Explore the vast range of titles available.

Greedy algorithms are a fundamental class of mathematics and computer science algorithms, defined by their iterative approach of making locally optimal decisions to approximate global optima. In this review, we focus on two greedy algorithms. First, we examine the relaxed greedy algorithm in the context of dictionaries in Hilbert spaces, analyzing the optimality of the definition of this algorithm. Next, we provide a general overview of the thresholding greedy algorithm and the Chebyshev thresholding greedy algorithm, with particular attention to their applications to bases in p -Banach spaces with 0 < p ≤ 1 . In both cases, we conclude by posing several questions for future research.

We investigate the prediction capability of the orthogonal greedy algorithm (OGA) in high-dimensional regression models with dependent observations. The rates of convergence of the prediction error of OGA are obtained under a variety of sparsity conditions. To prevent OGA from overfitting, we introduce a high-dimensional Akaike’s information criterion (HDAIC) to determine the number of OGA iterations. A key contribution of this work is to show that OGA, used in conjunction with HDAIC, can achieve the optimal convergence rate without knowledge of how sparse the underlying high-dimensional model is.

Sentiment analysis is crucial in various systems such as opinion mining and predicting. Considerable research has been done to analyze sentiment using various machine learning techniques. However, the high error rates in these studies can reduce the entire system’s efficiency. We introduce a novel big data and machine learning technique for evaluating sentiment analysis processes to overcome this problem. The data are collected from a huge volume of datasets, helpful in the effective analysis of systems. The noise in the data is eliminated using a preprocessing data mining concept. From the cleaned sentiment data, effective features are selected using a greedy approach that selects optimal features processed by an optimal classifier called cat swarm optimization-based long short-term memory neural network (CSO-LSTMNN). The classifiers analyze sentiment-related features according to cat behavior, minimizing error rate while examining features. This technique helps improve system efficiency, analyzed using experimental results of error rate, precision, recall, and accuracy. The results obtained by implementing the greedy feature and CSO-LSTMNN algorithm and the particle swarm optimization (PSO) algorithm are compared; CSO-LSTMNN outperforms PSO in terms of increasing accuracy and decreasing error rate.

The combination of unmanned aerial vehicles (UAVs) and mobile edge computing (MEC) technology breaks through the limitations of traditional terrestrial communications. The effective line-of-sight channel provided by UAVs can greatly improve the communication quality between edge servers and mobile devices (MDs). To further enhance the Quality-of-Service (QoS) of MEC systems, a multi-UAV-enabled MEC system model is designed. In the proposed model, UAVs are regarded as edge servers to offer computing services for MDs, aiming to minimize the average task response time by jointly optimizing UAV deployment and computation offloading. Based on the problem definition, a two-layer joint optimization method (PSO-GA-G) is proposed. First, the outer layer utilizes a Particle Swarm Optimization algorithm combined with Genetic Algorithm operators (PSO-GA) to optimize UAV deployment. Next, the inner layer adopts a greedy algorithm to optimize computation offloading. The extensive simulation experiments verify the feasibility and effectiveness of the proposed PSO-GA-G. The results show that the PSO-GA-G can achieve a lower average task response time than the other three baselines.

This study introduces a greedy algorithm for deriving decision rules from decision tree ensembles, targeting enhanced interpretability and generalization in distributed data environments. Decision rules, known for their transparency, provide an accessible method for knowledge extraction from data, facilitating decision-making processes across diverse fields. Traditional decision tree algorithms, such as CART and ID3, are employed to induce decision trees from bootstrapped datasets, which represent distributed data sources. Subsequently, a greedy algorithm is applied to derive decision rules that are true across multiple decision trees. Experiments are performed, taking into account knowledge representation and discovery perspectives. They show that, as the value of α, 0≤α<1, increases, shorter rules are obtained, and also it is possible to improve the classification accuracy of rule-based models.

In this paper, we continue the study of Lebesgue-type inequalities for greedy algorithms. We introduce the notion of strong partially greedy Markushevich bases and study the Lebesgue-type parameters associated with them. We prove that this property is equivalent to that of being conservative and quasi-greedy, extending a similar result given in Dilworth et al. (Constr Approx 19:575–597, 2003) for Schauder bases. We also give a characterization of 1-strong partial greediness, following the study started in Albiac and Ansorena (Rev Matem Compl 30(1):13–24, 2017), Albiac and Wojtaszczyk (J Approx Theory 138:65–86, 2006).

Herein, a combined multipoint picking scheme was proposed, and the sizes of the end of the bud picker were selectively designed. Firstly, the end of the bud picker was abstracted as a fixed-size picking box, and it was assumed that the tea buds in the picking box have a certain probability of being picked. Then, the picking box coverage and the greedy algorithm were designed to make as few numbers of picking box set as possible to cover all buds to reduce the numbers of picking. Furthermore, the Graham algorithm and the minimum bounding box were applied to fine-tune the footholds of each picking box in the optimal coverage picking box set, so that the buds were concentrated in the middle of the picking boxes as much as possible. Moreover, the geometric center of each picking box was taken as a picking point, and the ant colony algorithm was used to optimize the picking path of the end of the bud picker. Finally, by analyzing the influence of several parameters on the picking performance of the end of the bud picker, the optimal sizes of the picking box were calculated successfully under different conditions. The experimental results showed that the average picking numbers of the combined multipoint picking scheme were reduced by 31.44%, the shortest picking path was decreased by 11.10%, and the average consumed time was reduced by 50.92% compared to the single-point picking scheme. We believe that the proposed scheme can provide key technical support for the subsequent design of intelligent bud-picking robots.

In this research, we are studying the scheduling problem of a professional ball manufacturing company in Taiwan. The problem is related to scheduling a flexible flow shop that includes setups with the aim of minimizing total weighted tardiness. We first present a mathematical model for the studied problem. Next, we conduct data processing and generate initial solutions. This involves extracting ordering data from the company, aggregating the total demand based on the product types of all orders, and splitting the demand into sublots. For production purposes, each subplot will be matched with a production lot, abbreviated as PLot. We assign a score to each order based on customer priority, order amount, due date, and order profitability. This has allowed us to propose a strategy in which orders compete for production priority based on their scores. We also proposed four dispatching rules to assign PLots to machines based on their production priority. Finally, we have suggested an iterated greedy algorithm with mutation (IGm algorithm) to improve the initial solutions obtained through dispatching rules. Extensive computational runs based on real data have been conducted to compare the performances of the proposed orders competing for production priority, the four dispatching rules, and the IGm algorithm with sequences generated by the EDD (Earliest Due Date) and WEDD (Weighted Earliest Due Date) rules. Computational results demonstrate that the proposed orders competing for production priority, along with the dispatching rules and the IGm algorithm, are effective in providing promising results for the scheduling problem.

The autonomous task success of an unmanned aerial vehiclel (UAV) or its military specialization called the unmanned combat aerial vehicle (UCAV) has a direct relationship with the planned path. However, planning a path for a UAV or UCAV system requires solving a challenging problem optimally by considering the different objectives about the enemy threats protecting the battlefield, fuel consumption or battery usage and kinematic constraints on the turning maneuvers. Because of the increasing demands to the UAV systems and game-changing roles played by them, developing new and versatile path planning algorithms become more critical and urgent. In this study, a greedy algorithm named as the Back-and-Forth (BaF) was designed and introduced for solving the path planning problem. The BaF algorithm gets its name from the main strategy where a heuristic approach is responsible to generate two predecessor paths, one of which is calculated from the start point to the target point, while the other is calculated in the reverse direction, and combines the generated paths for utilizing their advantageous line segments when obtaining more safe, short and maneuverable path candidates. The performance of the BaF was investigated over three battlefield scenarios and twelve test cases belonging to them. Moreover, the BaF was integrated into the workflow of a well-known meta-heuristic, artificial bee colony (ABC) algorithm, and detailed experiments were also carried out for evaluating the possible contribution of the BaF on the path planning capabilities of another technique. The results of the experiments showed that the BaF algorithm is able to plan at least promising or generally better paths with the exact consistency than other tested meta-heuristic techniques and runs nine or more times faster as validated through the comparison between the BaF and ABC algorithms. The results of the experiments further proved that the integration of the BaF boosts the performance of the ABC and helps it to outperform all of fifteen competitors for nine of twelve test cases.

Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality of the physical and velocity/angular variables and the fact that the problem is multiscale in nature. Leveraging the existence of a hidden low-rank structure hinted by the diffusive limit, in this work, we design and test the angular-space reduced order model for the linear radiative transfer equation, the first such effort based on the celebrated reduced basis method (RBM). Our method is built upon a high-fidelity solver employing the discrete ordinates method in the angular space, an asymptotic preserving upwind discontinuous Galerkin method for the physical space, and an efficient synthetic accelerated source iteration for the resulting linear system. Addressing the challenge of the parameter values (or angular directions) being coupled through an integration operator, the first novel ingredient of our method is an iterative procedure where the macroscopic density is constructed from the RBM snapshots, treated explicitly and allowing a transport sweep, and then updated afterwards. A greedy algorithm can then proceed to adaptively select the representative samples in the angular space and form a surrogate solution space. The second novelty is a least squares density reconstruction strategy, at each of the relevant physical locations, enabling the robust and accurate integration over an arbitrarily unstructured set of angular samples toward the macroscopic density. Numerical experiments indicate that our method is effective for computational cost reduction in a variety of regimes.