A dynamic programming based reduction procedure for the multidimensional 0–1 knapsack problem

This paper presents a preprocessing procedure for the 0–1 multidimensional knapsack problem. First, a non-increasing sequence of upper bounds is generated by solving LP-relaxations. Then, a non-decreasing sequence of lower bounds is built using dynamic programming. The comparison of the two sequence...

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Bibliographic Details
Published in:European journal of operational research Vol. 186; no. 1; pp. 63 - 76
Main Authors: Balev, Stefan, Yanev, Nicola, Fréville, Arnaud, Andonov, Rumen
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.04.2008
Elsevier
Elsevier Sequoia S.A
Series:European Journal of Operational Research
Subjects:
Applied sciences
Comparative analysis
Computer Science
Discrete Mathematics
Dynamic programming
Exact sciences and technology
Flows in networks. Combinatorial problems
Heuristic
Heuristics
Integer programming
Knapsack problem
Multidimensional knapsack problem
Operational research and scientific management
Operational research. Management science
Operations Research
Studies
Variable reduction
Integer programming
Variable reduction
Dynamic programming
Heuristics
Multidimensional knapsack problem
Lower bound
Computation time
Upper bound
Heuristic method
Large scale
Knapsack problem
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:This paper presents a preprocessing procedure for the 0–1 multidimensional knapsack problem. First, a non-increasing sequence of upper bounds is generated by solving LP-relaxations. Then, a non-decreasing sequence of lower bounds is built using dynamic programming. The comparison of the two sequences allows either to prove that the best feasible solution obtained is optimal, or to fix a subset of variables to their optimal values. In addition, a heuristic solution is obtained. Computational experiments with a set of large-scale instances show the efficiency of our reduction scheme. Particularly, it is shown that our approach allows to reduce the CPU time of a leading commercial software.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2006.02.058