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Optimal Subscription Planning for Digital Goods

OPERATIONS RESEARCH 2023年第6期71卷 2245页

作者： Alaei, Saeed Makhdoumi, Ali Malekian, Azarakhsh Google Res Mountain View CA 94043 USA Duke Univ Fuqua Sch Business Durham NC 27708 USA Univ Toronto Rotman Sch Management Toronto ON M5S 3E6 Canada

We consider a media service provider that gives users access to digital goods through subscription. In our model, different types of users with heterogeneous usage rates repeatedly use a platform over a period of time. There are multiple item types on the platform, and the value of an item to a user is random and depends on both the user type and the item type. The design of the platform's subscription planning comprises selecting a subscription fee for each set of item types. Before the beginning of the subscription period, given the subscription planning, users decide which set of item types to subscribe to (if any). During the subscription period, a user pays zero price to use an item if it has subscribed to a set that includes it and pays its rental price otherwise. For an exogenously given rental price, we establish the sufficient and necessary condition for the optimality of grand subscription-offering a single subscription set that includes all items. We then consider a setting in which the platform chooses both the subscription fee for each set of item types and the rental price of each item type and establish that there exist subscription fees proportional to the cardinality of each set of item types (with no rental offers) that achieve a logarithmic approximation (in the number of item types) of the optimal revenue. Finally, we demonstrate that our performance guarantee is tight for a class of problem instances.

关键词： subscription planning digital goods approximation algorithms pricing

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Strengthening Gradient Descent by Sequential Motion Optimization for Deep Neural Networks

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2023年第3期27卷 565-579页

作者： Le-Duc, Thang Nguyen, Quoc-Hung Lee, Jaehong Nguyen-Xuan, H. Sejong Univ Deep Learning Architecture Res Ctr Seoul 05006 South Korea Vietnamese German Univ Dept Computat Engn Ho Chi Minh 75000 Vietnam HUTECH Univ CIRTech Inst Ho Chi Minh 70000 Vietnam

In this article, we explore the advantages of heuristic mechanisms and devise a new optimization framework named sequential motion optimization (SMO) to strengthen gradient-based methods. The key idea of SMO is inspired from a movement mechanism in a recent metaheuristic method called balancing composite motion optimization (BCMO). Specifically, SMO establishes a sequential motion chain of two gradient-guided individuals, including a leader and a follower to enhance the effectiveness of parameter updates in each iteration. A surrogate gradient model with low computation cost is theoretically established to estimate the gradient of the follower by that of the leader through chain rule during the training process. Experimental results in terms of training quality on both fully connected multilayer perceptrons (MLPs) and convolutional neural networks (CNNs) with respect to three popular benchmark datasets, including MNIST, Fashion-MNIST, and CIFAR-10 demonstrate the superior performance of the proposed framework in comparison with the vanilla stochastic gradient descent (SGD) implemented via backpropagation (BP) algorithm. Although this study only introduces the vanilla gradient descent (GD) as a main gradient-guided factor in SMO for deep neural network (DNN) training application, it is great potential to combine with other gradient-based variants to improve its effectiveness and solve other large-scale optimization problems in practice.

关键词： Training Optimization Metaheuristics Stochastic processes Neural networks Computational modeling approximation algorithms Backpropagation (BP) algorithm deep neural networks (DNNs) large-scale optimization metaheuristic algorithms sequential motion optimization (SMO) stochastic gradient descent (SGD) surrogate gradient

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Modified Artificial Bee Colony Algorithm for Multiple-Choice Multidimensional Knapsack Problem

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IEEE ACCESS 2023年 11卷 45255-45269页

作者： Mkaouar, Arij Htiouech, Skander Chabchoub, Habib Univ Sfax OLID Lab ISGIS Sfax Tunisia Univ Jeddah CS & AI Dept Jeddah Saudi Arabia Al Ain Univ Coll Business Abu Dhabi U Arab Emirates

The multiple-choice multidimensional knapsack problem (MMKP) is a well-known NP-hard problem that has many real-time applications. However, owing to its complexity, finding computationally efficient solutions for the MMKP remains a challenging task. In this study, we propose a Modified Artificial Bee Colony algorithm (MABC) to solve the MMKP. The MABC employs surrogate relaxation, Hamming distance, and a tabu list to enhance the local search process and exploit neighborhood information. We evaluated the performance of the MABC on standard benchmark instances and compared it with several state-of-the-art algorithms, including RLS, ALMMKP, ACO, PEGF-PERC, TIKS-TIKS2 and D-QPSO. The experimental results reveal that MABC produces highly competitive solutions in terms of the best solutions found, achieving approximately 2% of the optimal solutions with trivial (milliseconds) CPU time. The Kruskal-Wallis test revealed that there was no statistically significant difference in the objective function values between the MABC algorithm and other state-of-the-art algorithms (H = 0.31506, p = 0.98882). However, for CPU efficiency, the test showed a statistically significant difference (H = 84.90850, p = 0), indicating that the MABC algorithm exhibited significantly better CPU efficiency (with shorter execution times) than the other algorithms did. Along with these findings, the ease of implementation of the algorithm and the small number of control parameters make our approach highly adaptive for large-scale real-time systems.

关键词： Artificial bee colony algorithm approximation algorithms Heuristic algorithms Search problems Hamming distances Linear programming Convergence multiple-choice multidimensional knapsack problem hamming distance surrogate relaxation

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Probabilistic Analysis of Optimization Problems on Sparse Random Shortest Path Metrics

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ALGORITHMICA 2023年第12期85卷 3793-3815页

作者： Klootwijk, Stefan Manthey, Bodo Univ Twente Enschede Netherlands

Simple heuristics for (combinatorial) optimization problems often show a remarkable performance in practice. Worst-case analysis often falls short of explaining this performance. Because of this, "beyond worst-case analysis" of algorithms has recently gained a lot of attention, including probabilistic analysis of algorithms. The instances of many (combinatorial) optimization problems are essentially a discretemetric space. Probabilistic analysis for such metric optimization problems has nevertheless mostly been conducted on instances drawn from Euclidean space, which provides a structure that is usually heavily exploited in the analysis. However, most instances from practice are not Euclidean. Little work has been done on metric instances drawn from other, more realistic, distributions. Some initial results have been obtained in recent years, where random shortest path metrics generated from dense graphs (either complete graphs or Erdos-Renyi random graphs) have been used so far. In this paper we extend these findings to sparse graphs, with a focus on sparse graphs with 'fast growing cut sizes', i.e. graphs for which vertical bar delta(U)vertical bar = Omega (vertical bar U vertical bar(epsilon)) for some constant epsilon is an element of(0, 1) for all subsets U of the vertices, where delta(U) is the set of edges connecting U to the remaining vertices. A random shortest path metric is constructed by drawing independent random edge weights for each edge in the graph and setting the distance between every pair of vertices to the length of a shortest path between them with respect to the drawn weights. For such instances generated from a sparse graph with fast growing cut sizes, we prove that the greedy heuristic for the minimum distance maximum matching problem, and the nearest neighbor and insertion heuristics for the traveling salesman problem all achieve a constant expected approximation ratio. Additionally, for instances generated from an arbitrary sparse graph, w

关键词： Random shortest path metrics First-passage percolation approximation algorithms Probabilistic analysis Average-case analysis

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Few Cuts Meet Many Point Sets

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ALGORITHMICA 2023年第4期85卷 965-975页

作者： Har-Peled, Sariel Jones, Mitchell Univ Illinois Dept Comp Sci 201 N Goodwin Ave Urbana IL 61801 USA

We study the problem of how to split many point sets in R-d into smaller parts using a few (shared) splitting hyperplanes. This problem is related to the classical Ham-Sandwich Theorem. We provide a logarithmic approx... 详细信息

关键词： Ham-Sandwich Theorem Submodular optimization approximation algorithms

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Parallel Graph Signal Processing: Sampling and Reconstruction

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IEEE TRANSACTIONS ON SIGNAL AND INFORMATION PROCESSING OVER NETWORKS 2023年 9卷 190-206页

作者： Dapena, Daniela Lau, Daniel L. L. Arce, Gonzalo R. R. Univ Delaware Financial Serv Analyt Newark DE 19713 USA Univ Kentucky Elect & Comp Engn Lexington KY 40506 USA Univ Delaware Elect Engn Newark DE 19716 USA

Graph signal processing (GSP) extends classical signal processing methods to analyzing signals supported over irregular grids represented by graphs. Within the scope of GSP, sampling and reconstruction represent fundamental tools that have received considerable attention. For very large graphs, however, many of the current methods struggle with the computational and memory requirements. Vertex domain and randomized sampling strategies somewhat ameliorate the computational requirements, but these algorithms perform poorly at preserving signal fidelity for graphs with hundreds of thousands of vertices. To address these shortcomings, this article introduces a new and scalable approach that can be easily parallelized. This new approach uses existing graph partitioning algorithms in concert with vertex-domain blue-noise sampling and reconstruction, performed independently across partitions. In the reconstruction, some degree of overlapping is added to the partitions to induce trans-partition smoothness in the recovered signal. We also propose two sampling schemes based on the spatial characteristic of the graph that minimizes the recovery error. The first combines graph partitioning with the Void-and-Cluster algorithm, while the second approach uses Error Diffusion. We conclude this article with experiments on synthetic and real data that show the effectiveness of these new approaches on very large graphs.

关键词： Partitioning algorithms approximation algorithms Signal processing algorithms Signal processing Laplace equations Information processing Parallel processing Graph signal reconstruction blue-noise graph signal sampling graph signal processing

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A Decision Aiding Framework for Two-Way Selection of Cloud Vendors in Medical Centers With Generalized Orthopair Fuzzy Information

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IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT 2023年第10期70卷 3653-3664页

作者： Krishankumar, R. Arun, Karthik Pamucar, Dragan Ravichandran, K. S. Amrita Vishwa Vidyapeetham Dept Comp Sci & Engn Amrita Sch Engn Coimbatore 641112 Tamil Nadu India SASTRA Univ Sch Comp Thanjavur 613401 India Mil Acad Univ Def Belgrade Dept Logist Belgrade 11000 Serbia Rajiv Gandhi Natl Inst Youth Dev Sriperumbudur 602105 India

With the increase of data and computation in the healthcare industry, officials are looking for reliable alternatives to compete globally. Cloud technology is a viable option that reduces data and computation overhead at the host side. Due to the fast growth of cloud vendors (CVs), the apt selection of a vendor becomes crucial. Extant CV selection models 1) have reduced scope for minimizing subjective randomness;2) cannot offer agents with flexible preference window;and 3) have higher human intervention during the decision process. Driven by these lacunae and to counter the same, a novel scientific model is developed in this article. Generalized orthopair fuzzy information is adopted to express preferences. Later, the attitudinal-CRITIC approach is put forward to determine the significance of functional factors. Agents' attitude values are calculated by extending the variance approach. Agent wise personalized prioritization algorithm is developed to rank CVs based on individual perceptions, query vectors, and cumulative rank factors. The scientific model's usefulness is verified by adopting a case study of CV selection in a private medical unit in Trichy. Finally, sensitivity analysis and comparison with extant models help understand the merits and limitations of the proposed work.

关键词： Uncertainty Decision making approximation algorithms Quality of service Power measurement Optical fibers Mathematical model Attitudinal critic cloud vendors (CVs) generalized orthopair variance method

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An estimator for matching size in low arboricity graphs with two applications

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2023年第1期45卷 1-14页

作者： Jowhari, Hossein KN Toosi Univ Technol Fac Math Dept Comp Sci & Stat Tehran Iran

In this paper, we present a new degree-based estimator for the size of maximum matching in bounded arboricity graphs. When the arboricity of the graph is bounded by alpha, the estimator gives a alpha + 2 factor approximation of the matching size. For planar graphs, we show the estimator does better and returns a 3.5 approximation of the matching size. Using this estimator, we get new results for approximating the matching size of planar graphs in the streaming and distributed models of computation. In particular, in the vertex-arrival streams, we get a randomized O (root n/epsilon(2) log n) space algorithm for approximating the matching size of a planar graph on n vertices within (3.5+epsilon) factor. Similarly, we get a simultaneous protocol in the vertex-partition model for approximating the matching size within (3.5 + epsilon) factor using O (n(2/3)/epsilon(2) log n) communication from each player. In comparison with previous works, the estimator in this paper does not need to know the arboricity of the input graph and improves the approximation factor in the case of planar graphs.

关键词： Maximum matching approximation algorithms Data stream algorithms

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Learning to Beamform in Heterogeneous Massive MIMO Networks

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2023年第7期22卷 4901-4915页

作者： Zhu, Minghe Chang, Tsung-Hui Hong, Mingyi Chinese Univ Hong Kong Sch Sci & Engn Shenzhen 518172 Peoples R China Univ Minnesota Twin Cities Dept Elect & Comp Engn Minneapolis MN 55455 USA

Finding the optimal beamformers in massive multiple-input multiple-output (MIMO) networks is challenging because of its non-convexity, and conventional optimization based algorithms suffer from high computational costs. Recently, deep learning based methods have been proposed because of their computational efficiency, but they typically can not generalize well when deployed in heterogeneous scenarios where the base stations (BSs) are equipped with different numbers of antennas and have different inter-BS distances. This paper proposes a novel deep learning based beamforming algorithm to address above challenges. Specifically, we consider the weighted sum rate (WSR) maximization problem in multi-input and single-output (MISO) interference channels, and propose a beamforming learning architecture by unfolding a parallel gradient projection algorithm. By leveraging the low-dimensional structures of the optimal beamforming solution, our constructed learning network can be made independent of the numbers of transmit antennas and BSs. Moreover, such a design can be further extended to a cooperative multicell network where users are jointly served by multiple BSs. Numerical results based on both synthetic and ray-tracing channel models show that the proposed neural network can achieve high WSRs with significantly reduced runtime, while exhibiting favorable generalization capability with respect to the antenna number, BS number and the inter-BS distance.

关键词： Array signal processing Antennas approximation algorithms Transmitting antennas MISO communication Signal to noise ratio Massive MIMO Beamforming deep neural network Index Terms MISO interfering channel cooperative multicell beamforming

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Deep Unfolding Network for ISAR Imaging Based on Hypernetwork

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2023年第6期59卷 8076-8089页

作者： Guo, Jianwen Shi, Hongyin Yang, Ting Liu, Da Qiao, Zhijun Yanshan Univ Sch Informat Sci & Engn Qinhuangdao 066004 Peoples R China Beijing Univ Civil Engn & Architecture Sch Elect & Informat Engn Beijing 100044 Peoples R China Univ Texas Rio Grande Valley Sch Math & Stat Sci Edinburg TX 78539 USA

Inverse synthetic aperture radar (ISAR) imaging can provide high-resolution images of targets. More recently, the unfolding algorithm has successfully realized fast and efficient ISAR imaging by providing a systematic connection between the traditional iterative algorithms widely used in ISAR imaging and data-based deep learning. However, once the unfolding framework is trained, the layer-dependent parameters are fixed and difficult to adapt to the variations in test scenarios, and usually, retraining is required. This article proposes an ISAR imaging framework based on a hypernetwork that can dynamically generate the unfolding network's internal parameters to accommodate the various scenarios. Specifically, the basis of the framework is an unfolding network based on the generalized expectation consistent (GEC) approximation phase recovery algorithm, where the damping factor is employed for data-driven learning. Instead of directly learning a set of optimal damping factors, the key is to develop a hypernetwork that trains an intelligent controller as the main unfolding network that can dynamically generate the damping factors according to testing scenarios. Thus, it exhibits strong robustness in various scenarios. Simulation and measurement experiments show that the proposed method exhibits excellent performance, robustness, and focusing accuracy.

关键词： Imaging Radar imaging Damping Image reconstruction Heuristic algorithms Task analysis approximation algorithms Deep neural network generalized expectation consistent approximation (GEC) hypernetwork inverse synthetic aperture radar (ISAR) phase retrieval (PR) unfolding

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