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作者： Yitian Wu School of Computer Science South-Central Minzu University

The 0-1 knapsack problem is widely used in reality and it belongs to NP-hard *** from the basic ideas and time complexity of the algorithm,this paper analyzes how to choose a strategy to solve the *** paper aims to solve practical problems and analyzes the 0-1 knapsack problem in combination with the real-life cargo delivery *** programming and greedy algorithms are used to tackle the problem respectively,and the advantages and disadvantages of two strategies are discussed,so as to analyze how to decide which strategy to adopt to solve the problem when encountering the 0-1 knapsack problem in an actual *** the face of large-scale problems,this paper suggests choosing greedy algorithm because it will save a lot of *** the face of small-scale problems that require absolute solutions,this paper suggests choosing dynamic programming to solve the problem.

关键词： 0-1 Knapsack Problem Dynamic Programming greedy algorithm Maximal Knapsack Packing Optimal Solution

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greedy and Adaptive algorithms for Multi-Depot Vehicle Routing with Object Alternation

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AUTOMATION AND REMOTE CONTROL 2023年第3期84卷 305-325页

作者： Medvedev, S. N. Voronezh State Univ Voronezh Russia

This paper considers the multi-depot vehicle routing problem with object alternation. We propose a formal statement of the problem with two types of objects and a mathematical model with two blocks of Boolean variables. First, the model is studied without gathering vehicles (mobile objects). Then, a special object (a single collection point) is introduced in the model. We show additional constraints of the mathematical model with this object. Special attention is paid to the condition of no subcycles. This condition is considered based on the adjacency matrix. Five greedy algorithms are proposed for solving the problem, two of which are iterative. One of the greedy algorithms is given a probabilistic modification based on the randomization of variables (an adaptive algorithm). Finally, the proposed algorithms are compared in terms of the average value of the objective function and the running time in a computational experiment. Also, the results of another experiment-the parametric tuning of the adaptive algorithm-are presented.

关键词： vehicle routing problem adaptive algorithm greedy algorithm

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greedy guarantees for minimum submodular cost submodular/non-submodular cover problem

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2023年第1期45卷 1-16页

作者： Shi, Majun Yang, Zishen Wang, Wei Xi An Jiao Tong Univ Sch Math & Stat 28 Xianning West Rd Xian 710049 Peoples R China

Minimum Submodular Cost Submodular Cover problem (MIN-SCSC) often occurs naturally in the areas of combinatorial optimization and particularly machine learning. It is well-known that the greedy algorithm proposed by Wan et al. yields a rho H(delta)-approximation for an integer-valued submodular function f, where rho is the curvature of submodular cost function c, delta is the maximum value of f over all singletons and H(delta) is the delta-th harmonic number (Wan et al. in Comput Optim Appl 45(2):463-474). In this paper, we first extend MIN-SCSC to Minimum Submodular Cost Nonsubmodular Cover problem and analyze the performances of the widely used greedy algorithm for integer-valued and fraction-valued potential functions respectively. In addition, we also study MIN-SCSC with fraction-valued potential functions, with a new analysis of the performance ratio of the greedy algorithm, improving upon the result of Wan et al. (2010).

关键词： greedy algorithm Performance ratio Submodular function Submodular cover

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A greedy Galerkin method to efficiently select sensors for linear dynamical systems

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LINEAR ALGEBRA AND ITS APPLICATIONS 2023年 679卷 275-304页

作者： Kouri, Drew P. Hua, Zuhao Udell, Madeleine Sandia Natl Labs Optimizat & Uncertainty Quantificat Albuquerque NM 87185 USA Cornell Univ Phys Ithaca NY 14850 USA Stanford Univ Management Sci & Engn Stanford CA 94305 USA

A key challenge in inverse problems is the selection of sensors to gather the most effective data. In this paper, we consider the problem of inferring the initial condition to a linear dy-namical system and develop an efficient control-theoretical approach for greedily selecting sensors. Our method employs a Galerkin projection to reduce the size of the inverse problem, resulting in a computationally efficient algorithm for sensor selection. As a byproduct of our algorithm, we obtain a pre -conditioner for the inverse problem that enables the rapid recovery of the initial condition. We analyze the theoretical performance of our greedy sensor selection algorithm as well as the performance of the associated preconditioner. Finally, we verify our theoretical results on various inverse problems involving partial differential equations. (c) 2023 Elsevier Inc. All rights reserved.

关键词： Sensor placement Linear dynamics Gramian Observability Lyapunov equation Preconditioning Galerkin method greedy algorithm Inverse problems Optimal control Submodularity

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Real-Time Prediction for Future Profile of Car Travel Based on Statistical Data and greedy algorithm

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SICE Journal of Control, Measurement, and System Integration 2015年第1期8卷 7-14页

作者： Takuma Yamaguchi Akihiko Kawashima Akira Ito Shinkichi Inagaki Tatsuya Suzuki Nagoya University Nagoya UniversityDENSO CORPORATION Nagoya UniversityJST CREST

Electric Vehicles (EVs) and Plug-in Hybrid Vehicles (PHVs) are expected to be used as power-storage devices in Home Energy Management Systems (HEMSs) due to their high capacity batteries. When planning the charge and discharge of the vehicle's battery by the HEMS, the expected profile of car's departures and arrivals for home is required. This paper presents a real-time estimation method for the Profile of Departure and Arrival Times (PDATs) over one day. The PDAT prediction problem is formulated as a maximum-likelihood estimation problem with the probability based on the Statistics of Departure and Arrival Times (SDAT). In the proposed method, the maximum-likelihood estimation problem is decomposed to optimization subproblems, each of which is solved by a greedy algorithm. Due to this decomposition, it is possible to find a plausible solution of the PDAT with a reasonable computational cost. The utility of the proposed method is evaluated by numerical experiments with SDATs derived from the real data of three subjects who use gasoline vehicles.

关键词： profile of the departure and arrival time greedy algorithm maximum-likelihood estimation energy management system

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greedy Guarantees for Non-submodular Function Maximization Under Independent System Constraint with Applications

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2023年第2期196卷 516-543页

作者： Shi, Majun Yang, Zishen Wang, Wei Xi An Jiao Tong Univ Sch Math & Stat 28 Xianning West Rd Xian 710049 Peoples R China

We study the problems of maximizing a monotone non-submodular function subject to two types of constraints, either an independent system constraint or ap-matroidconstraint. These problems often occur in the context of combinatorial optimization, operations research, economics and especially, machine learning and data science. Using the generalized curvature alpha and the submodularity ratio gamma or the diminishingreturns ratio xi, we analyze the performances of the widely used greedy algorithm, which yields theoretical approximation guarantees of 1/alpha[1-(1-alpha gamma/K)(k)]and xi/p+alpha xi for the two types of constraints, respectively, where k ,K are, respectively, the min-imum and maximum cardinalities of a maximal independent set in the independent system, and p is the minimum number of matroids such that the independent sys-tem can be expressed as the intersection of p matroids. When the constraint is acardinality one, our result maintains the same approximation ratio as that in Bian etal. (Proceedings of the 34th international conference on machine learning, pp 498-507, 2017);however, the proof is much simpler owning to the new definition of the greedy curvature. In the case of a single matroid constraint, our result is competitive compared with the existing ones in Chen et al. (Proceedings of the 35th international conference on machine learning, pp 804-813, 2018) and Gatmiry and Rodriguez (Non-submodular function maximization subject to a matroid constraint, with applications,***:1811.07863v4). In addition, we bound the generalized curvature, thesubmodularity ratio and the diminishing returns ratio for several important real-worldapplications. Computational experiments are also provided supporting our analyses.

关键词： Non-submodular function Independent system p-matroid greedy algorithm

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Analysis and comparison of two classical greedy algorithms for minimum spanning tree

Analysis and comparison of two classical greedy algorithms f...

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作者： Xinyi Yu Hebei University of technology

The total weight of the minimum spanning is the smallest in the connected *** can be used to solve many practical problems in urban ***'s algorithm and Kruskal's algorithm are greedy algorithms for solving the minimum spanning tree *** they make greedy choices in different *** paper focuses on two greedy algorithms for solving the minimum spanning tree *** author will evaluate each algorithm's complexity and determine their most suitable condition as *** author compares the running process of the two algorithms and analyzes the relationship between their algorithm complexity and the number of edges,which can describe the sparsity of the *** result shows that Kruskal's complexity is related to the number of edges,so it is better for sparse ***'s complexity is related to the number of vertices,so it is better at analyzing connected graphs with lots of vertices,that is,dense *** a consequence,Prim's algorithm is better for dense graphs.

关键词： minimum spanning tree greedy algorithm Kruskal prim connected graph

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Adaptive greedy algorithms based on parameter-domain decomposition and reconstruction for the reduced basis method

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2020年第23期121卷 5426-5445页

作者： Jiang, Jiahua Chen, Yanlai Virginia Tech Univ Dept Math Blacksburg VA USA Univ Massachusetts Dept Math Dartmouth MA 02747 USA

The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy algorithm repeatedly scanning the training set, a fine discretization of the parameter domain, to identify the next dimension of the parameter-induced solution manifold along which we expand the surrogate solution space. Although successfully applied to problems with fairly high parametric dimensions, the challenge is that this scanning cost dominates the offline cost due to it being proportional to the cardinality of the training set which is exponential with respect to the parameter dimension. In this work, we review three recent attempts in effectively delaying this curse of dimensionality, and propose two new hybrid strategies through successive refinement and multilevel maximization of the error estimate over the training set. All five offline-enhanced methods and the original greedy algorithm are tested and compared on two types of problems: the thermal block problem and the geometrically parameterized Helmholtz problem.

关键词： greedy algorithm reduced basis method

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A Landmark Selection Method for L-Isomap Based on greedy algorithm and its Application

A Landmark Selection Method for L-Isomap Based on Greedy Alg...

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IEEE Annual Conference on Decision and Control

作者： Hao Shi Baoqun Yin Xiaofeng Zhang Yu Kang Yingke Lei Department of Automation University of Science and Technology of China 230027 Hefei China Electronic Engineering Institute 230027 Hefei China

ISBN: (纸本)9781479978878

Isometric feature mapping (Isomap) is a widely-used nonlinear dimensionality reduction method, but it suffers from high computational complexity. L-Isomap is a variant of Isomap which is faster than Isomap. In this algorithm, a subset of points are chosen out of the total data points as landmark points so as to simplify the embedding computation. In this paper, we propose a novel landmark selection method for L-Isomap based on a greedy algorithm. Experiments performed on synthetic and physical data sets validate the effectiveness of the proposed method. Internet traffic matrix has been an effective model to analyzing the Internet. However, the Internet traffic matrix data usually possesses high dimensionality. In this paper, we apply the improved L-Isomap to the real Internet traffic matrix data to investigate its low-dimensional features. The experiment results show that the Internet traffic matrix has a small intrinsic dimension and there indeed exists a low-dimensional manifold structure.

关键词： greedy algorithm flow matrix landmarks Internets total Information selection methods

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Rank-Based greedy Model Averaging for High-Dimensional Survival Data

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2023年第544期118卷 2658-2670页

作者： He, Baihua Ma, Shuangge Zhang, Xinyu Zhu, Li-Xing Univ Sci & Technol China Sch Management Int Inst Finance Hefei Peoples R China Yale Univ Dept Biostat New Haven CT USA Chinese Acad Sci Acad Math & Syst Sci Beijing Peoples R China Beijing Normal Univ Zhuhai Ctr Stat & Data Sci Zhuhai Peoples R China Hong Kong Baptist Univ Dept Math Kowloon Tong Hong Kong Peoples R China

Model averaging is an effective way to enhance prediction accuracy. However, most previous works focus on low-dimensional settings with completely observed responses. To attain an accurate prediction for the risk effect of survival data with high-dimensional predictors, we propose a novel method: rank-based greedy (RG) model averaging. Specifically, adopting the transformation model with splitting predictors as working models, we doubly use the smooth concordance index function to derive the candidate predictions and optimal model weights. The final prediction is achieved by weighted averaging all the candidates. Our approach is flexible, computationally efficient, and robust against model misspecification, as it neither requires the correctness of a joint model nor involves the estimation of the transformation function. We further adopt the greedy algorithm for high dimensions. Theoretically, we derive an asymptotic error bound for the optimal weights under some mild conditions. In addition, the summation of weights assigned to the correct candidate submodels is proven to approach one in probability when there are correct models included among the candidate submodels. Extensive numerical studies are carried out using both simulated and real datasets to show the proposed approach's robust performance compared to the existing regularization approaches. Supplementary materials for this article are available online.

关键词： greedy algorithm High-dimensional survival data Model averaging Prediction Smooth concordance index

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