Iterative Algorithm Research Articles

Total Least Squares Estimation in Hedonic House Price Models

In real estate valuation using the Hedonic Price Model (HPM) estimated via Ordinary Least Squares (OLS) regression, subjectivity and measurement errors in the independent variables violate the Gauss–Markov theorem assumption of a non-random coefficient matrix, leading to biased parameter estimates and incorrect precision assessments. In this contribution, the Errors-in-Variables model equipped with Total Least Squares (TLS) estimation is proposed to address these issues. It fully considers random errors in both dependent and independent variables. An iterative algorithm is provided, and posterior accuracy estimates are provided to validate its effectiveness. Monte Carlo simulations demonstrate that TLS provides more accurate solutions than OLS, significantly improving the root mean square error by over 70%. Empirical experiments on datasets from Boston and Wuhan further confirm the superior performance of TLS, which consistently yields a higher coefficient of determination and a lower posterior variance factor, which shows its more substantial explanatory power for the data. Moreover, TLS shows comparable or slightly superior performance in terms of prediction accuracy. These results make it a compelling and practical method to enhance the HPM.

Availability simulation and transfer prediction for bike sharing systems based on discrete event simulation

To improve the operational efficiency of Bike Sharing Systems (BSSs), predicting users’ real demand plays an essential role. Previous demand predictions have heavily relied on the historical rides (explicit demand) recorded in the BSS management information system. Since there are no bikes available for rent, users' unfulfilled ride expectations (implicit demand) cannot be captured in the system. This paper presents an approach for simulating station-level availability and predicting transfers for BSS. Firstly, the (s,S) inventory strategy combined with an iterative optimization-seeking algorithm to improve the existing simulation model. Then, the K-means method is used to cluster the similarity among stations. The transfer prediction uses source data to aid the learning of target data quickly. Finally, a real case study is conducted to validate the practicability. The simulation experiment indicates that it is possible to estimate the maximum percentage of underestimation of real demand at a station. Through regression analysis, this paper investigates the complex nonlinear relationship between the percentage underestimation of real demand and the easily accessible implicit demand influencing factors. In practical applications, managers can use this method to optimize the number of bikes placed for BSSs.

Estimation of the Living Vegetation Volume (LVV) for Individual Urban Street Trees Based on Vehicle-Mounted LiDAR Data

The living vegetation volume (LVV) can accurately describe the spatial structure of greening trees and quantitatively represent the relationship between this greening and its environment. Because of the mostly line shape distribution and the complex species of street trees, as well as interference from artificial objects, current LVV survey methods are normally limited in their efficiency and accuracy. In this study, we propose an improved methodology based on vehicle-mounted LiDAR data to estimate the LVV of urban street trees. First, a point-cloud-based CSP (comparative shortest-path) algorithm was used to segment the individual tree point clouds, and an artificial objects and low shrubs identification algorithm was developed to extract the street trees. Second, a DBSCAN (density-based spatial clustering of applications with noise) algorithm was utilized to remove the branch point clouds, and a bottom-up slicing method combined with the random sampling consistency iterative method algorithm (RANSAC) was employed to calculate the diameters of the tree trunks and obtain the canopy by comparing the variation in trunk diameters in the vertical direction. Finally, an envelope was fitted to the canopy point cloud using the adaptive AlphaShape algorithm to calculate the LVVs and their ecological benefits (e.g., O2 production and CO2 absorption). The results show that the CSP algorithm had a relatively high overall accuracy in segmenting individual trees (overall accuracy = 95.8%). The accuracies of the tree height and DBH extraction based on vehicle-mounted LiDAR point clouds were 1.66~3.92% (rRMSE) and 4.23~15.37% (rRMSE), respectively. For the plots on Zijin Mountain, the LVV contribution by the maple poplar was the highest (1049.667 m3), followed by the sycamore tree species (557.907 m3), and privet’s was the lowest (16.681 m3).

Optimization of Energy Efficiency for Federated Learning over Unmanned Aerial Vehicle Communication Networks

Federated learning (FL) is considered a promising machine learning technique that has attracted increasing attention in recent years. Instead of centralizing data in one location for training a global model, FL allows the model training to occur on user devices, such as smartphones, IoT devices, or local servers, thereby respecting data privacy and security. However, implementing FL in wireless communication faces a significant challenge due to the inherent unpredictability and constant fluctuations in channel characteristics. A key challenge in implementing FL over wireless communication lies in optimizing energy efficiency. This holds significant importance, especially considering user devices with restricted power resources. On the other hand, unmanned aerial vehicle (UAV) technologies present a cost-effective solution owing to flexibility and mobility compared to terrestrial base stations. Consequently, the deployment of UAV communication in FL is viewed as a potential approach to deal with the energy efficiency challenge. In this paper, we address the problem of minimizing the total energy consumption of all user equipment (UE) during the training phase of FL over a UAV communication network. Our proposed system facilitates UE to operate concurrently at the same time and frequency, thereby improving bandwidth utilization efficiently. In this paper, we address the problem of minimizing the total energy consumption during the training phase of FL over a UAV communication network. To deal with the proposed nonconvex problem, we propose a novel alternating optimization approach by dividing the problem into two suboptimal problems. We then develop iterative algorithms based on the inner approximation method, yielding at least one locally optimal solution. The numerical results demonstrate the superiority of the proposed algorithm in solving the proposed problem compared to other benchmark algorithms, particularly in determining the optimal trajectory of the UAVs. In addition, we conduct extensive experiments to evaluate how different parameter settings affect performance after implementing the proposed optimization approaches for deploying FL within the UAV communication system. These analyses yield valuable insights into the comparative effectiveness of the proposed optimization algorithms concerning overall energy consumption reduction.

Iterative algorithm to the generalized coupled Sylvester‐transpose matrix equations with application in robust and minimum norm observer design of linear systems

AbstractThis article consider a class of generalized coupled Sylvester‐transpose matrix equations which play an important role in control and systems theory. Based on the Jacobi iterative algorithm, the full‐row rank accelerated Jacobi gradient based iterative (RRAJGI) algorithm and the full‐column rank accelerated Jacobi gradient based iterative (CRAJGI) algorithm are proposed. By using the Frobenius norm of matrix and the trace function of matrix, the convergence of the algorithms are proved. The results show that the new algorithms are convergent for arbitrary initial matrices under the convergence number satisfies appropriate conditions. Numerical examples show that RRAJGI algorithm and CRAJGI algorithm have the advantages of faster convergence speed and higher convergence accuracy than other existing algorithms. Finally, an application example for robust and minimum norm observer design of linear systems is given.

Investigation of a potential upstream harmonization based on image appearance matching to improve radiomics features robustness: a phantom study

Objective. Radiomics is a promising valuable analysis tool consisting in extracting quantitative information from medical images. However, the extracted radiomics features are too sensitive to variations in used image acquisition and reconstruction parameters. This limited robustness hinders the generalizable validity of radiomics-assisted models. Our aim is to investigate a possible harmonization strategy based on matching image quality to improve feature robustness. Approach. We acquired CT scans of a phantom with two scanners across different dose levels and percentages of Iterative Reconstruction algorithms. The detectability index was used as a comprehensive task-based image quality metric. A statistical analysis based on the Intraclass Correlation Coefficient was performed to determine if matching image quality/appearance could enhance the robustness of radiomics features extracted from the phantom images. Additionally, an Artificial Neural Network was trained on these features to automatically classify the scanner used for image acquisition. Main results. We found that the ICC of the features across protocols providing a similar detectability index improves with respect to the ICC of the features across protocols providing a different detectability index. This improvement was particularly noticeable in features relevant for distinguishing between scanners. Significance. This preliminary study demonstrates that a harmonization based on image quality/appearance matching could improve radiomics features robustness and heterogeneous protocols can be used to obtain a similar image appearance in terms of the detectability index. Thus protocols with a lower dose level could be selected to reduce the amount of radiation dose delivered to the patient and simultaneously obtain a more robust quantitative analysis.

Emergency control of firefighting vehicles based on distributed integer programming

Fire-related emergency vehicle scheduling has always been an important part of autonomous vehicle emergency management. To maintain the fire safety of buildings and reduce the transportation loss of emergency resources, this paper constructs a multi-objective integer planning model for fire emergency resource scheduling, which minimizes the time spent in the transportation of fire materials and considers the transportation needs of potential fire vehicles. The fixed-point iterative algorithm is realized and optimized, and distributed computing is adopted to improve the solving speed. In this paper, the comparison and simulation experiments with Branch and Bound, improved particle swarm optimization and other algorithms are carried out. The results show that the model and the algorithm can effectively deal with the fire emergency vehicle scheduling problem under different simulated fires and multiple fires occurring at the same time, and have certain advantages in numerical stability and convergence speed.

Energy-efficient resource allocation for bidirectional wireless power and information transfer over interference channels

Energy efficiency is an important performance metric for the sustainable operation of energy-limited communication networks. This study investigates an energy-efficient resource allocation strategy to maximize the energy efficiency of wireless-powered bidirectional communication over interference channels. The receivers in the system harvest energy and decode information simultaneously using a time switching or power splitting policy from data signals sent by transmitters in the forward link. The harvested energy is subsequently used to send response signals back to the transmitters in the backward link. Our objective is to jointly optimize the transmit power of the transmitters and the energy harvesting ratio of the receivers to maximize the energy efficiency of the entire system while maintaining the minimum required data rates in both the forward and backward links. Considering the non-convexity and NP-hardness of this optimization problem, we first apply nonlinear fractional programming and a dual method to derive an analytical expression for each control parameter and then propose an iterative algorithm to find suboptimal solutions with low computational complexity. The simulation results show that the proposed algorithm adjusts both the transmit power and energy harvesting ratio adaptively considering the co-channel interference and thus achieves near-optimal energy efficiency performance within a short computation time.

Smooth morphing of immersed spherical curves and application to ruled surfaces

In this paper, we realize a rapid, smooth iterative morphing algorithm between two immersed and closed spherical curves of arbitrary turning numbers. By compensating in turning numbers, we linearly interpolate between geodesic curvatures and the side lengths of their accurate spherical polygons approximation. Our algorithm is essentially based on a geometrical closure condition for a flow of spherical polygons involving the variation of both sides and exterior angles. A curvature smoothing flow using discrete geodesic curvature is adopted for smooth curve generation. To demonstrate the good properties of the method, a morphing of spherical curves and ruled surfaces is illustrated.

A gradient-descent iterative learning control algorithm for a non-linear system

Original iterative learning control (OILC) has been proved a powerful tool in dealing with the model-free control problems by repetitively corrections based on the control error. However, the steady-state error under widely-used proportional-type original iterative learning control (P-type OILC) is highly corresponded to the proportional learning gain, making the algorithm parameter-determined. Therefore, a new gradient-descent iterative learning control (GDILC) algorithm is proposed to achieve a parameter-free approach by simulating the gradient-descent process. First, GDILC problem is formulated mathematically. Next, the idea of the algorithm is proposed, the analyses of the convergence and the steady-state error are conducted and the algorithm is implemented. GDILC will generate a random correction with a gradient-descent upper bound, rather than a correction proportional to the error in P-type OILC. Finally, illustrative and application simulations are conducted to validate the algorithm. Results show that the algorithm will be convergent after adequate iterations under proper corrections. The steady-state error will be less affected by the algorithm parameters under GDILC than that under OILC.

Optimal bipartite consensus control for heterogeneous unknown multi-agent systems via reinforcement learning

This study focuses on addressing optimal bipartite consensus control (OBCC) problems in heterogeneous multi-agent systems (MASs) without relying on the agents' dynamics. Motivated by the need for model-free and optimal consensus control in complex MASs, a novel distributed scheme utilizing reinforcement learning (RL) is proposed to overcome these challenges. The MAS network is randomly partitioned into sub-networks where agents collaborate within each subgroup to attain tracking control and ensure convergence of positions and speeds to a common value. However, agents from distinct subgroups compete to achieve diverse tracking objectives. Furthermore, the heterogeneous MASs considered have unknown first and second-order dynamics, adding to the complexity of the problem. To address the OBCC issue, the policy iteration (PI) algorithm is used to acquire solutions for discrete-time Hamilton-Jacobi-Bellman (HJB) equations while implementing a data-driven actor-critic neural network (ACNN) framework. Ultimately, the accuracy of our proposed approach is confirmed through the presentation of numerical simulations.

Error estimates for a mixed finite element method for the Maxwell’s transmission eigenvalue problem

In this paper, we analyze a numerical method combining the Ciarlet-Raviart mixed finite element formulation and an iterative algorithm for the Maxwell’s transmission eigenvalue problem. The eigenvalue problem is first written as a nonlinear quad-curl eigenvalue problem. Then the real transmission eigenvalues are proved to be the roots of a non-linear function. They are the generalized eigenvalues of a related linear self-adjoint quad-curl eigenvalue problem. These generalized eigenvalues are computed by a mixed finite element method. We derive the error estimates using the spectral approximation of compact operators, the theory of mixed finite element method for quad-curl problems, and the derivatives of eigenvalues.

An iterative algorithm to simultaneously retrieve aerosol extinction and effective radius profiles using CALIOP

Abstract. The Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) on board the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) satellite has been widely used in climate and environment studies to obtain the vertical profiles of atmospheric aerosols. To retrieve the vertical profile of aerosol extinction, the CALIOP algorithm assumes column-averaged lidar ratios based on a clustering of aerosol optical properties measured at surface stations. On one hand, these lidar ratio assumptions may not be appropriate or representative at certain locations. One the other hand, the two-wavelength design of CALIOP has the potential to constrain aerosol size information, which has not been considered in the operational algorithm. In this study, we present a modified inversion algorithm to simultaneously retrieve aerosol extinction and effective radius profiles using two-wavelength elastic lidars such as CALIOP. Specifically, a lookup table is built to relate the lidar ratio with the Ångström exponent calculated using aerosol extinction at the two wavelengths, and the lidar ratio is then determined iteratively without a priori assumptions. The retrieved two-wavelength extinction at each layer is then converted to the particle effective radius assuming a lognormal distribution. The algorithm is tested on synthetic data, Raman lidar measurements and then finally the real CALIOP backscatter measurements. Results show improvements over the CALIPSO operational algorithm by comparing with ground-based Raman lidar profiles.

A Nonlinear Quantile Regression for Accelerated Destructive Degradation Testing Data

Traditional regression approaches to accelerated destructive degradation test (ADDT) data have modeled the mean curve as representative. However, maximum likelihood estimates (MLEs) of the mean model are likely to be biased when the data are non-Gaussian or highly skewed. The median model can be an alternative for skewed degradation data. In this work, we introduce a nonlinear quantile regression (QR) approach for estimating quantile curves of ADDT data. We propose an iterative QR algorithm that uses the generalized expectation-maximization (GEM) framework to estimate the parameters of the nonlinear QR ADDT model, based on the asymmetric Laplace distribution to accommodate non-Gaussian and skewed errors. Using the asymptotic properties of the QR parameter estimates, we estimate variance-covariance matrix for the τ th QR parameters using order statistics and bootstrap methods. We propose a new prediction method of the quantile of the failure-time distribution in the normal use condition. Confidence intervals for the quantiles of the failure-time distribution are constructed using the parametric bootstrap method. The proposed model is illustrated using an industrial application and compared with the existing model. Various quantile curve estimates derived using the QR ADDT model provide a more flexible modeling framework than the traditional mean ADDT modeling approach.

Dual-learning Multi-hop Nonnegative Matrix Factorization for community detection

As an important branch of network science, community detection has garnered significant attention. Among various community detection methods, nonnegative matrix factorization (NMF)-based community detection approaches have become a popular research topic. However, most NMF-based methods overlook the network’s multi-hop information, let alone the community detection results specific to each hop of the network. In this paper, we propose Dual-learning Multi-hop NMF (DL-MHNMF), a method that considers not only the multi-hop connectivity between two nodes but also factors in the shared results across multiple hops and the impact of differences in the specific results at each hop on the shared outcomes. An efficient iterative optimization algorithm with guaranteed theoretical convergence is proposed for solving DL-MHNMF. Methodologically, by iteratively removing the specific results during the optimization process of DL-MHNMF, we achieve enhanced detection accuracy, which is also verified by subsequent experiments. Specifically, we compare fourteen algorithms on eleven publicly available datasets, and experimental results show that our algorithm outperforms most state-of-the-art methods. The source code is availiable at https://github.com/bx20000827/DL-MHNMF.git.

Learning to Optimize Contextually Constrained Problems for Real-Time Decision Generation

The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities. In this paper, we combine ideas from both fields to address the problem of learning to generate decisions to instances of optimization problems with potentially nonlinear or nonconvex constraints where the feasible set varies with contextual features. We propose a novel framework for training a generative model to produce provably optimal decisions by combining interior point methods and adversarial learning, which we further embed within an iterative data generation algorithm. To this end, we first train a classifier to learn feasibility and then train the generative model to produce optimal decisions to an optimization problem using the classifier as a regularizer. We prove that decisions generated by our model satisfy in-sample and out-of-sample optimality guarantees. Furthermore, the learning models are embedded in an active learning loop in which synthetic instances are iteratively added to the training data; this allows us to progressively generate provably tighter optimal decisions. We investigate case studies in portfolio optimization and personalized treatment design, demonstrating that our approach yields advantages over predict-then-optimize and supervised deep learning techniques, respectively. In particular, our framework is more robust to parameter estimation error compared with the predict-then-optimize paradigm and can better adapt to domain shift as compared with supervised learning models. This paper was accepted by Chung Piaw Teo, optimization. Funding: This work was supported in part by the Natural Sciences and Engineering Research Council of Canada. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2020.03565 .

On cost-efficient parallel iterative solvers for 3D frequency-domain seismic multisource viscoelastic anisotropic wave modeling

Solving large sparse linear systems in 3D frequency-domain seismic wave modeling, especially in viscoelastic anisotropic media, poses significant challenges due to the increasing number of discrete moduli and nonzero elements in the linear system matrix. The computational load surpasses that of acoustic or viscoacoustic media, making it even more challenging when dealing with multisource problems. Popular scientific tools for solving a linear system, such as multifrontal massively parallel sparse direct solver (MUMPS), structured matrix package (STRUMPACK), and portable extensible toolkit for scientific computation (PETSc), can be used, but their applicability to our specific problem has not been comprehensively evaluated. Our study aims to tackle the challenges in solving large, sparse, complex-valued symmetric linear systems with multiple right-hand side vectors for 3D frequency-domain seismic wave modeling. We have adopted the preconditioned conjugate gradient iterative algorithms as the foundation for our research, introducing two highly cost-effective parallel iterative solvers: the parallel symmetric successive overrelaxation conjugate gradient (P-SSORCG) and the parallel incomplete Cholesky conjugate gradient (P-ICCG). These novel solvers are subjected to a comprehensive comparative analysis against well-established scientific tools, such as MUMPS, STRUMPACK, and PETSc, in the context of 3D frequency-domain seismic wave modeling. We show their promising performances in a practical 3D SEG/EAGE overthrust model and demonstrate that the grouped P-SSORCG offers an efficient alternative to parallel direct solvers, particularly in situations wherein computational resources are limited.

An Iterative Algorithm for Maximal and Minimal Solutions of a Class Matrix Equations

In the paper, the peak solutions of a class equation is studied, the peak solutions are the maximal and minimal solutions. There is an iterative algorithm given for the solutions of the class equation. First, the existence of the peak solutions of the class equations is obtained. Second, when the peak solutions exist, an iterative algorithm is established to converge to the peak solutions of the class equation. By an upper bound and a lower bound of the solutions of the equation solution as the initial matrix, the iterative algorithm of the paper converges to the peak solutions of the class equation. The convergence problem of the algorithm is proved by the mathematical induction in the paper. The above results are verified by the examples.

Generalized and Robust Least Squares Regression.

As a simple yet effective method, least squares regression (LSR) is extensively applied for data regression and classification. Combined with sparse representation, LSR can be extended to feature selection (FS) as well, in which l1 regularization is often applied in embedded FS algorithms. However, because the loss function is in the form of squared error, LSR and its variants are sensitive to noises, which significantly degrades the effectiveness and performance of classification and FS. To cope with the problem, we propose a generalized and robust LSR (GRLSR) for classification and FS, which is made up of arbitrary concave loss function and the l2,p -norm regularization term. Meanwhile, an iterative algorithm is applied to efficiently deal with the nonconvex minimization problem, in which an additional weight to suppress the effect of noises is added to each data point. The weights can be automatically assigned according to the error of the samples. When the error is large, the value of the corresponding weight is small. It is this mechanism that allows GRLSR to reduce the impact of noises and outliers. According to the different formulations of the concave loss function, four specific methods are proposed to clarify the essence of the framework. Comprehensive experiments on corrupted datasets have proven the advantage of the proposed method.

Towards robust fault detection for Takagi–Sugeno nonlinear systems

This paper addresses robust fault detection observer design for a class of discrete-time Takagi–Sugeno nonlinear systems. A novel design method is presented based on finite-frequency H−/H∞ indices and peak-to-peak analysis. The finite-frequency H− and H∞ indices are utilized to characterize fault sensitivity and disturbance robustness, respectively. The peak-to-peak analysis is used to derive a dynamic threshold. An iterative algorithm is further developed to reduce conservatism. Theoretical proof shows that the performance of the proposed method is not worse than some existing works. Simulation results demonstrate the validity and viability of the proposed method.