Improved convergent heuristics for the 0-1 multidimensional knapsack problem

At the end of the seventies, Soyster et al. (Eur. J. Oper. Res. 2:195–201, 1978 ) proposed a convergent algorithm that solves a series of small sub-problems generated by exploiting information obtained through a series of linear programming relaxations. This process is suitable for the 0-1 mixed int...

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Bibliographic Details
Published in:Annals of operations research Vol. 183; no. 1; pp. 125 - 142
Main Authors: Hanafi, Saïd, Wilbaut, Christophe
Format: Journal Article
Language:English
Published: Boston Springer US 01.03.2011
Springer Science + Business Media
Springer
Springer Nature B.V
Springer Verlag
Subjects:
Algorithms
Business and Management
Combinatorics
Computer Science
Convergence
Dominance
Dynamic programming
Heuristic
Integer programming
Knapsack problem
Linear programming
Mathematical analysis
Methods
Mixed integer
Operations Research
Operations Research/Decision Theory
Optimization
Optimization techniques
Studies
Theory of Computation
Variables
Multidimensional knapsack problem
Relaxation
Heuristic
Multidimensional knapsack problem
ISSN:0254-5330, 1572-9338
Online Access:Get full text
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Summary:At the end of the seventies, Soyster et al. (Eur. J. Oper. Res. 2:195–201, 1978 ) proposed a convergent algorithm that solves a series of small sub-problems generated by exploiting information obtained through a series of linear programming relaxations. This process is suitable for the 0-1 mixed integer programming problems when the number of constraints is relatively smaller when compared to the number of variables. In this paper, we first revisit this algorithm, once again presenting it and some of its properties, including new proofs of finite convergence. This algorithm can, in practice, be used as a heuristic if the number of iterations is limited. We propose some improvements in which dominance properties are emphasized in order to reduce the number of sub problems to be solved optimally. We also add constraints to these sub-problems to speed up the process and integrate adaptive memory. Our results show the efficiency of the proposed improvements for the 0-1 multidimensional knapsack problem.
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ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-009-0546-z