Sensitivity analysis of the optimum to perturbation of the profit of a subset of items in the binary knapsack problem

Belgacem, Tarik; Hifi, Mhand

doi:10.1016/j.disopt.2008.05.001

Cited by 11 publications

(10 citation statements)

References 13 publications

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“…2) The largest perturbation | | 3) The obtained results are better than the results of the previous work (see Hifi (2007 &2008)) since for the last case, the largest perturbation to be divided over all perturbed items is equal to one unit. …”

Section: An Examplecontrasting

confidence: 42%

“…We proposed new lower and upper bound limits of the sensitivity intervals, by improving the previous results Hifi (2007 &2008)). Throughout an instance of P, we showed how the new results can produce a better (large one) cumulative perturbation compared to the existing one.…”

Section: Resultsmentioning

confidence: 99%

“…s s s N w w ∀ ∈ = As shown in Hifi (2007 &2008), both P and ' P Γ have the same set of feasible solutions and if their optimal solutions coincide, i.e., ' ,…”

Section: Itemsmentioning

confidence: 98%

“…In Hifi et al (2004) an adaptive algorithm has been proposed for providing the set of all interval limits when perturbing either any profit or weight. In Hifi (2007 &2008), the authors tackled the sensitivity analysis of the knapsack sharing problem -a special extension of the binary knapsack-when perturbing an arbitrary profit item; they considered the cases of single and multiple optimal solutions. Finally, in Belgacem and Hifi (2007) the authors studied the sensitivity analysis of the knapsack sharing when a single weight item is perturbed (for more details on the sensitivity and stability analysis, the reader can refer to Greenberg 1998 andNauss 1979).…”

Section: Introductionmentioning

confidence: 99%

“…We now summarize the main results proposed inHifi (2007 &2008), when the profits of Γ are perturbed in . P Result 2.2 Let x be an optimal solution of P.…”

mentioning

confidence: 99%

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Sensitivity analysis of the knapsack problem: Tighter lower and upper bound limits

Belgacem

Hifi

2008

J. Syst. Sci. Syst. Eng.

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In this paper, we study the sensitivity of the optimum of the knapsack problem to the perturbation of the profit of a subset of items. We propose a polynomial heuristic in order to establish both lower and upper bound limits of the sensitivity interval. The aim is to stabilize any given optimal solution obtained by applying any exact algorithm. We then evaluate the effectiveness of the proposed solution procedure on an example and a set of randomly generated problem instances.

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Section: An Examplecontrasting

confidence: 42%

Section: Resultsmentioning

confidence: 99%

“…s s s N w w ∀ ∈ = As shown in Hifi (2007 &2008), both P and ' P Γ have the same set of feasible solutions and if their optimal solutions coincide, i.e., ' ,…”

Section: Itemsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

“…We now summarize the main results proposed inHifi (2007 &2008), when the profits of Γ are perturbed in . P Result 2.2 Let x be an optimal solution of P.…”

mentioning

confidence: 99%

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Sensitivity analysis of the knapsack problem: Tighter lower and upper bound limits

Belgacem

Hifi

2008

J. Syst. Sci. Syst. Eng.

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DGSA: discrete gravitational search algorithm for solving knapsack problem

Sajedi

Razavi

2016

Oper Res Int J

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The 0-1 knapsack problem is one of the classic NP-hard problems. It is an open issue in discrete optimization problems, which plays an important role in the real applications. Therefore, several algorithms have been developed to solve it. The Gravitational Search Algorithm (GSA) is an optimization algorithm based on the law of gravity and mass interactions. In the GSA, the searcher agents are a collection of masses that interact with each other based on the Newtonian gravity and the laws of motion. In this algorithm the position of the agents can be considered as the solutions. The GSA is a nature-inspired algorithm that is used for finding the optimum value of continuous functions. This paper introduces a Discrete version of the GSA (DGSA) for solving 0-1 knapsack problem. In this regard, we introduce an approach for discretely updating the position of each agent. In addition, a fitness function has been proposed for 0-1 knapsack problem. Our experimental results show the effectiveness of the DGSA in comparison with other similar algorithms in terms of the accuracy and overcoming the defect of local convergence.

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Reoptimization in Lagrangian methods for the 0–1 quadratic knapsack problem

Létocart

Nagih²,

Plateau

2012

Computers & Operations Research

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The 0-1 quadratic knapsack problem consists in maximizing a quadratic objective function subject to a linear capacity constraint. To solve exactly large instances of this problem with a tree search algorithm (e.g. a branch and bound method), the knowledge of good lower and upper bounds is crucial for pruning the tree but also for fixing as many variables as possible in a preprocessing phase. The upper bounds used in the best known exact approaches are based on Lagrangian relaxation and decomposition. It appears that the computation of these Lagrangian dual bounds involves the resolution of numerous 0-1 linear knapsack subproblems. Thus, taking this huge number of solvings into account, we propose to embed reoptimization techniques for improving the efficiency of the preprocessing phase of the 0-1 quadratic knapsack resolution. Namely, reoptimization is introduced to accelerate each independent sequence of 0-1 linear knapsack problems induced by the Lagrangian relaxation as well as the Lagrangian decomposition. Numerous numerical experiments validate the relevance of our approach.

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Sensitivity analysis of the optimum to perturbation of the profit of a subset of items in the binary knapsack problem

Cited by 11 publications

References 13 publications

Sensitivity analysis of the knapsack problem: Tighter lower and upper bound limits

Sensitivity analysis of the knapsack problem: Tighter lower and upper bound limits

DGSA: discrete gravitational search algorithm for solving knapsack problem

Reoptimization in Lagrangian methods for the 0–1 quadratic knapsack problem

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