Computational performance of basic state reduction based dynamic programming algorithms for bi-objective 0–1 knapsack problems
This paper studies a group of basic state reduction based dynamic programming (DP) algorithms for the multi-objective 0–1 knapsack problem (MKP), which are related to the backward reduced-state DP space (BRDS) and forward reduced-state DP space (FRDS). The BRDS is widely ignored in the literature be...
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| Published in | Computers & mathematics with applications (1987) Vol. 63; no. 10; pp. 1462 - 1480 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.05.2012
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| Online Access | Get full text |
| ISSN | 0898-1221 1873-7668 |
| DOI | 10.1016/j.camwa.2012.03.057 |
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| Abstract | This paper studies a group of basic state reduction based dynamic programming (DP) algorithms for the multi-objective 0–1 knapsack problem (MKP), which are related to the backward reduced-state DP space (BRDS) and forward reduced-state DP space (FRDS). The BRDS is widely ignored in the literature because it imposes disadvantage for the single objective knapsack problem (KP) in terms of memory requirements. The FRDS based DP algorithm in a general sense is related to state dominance checking, which can be time consuming for the MKP while it can be done efficiently for the KP. Consequently, no algorithm purely based on the FRDS with state dominance checking has ever been developed for the MKP. In this paper, we attempt to get some insights into the state reduction techniques efficient to the MKP. We first propose an FRDS based algorithm with a local state dominance checking for the MKP. Then we evaluate the relative advantage of the BRDS and FRDS based algorithms by analyzing their computational time and memory requirements for the MKP. Finally different combinations of the BRDS and FRDS based algorithms are developed on this basis. Numerical experiments based on the bi-objective KP instances are conducted to compare systematically between these algorithms and the recently developed BRDS based DP algorithm as well as the existing FRDS based DP algorithm without state dominance checking. |
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| AbstractList | This paper studies a group of basic state reduction based dynamic programming (DP) algorithms for the multi-objective 0–1 knapsack problem (MKP), which are related to the backward reduced-state DP space (BRDS) and forward reduced-state DP space (FRDS). The BRDS is widely ignored in the literature because it imposes disadvantage for the single objective knapsack problem (KP) in terms of memory requirements. The FRDS based DP algorithm in a general sense is related to state dominance checking, which can be time consuming for the MKP while it can be done efficiently for the KP. Consequently, no algorithm purely based on the FRDS with state dominance checking has ever been developed for the MKP. In this paper, we attempt to get some insights into the state reduction techniques efficient to the MKP. We first propose an FRDS based algorithm with a local state dominance checking for the MKP. Then we evaluate the relative advantage of the BRDS and FRDS based algorithms by analyzing their computational time and memory requirements for the MKP. Finally different combinations of the BRDS and FRDS based algorithms are developed on this basis. Numerical experiments based on the bi-objective KP instances are conducted to compare systematically between these algorithms and the recently developed BRDS based DP algorithm as well as the existing FRDS based DP algorithm without state dominance checking. |
| Author | Figueira, José Rui Rong, Aiying |
| Author_xml | – sequence: 1 givenname: Aiying surname: Rong fullname: Rong, Aiying email: arong@iseg.utl.pt organization: Cemapre (Center of Applied Mathematics and Economics), ISEG -Technical University of Lisbon, Rua do Quelhas 6, 1200-781 Lisboa, Portugal – sequence: 2 givenname: José Rui surname: Figueira fullname: Figueira, José Rui email: figueira@ist.utl.pt organization: CEG-IST, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal |
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| CitedBy_id | crossref_primary_10_1016_j_cor_2021_105693 crossref_primary_10_1016_j_aei_2025_103163 crossref_primary_10_1016_j_ress_2022_108340 crossref_primary_10_1016_j_ejor_2013_05_045 crossref_primary_10_36680_j_itcon_2021_007 crossref_primary_10_1016_j_asoc_2015_11_045 crossref_primary_10_1109_ACCESS_2024_3462765 crossref_primary_10_1080_0305215X_2018_1558445 |
| Cites_doi | 10.1109/MCDM.2007.369436 10.1016/j.cor.2007.09.009 10.1287/mnsc.49.12.1726.25117 10.1002/(SICI)1520-6750(200002)47:1<57::AID-NAV4>3.0.CO;2-4 10.1016/j.camwa.2011.07.067 10.1016/j.amc.2007.04.062 10.1007/978-3-642-13193-6_22 10.1016/S0377-2217(99)00265-9 10.1016/S0305-0548(02)00112-0 10.1023/A:1008258310679 10.1016/j.ejor.2004.08.005 10.1016/j.cor.2009.06.026 10.1016/j.ejor.2008.07.047 10.1023/A:1009682532542 10.1016/j.cor.2008.11.001 |
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| Keywords | Multi-objective optimization Dynamic programming Basic state reduction techniques Bi-objective knapsack problem |
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