Sac à dos multidimensionnel en variables 0-1 : encadrement de la somme des variables à l'optimum

Fréville, Arnaud; Plateau, Gérard

doi:10.1051/ro/1993270201691

Cited by 11 publications

(9 citation statements)

References 10 publications

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“…The second two constraints (13) impose bounds on the sum of problem variables. Glover (1965) has already proposed ways to exploit these kinds of constraints, and both Fréville and Plateau (1993) and Vasquez and Hao (2001) have shown that these constraints can improve the efficacy of algorithms for the MKP. More specifically, we add the two constraints:…”

Section: Accelerating the Solving Of The Reduced Problemsmentioning

confidence: 99%

Improved convergent heuristics for the 0-1 multidimensional knapsack problem

Hanafi

Wilbaut

2009

Ann Oper Res

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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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Section: Accelerating the Solving Of The Reduced Problemsmentioning

confidence: 99%

Improved convergent heuristics for the 0-1 multidimensional knapsack problem

Hanafi

Wilbaut

2009

Ann Oper Res

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“…These kinds of constraints were proposed by Fréville and Plateau (1993) and they were used in several works on the multidimensional knapsack problem (e.g., Vasquez and Hao (2001), Vasquez and Vimont (2005), Boussier, Vasquez, Vimont, Hanafi, and Michelon (2010)). If r (respectively, r) denotes a lower (resp.…”

Section: Reducing the Search Spacementioning

confidence: 99%

A hybrid heuristic for the 0–1 Knapsack Sharing Problem

Haddar

Khemakhem²,

Hanafi³

et al. 2015

Expert Systems with Applications

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“…a subgradient algorithm to determine the value of a Lagrangian dual problem. Fréville & Plateau (1993 have proposed several techniques to exactly solve the TKP based in part on the solving of a surrogate dual problem. The method is divided into two phases: in the first one, the algorithm tries to reduce the size of the problem by fixing the most possible variables using upper bounds.…”

Section: The Two-dimensional Knapsack Problemmentioning

confidence: 99%

A survey of effective heuristics and their application to a variety of knapsack problems

Wilbaut¹,

Hanafi²,

Salhi³

2007

IMA Journal of Management Mathematics

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We present a family of knapsack problems (KPs) while highlighting their particular applications. Though most of the problems are derived from the classical KP, the differences arise in the addition or modification of the constraints or in the way the objective function is defined. Appropriate techniques that were found to be successful in solving these problems are briefly reviewed. Hybrid methods that combine the strengths of different methods such as exact and heuristics are also briefly discussed. Some research avenues that we believe to be useful and challenging are also pointed out.

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Sac à dos multidimensionnel en variables 0-1 : encadrement de la somme des variables à l'optimum

Cited by 11 publications

References 10 publications

Improved convergent heuristics for the 0-1 multidimensional knapsack problem

Improved convergent heuristics for the 0-1 multidimensional knapsack problem

A hybrid heuristic for the 0–1 Knapsack Sharing Problem

A survey of effective heuristics and their application to a variety of knapsack problems

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