Encoding transformation-based differential evolution algorithm for solving knapsack problem with single continuous variable

He, Yichao; Wang, Jinghong; Zhang, Xinlu; Li, Huanzhe; Liu, Xuejing

doi:10.1016/j.swevo.2019.03.002

Cited by 11 publications

(3 citation statements)

References 26 publications

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“…The work by Zhang (2011) presents an algorithm using artificial intelligence; Refaei et al (2020) proposes neural networks and machine learning. Approximation algorithms and extensive analyses of the performed computational experiments are included in the works: He et al (2024), Refaei et al (2020), andZhang (2011). An overview of packaging problems and methods of solving them is presented in the monograph of Kellerer et al (2004).…”

Section: State Of the Artmentioning

confidence: 99%

“…The possibility of multi-processor computing has resulted in a significant shift in the size of instances that can be solved exactly in an acceptable time. In addition to the exact and approximation algorithms that have been known for years (Zavala-Diaz et al, 2019;Vu & Derbel, 2016;Vasilchikov, 2018), parallel versions of algorithms inspired by nature have also been published (He et al, 2024), as well as: neural networks, artificial intelligence (Zhang, 2011;Ji et al, 2017) and learning techniques (Refaei et al, 2020).…”

Section: State Of the Artmentioning

confidence: 99%

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Optimal solving of a binary knapsack problem on a D-Wave quantum machine and its implementation in production systems

Bożejko,

Burduk,

Pempera

et al. 2024

Ann Oper Res

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The efficient management of complex production systems is a challenge in today’s logistics. In the field of intelligent and sustainable logistics, the optimization of production batches, especially in the context of a rapidly changing product range, requires fast and precise computational solutions. This paper explores the potential of quantum computers for solving these problems. Traditional computational methods are often limited when it comes to optimizing complex logistics systems. In response to these challenges, the paper proposes the use of a hybrid algorithm that combines quantum technologies with classical computational methods. Such integration allows the computational power of both types of technologies to be harnessed, leading to faster and more efficient identification of optimal solutions. In this work, we consider the knapsack problem, a classic NP-hard optimization problem that is commonly used to verify the effectiveness of new algorithm construction methods. The algorithm presented is based on the Branch and Bound method and aims to ensure solution optimality in the context of the non-determinism of quantum computers. Within the algorithm, computations are performed alternately on a classical processor and a quantum processor. In addition, the lower and upper bounds of the objective function are computed in constant time using the D-Wave quantum machine.

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Section: State Of the Artmentioning

confidence: 99%

Section: State Of the Artmentioning

confidence: 99%

Optimal solving of a binary knapsack problem on a D-Wave quantum machine and its implementation in production systems

Bożejko,

Burduk,

Pempera

et al. 2024

Ann Oper Res

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show abstract

“…Studies have been carried out on the structure, the cut selection, and the strengthening of the linear relaxation of this type of polyhedron by Marchand and Wolsey [36] as well as in the more general framework of linear programs in mixed variables [21,24,16]. Moreover, optimization methods on this polyhedron have been studied by Büther and Briskorn [14], Lin, Zhu, and Ali [34], Zhao and Li [46], He et al [28], and Liu [35].…”

Section: Application To the Unsplittable Flow Problemmentioning

confidence: 99%

On the integration of Dantzig-Wolfe and Fenchel decompositions via directional normalizations

Lamothe¹,

Haït²,

Rachelson³

et al. 2023

Preprint

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The strengthening of linear relaxations and bounds of mixed integer linear programs has been an active research topic for decades. Enumerationbased methods for integer programming like linear programming-based branchand-bound exploit strong dual bounds to fathom unpromising regions of the feasible space. In this paper, we consider the strengthening of linear programs via a composite of Dantzig-Wolfe and Fenchel decompositions. We provide geometric interpretations of these two classical methods. Motivated by these geometric interpretations, we introduce a novel approach for solving Fenchel sub-problems and introduce a novel decomposition combining Dantzig-Wolfe and Fenchel decompositions in an original manner. We carry out an extensive computational campaign assessing the performance of the novel decomposition on the unsplittable flow problem. Very promising results are obtained when the new approach is compared to classical decomposition methods.

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RG-NBEO: a ReliefF guided novel binary equilibrium optimizer with opposition-based S-shaped and V-shaped transfer functions for feature selection

et al. 2022

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Encoding transformation-based differential evolution algorithm for solving knapsack problem with single continuous variable

Cited by 11 publications

References 26 publications

Optimal solving of a binary knapsack problem on a D-Wave quantum machine and its implementation in production systems

Optimal solving of a binary knapsack problem on a D-Wave quantum machine and its implementation in production systems

On the integration of Dantzig-Wolfe and Fenchel decompositions via directional normalizations

RG-NBEO: a ReliefF guided novel binary equilibrium optimizer with opposition-based S-shaped and V-shaped transfer functions for feature selection

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