knapsack problem. This generalization covers, with few exceptions, all versions of knapsack problems that have been studied in the literature so far and allows for an objective function consisting of sums or products of possibly nonlinear, separable item profits, while the knapsack constraint states an upper bound on the sum of possibly nonlinear, separable item weights. Moreover, we extend our FPTAS to a multi-objective fully polynomial-time approximation scheme (MFPTAS) for the multi-objective version of the problem.
abstractGer	We present a fully polynomial-time approximation scheme (FPTAS) for a very general version of the well-known knapsack problem. This generalization covers, with few exceptions, all versions of knapsack problems that have been studied in the literature so far and allows for an objective function consisting of sums or products of possibly nonlinear, separable item profits, while the knapsack constraint states an upper bound on the sum of possibly nonlinear, separable item weights. Moreover, we extend our FPTAS to a multi-objective fully polynomial-time approximation scheme (MFPTAS) for the multi-objective version of the problem.
abstract_unstemmed	We present a fully polynomial-time approximation scheme (FPTAS) for a very general version of the well-known knapsack problem. This generalization covers, with few exceptions, all versions of knapsack problems that have been studied in the literature so far and allows for an objective function consisting of sums or products of possibly nonlinear, separable item profits, while the knapsack constraint states an upper bound on the sum of possibly nonlinear, separable item weights. Moreover, we extend our FPTAS to a multi-objective fully polynomial-time approximation scheme (MFPTAS) for the multi-objective version of the problem.
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title_short	Approximating single- and multi-objective nonlinear sum and product knapsack problems
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doi_str	10.1016/j.disopt.2023.100771
up_date	2024-07-06T16:36:16.546Z
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Approximating single- and multi-objective nonlinear sum and product knapsack problems

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