An Adapted Step Size Algorithm for a 0-1 Biknapsack Lagrangean Dual

Thiongane, Babacar; Nagih, Anass; Plateau, Gérard

doi:10.1007/s10479-005-3454-x

Cited by 10 publications

(5 citation statements)

References 35 publications

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“…It might therefore be advantageous to use "warmstarted" oraclesà la [56]. (v) Being specifically designed to maximize a concave function such as θ, the bundle method needs an exact oracle, to compute exact values of θ.…”

Section: Discussionmentioning

confidence: 99%

Comparison of bundle and classical column generation

Briant¹,

Lemaréchal

Meurdesoif

et al. 2006

Math. Program.

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Abstract. When a column generation approach is applied to decomposable mixed integer programming problems, it is standard to formulate and solve the master problem as a linear program. Seen in the dual space, this results in the algorithm known in the nonlinear programming community as the cutting-plane algorithm of Kelley and Cheney-Goldstein. However, more stable methods with better theoretical convergence rates are known and have been used as alternatives to this standard. One of them is the bundle method; our aim is to illustrate its differences with Kelley's method. In the process we review alternative stabilization techniques used in column generation, comparing them from both primal and dual points of view. Numerical comparisons are presented for five applications: cutting stock (which includes bin packing), vertex coloring, capacitated vehicle routing, multi-item lot sizing, and traveling salesman. We also give a sketchy comparison with the volume algorithm.

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Section: Discussionmentioning

confidence: 99%

Comparison of bundle and classical column generation

Briant¹,

Lemaréchal

Meurdesoif

et al. 2006

Math. Program.

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“…Section 3 deals with the introduction of reoptimization in the resolution of the 0-1 continuous linear knapsack problems solved in the preprocessing phase of the 0-1 quadratic knapsack problem. In this way, we propose to exploit reoptimization tools introduced successfully to improve the computation time of iterative algorithms (like subgradient methods) for a 0-1 bidimensional knapsack problem Lagrangian dual [36,37]. Finally, numerous numerical experiments validate the relevance of our approach (Section 4).…”

Section: Introductionmentioning

confidence: 92%

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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“…Any MPR is calculated so that from this set it is possible to reach all two-hop neighbors. Figure 6 shows the algorithm for calculating MPRs [10], [11] and described in more detail in RFC 3626. Figure 6.…”

Section: Multipoint Relay (Mpr) Electionmentioning

confidence: 99%

QoS routing in cluster OLSR by using the artificial intelligence model MSSP in the big data environnment

Oubaha

Lakki

Ouacha

2021

IJ-AI

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The most complex problems, in data science and more specifically in artificial intelligence, can be modeled as cases of the maximum stable set problem (MSSP). this article describes a new approach to solve the MSSP problem by proposing the continuous hopfield network (CHN) to build optimized link state protocol routing (OLSR) protocol cluster. our approach consists in proposing in two stages: the first acts at the level of the choice of the OLSR master cluster in order to quickly make a local minimum using the CHN, by modeling the MSSP problem. As for the second step, the objective is the improvement of the precision making a solution of efficient at the first rank of neighborhood as a linear constraint, and at the end, to find the resolution of the model using the CHN. We will show that this model determines a good solution of the MSSP problem. To test the theoretical results, we propose a comparison with a classic OLSR.

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An Adapted Step Size Algorithm for a 0-1 Biknapsack Lagrangean Dual

Cited by 10 publications

References 35 publications

Comparison of bundle and classical column generation

Comparison of bundle and classical column generation

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

QoS routing in cluster OLSR by using the artificial intelligence model MSSP in the big data environnment

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