Neural Knapsack: A Neural Network Based Solver for the Knapsack Problem

Nomer, Hazem A. A.; Alnowibet, Khalid Abdulaziz; Elsayed, Ashraf; Mohamed, Ali Wagdy

doi:10.1109/access.2020.3044005

Cited by 11 publications

(7 citation statements)

References 31 publications

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“…Although the distributions of simulated data may differ in different work (Hertrich and Skutella 2021;Nomer et al 2020;Yildiz 2022), we believe our Transformer Knapsack has shown strong power as a trainable module to approximate the DP solver of knapsack problem.…”

Section: Result As In Thementioning

confidence: 97%

“…The classical Knapsack Problem is often solved by adopting the dynamic programming algorithm, however which is non-differentiable. Recent studies have explored neural knapsack models (Nomer et al 2020;Hertrich and Skutella 2021;. Xu et al (2020a) use NNs to enhance dynamic programming and Hertrich and Skutella (2021) present a detailed mathematical study to investigate the expressivity of NNs, and find that a class of RNNs with feedforward RELU compute provably good solutions to the NP-hard Knapsack Problem.…”

Section: Trainable Length Controllermentioning

confidence: 99%

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Unsupervised Extractive Summarization with Learnable Length Control Strategies

Jie,

Meng,

Jiang

et al. 2024

AAAI

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Unsupervised extractive summarization is an important technique in information extraction and retrieval. Compared with supervised method, it does not require high-quality human-labelled summaries for training and thus can be easily applied for documents with different types, domains or languages. Most of existing unsupervised methods including TextRank and PACSUM rely on graph-based ranking on sentence centrality. However, this scorer can not be directly applied in end-to-end training, and the positional-related prior assumption is often needed for achieving good summaries. In addition, less attention is paid to length-controllable extractor, where users can decide to summarize texts under particular length constraint. This paper introduces an unsupervised extractive summarization model based on a siamese network, for which we develop a trainable bidirectional prediction objective between the selected summary and the original document. Different from the centrality-based ranking methods, our extractive scorer can be trained in an end-to-end manner, with no other requirement of positional assumption. In addition, we introduce a differentiable length control module by approximating 0-1 knapsack solver for end-to-end length-controllable extracting. Experiments show that our unsupervised method largely outperforms the centrality-based baseline using a same sentence encoder. In terms of length control ability, via our trainable knapsack module, the performance consistently outperforms the strong baseline without utilizing end-to-end training. Human evaluation further evidences that our method performs the best among baselines in terms of relevance and consistency.

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Section: Result As In Thementioning

confidence: 97%

Section: Trainable Length Controllermentioning

confidence: 99%

Unsupervised Extractive Summarization with Learnable Length Control Strategies

Jie,

Meng,

Jiang

et al. 2024

AAAI

View full text Add to dashboard Cite

show abstract

“…Applications include, but are not limited to, computer science [28,66], epidemic disease control [83,84], retail business organization [79], and modeling invasive species [9,10]. There exist different approaches to solving MKP, such as exact algorithms [51,70], approximation schema [55], heuristics and metaheuristics [16,26,29,33,69]. The main approaches used to obtain an exact solution of MKP are based on branch-and-bound and branch-and-cut.…”

Section: Related Workmentioning

confidence: 99%

A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack

Bushaj,

Büyüktahtakın

2024

J Glob Optim

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In this paper, we address the difficulty of solving large-scale multi-dimensional knapsack instances (MKP), presenting a novel deep reinforcement learning (DRL) framework. In this DRL framework, we train different agents compatible with a discrete action space for sequential decision-making while still satisfying any resource constraint of the MKP. This novel framework incorporates the decision variable values in the 2D DRL where the agent is responsible for assigning a value of 1 or 0 to each of the variables. To the best of our knowledge, this is the first DRL model of its kind in which a 2D environment is formulated, and an element of the DRL solution matrix represents an item of the MKP. Our framework is configured to solve MKP instances of different dimensions and distributions. We propose a K-means approach to obtain an initial feasible solution that is used to train the DRL agent. We train four different agents in our framework and present the results comparing each of them with the CPLEX commercial solver. The results show that our agents can learn and generalize over instances with different sizes and distributions. Our DRL framework shows that it can solve medium-sized instances at least 45 times faster in CPU solution time and at least 10 times faster for large instances, with a maximum solution gap of 0.28% compared to the performance of CPLEX. Furthermore, at least 95% of the items are predicted in line with the CPLEX solution. Computations with DRL also provide a better optimality gap with respect to state-of-the-art approaches.

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“…Neural networks have been used to solve the Knapsack Problem in (Vinyals et al, 2017), (Nomer et al, 2020), and (Bello et al, 2016). We follow the setup of Bello et al and (2) this coupled with 5000 iterations of their Active Search method.…”

Section: Knapsack Problemmentioning

confidence: 99%

Neural Simulated Annealing

Correia¹,

Worrall²,

Bondesan³

2022

Preprint

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Simulated annealing (SA) is a stochastic global optimisation technique applicable to a wide range of discrete and continuous variable problems. Despite its simplicity, the development of an effective SA optimiser for a given problem hinges on a handful of carefully handpicked components; namely, neighbour proposal distribution and temperature annealing schedule. In this work, we view SA from a reinforcement learning perspective and frame the proposal distribution as a policy, which can be optimised for higher solution quality given a fixed computational budget. We demonstrate that this Neural SA with such a learnt proposal distribution, parametrised by small equivariant neural networks, outperforms SA baselines on a number of problems: Rosenbrock's function, the Knapsack problem, the Bin Packing problem, and the Travelling Salesperson problem. We also show that Neural SA scales well to large problems-generalising to significantly larger problems than the ones seen during training-while achieving comparable performance to popular off-the-shelf solvers and other machine learning methods in terms of solution quality and wall-clock time.

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Neural Knapsack: A Neural Network Based Solver for the Knapsack Problem

Cited by 11 publications

References 31 publications

Unsupervised Extractive Summarization with Learnable Length Control Strategies

Unsupervised Extractive Summarization with Learnable Length Control Strategies

A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack

Neural Simulated Annealing

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