Convergence Of Algorithm Research Articles

Adaptive Nesterov momentum method for solving ill-posed inverse problems

Abstract Nesterov’s acceleration strategy is renowned in speeding up the convergence of gradient-based optimization algorithms and has been crucial in developing fast first order methods for well-posed convex optimization problems. Although Nesterov’s accelerated gradient method has been adapted as an iterative regularization method for solving ill-posed inverse problems, no general convergence theory is available except for some special instances. In this paper, we develop an adaptive Nesterov momentum method for solving ill-posed inverse problems in Banach spaces, where the step-sizes and momentum coefficients are chosen through adaptive procedures with explicit formulas. Additionally, uniform convex regularization functions are incorporated to detect the features of sought solutions. Under standard conditions, we establish the regularization property of our method when terminated by the discrepancy principle. Various numerical experiments demonstrate that our method outperforms the Landweber-type method in terms of the required number of iterations and the computational time.

A new method for recognizing geometric parameters of industrial robots

Intelligent algorithms that are commonly used to obtain errors in the geometric parameters of industrial robots have a low accuracy, easily fall into the local optimal solution, and involve complicated coding such that they are unsuitable for use in engineering. In this study, we first apply the D-H method to establish a model of error in industrial robots, and then use the set of errors in their geometric parameters as the objective function. Following this, we improve the accuracy of global optimization of the particle swarm optimization (PSO) algorithm by drawing on the wandering behavior of the wolf pack algorithm and hybridization behavior of the genetic algorithm. We balance the convergence of the PSO algorithm by using a linearly diminishing weight. This leads to an improved PSO algorithm that can accurately determine errors in the geometric parameters of industrial robots. We compared our improve PSO algorithm with commonly used particle swarm algorithms, and the results showed that the former had a higher accuracy of convergence on average. Moreover, the errors in the geometric parameters obtained by the improved PSO algorithm can enhance the accuracy of localization of errors in industrial robots.

Coordinate Partitioning for Difficult Euclidean Max-Sum Diversity Problems

Divide and Conquer: Solving the Euclidean Diversity Problem Through Coordinate Partitioning A common technique for solving difficult optimization problems is to break them into easier-to-manage pieces, yet it is rarely obvious how to do so. This is especially true for the Euclidean max-sum diversity problem, which becomes increasingly difficult as the number of coordinates grows despite the problem size remaining the same. In “Coordinate Partitioning for Difficult Euclidean Max-Sum Diversity Problems,” Spiers, Bui, and Loxton use an old result by Schoenberg to transform Euclidean distances into their squared counterparts, enabling a functional decomposition of the problem’s objective. The authors introduce novel partitioning strategies as well as a globally convergent cutting-plane algorithm, which can effectively solve high-dimension instances. They also present a new class of challenging instances characterized by locations on the surface of a hyperball.

An Optimization Design of Energy Consumption for Aluminum Smelting Based on a Multi-Objective Artificial Vulture Algorithm

In the process of regenerative aluminum smelting, the temperature of the furnace needs to be maintained between 700 and 850 by adjusting the setting parameters of the smelting furnace. The setting parameters are usually adjusted by manual work, and inaccuracies in manual operation can lead to wasted energy as well as unstable temperatures. Energy consumption and temperature stability are two conflicting objectives, which are difficult to find optimal parameters for the aluminum smelting process. In this paper, an improved multi-objective artificial vulture algorithm (IMOAVOA) is developed to solve a multi-objective problem of energy consumption and temperature deviations in the regenerative aluminum smelting process. The dynamic switching–elimination mechanism based on crowding distance is proposed to maintain the archive, which enhances the diversity of solutions by dynamically switching the operation space for deleting redundant solutions in the archive and dynamically deleting the solution with the smallest crowding distance in the operation space. The multi-directional leader selection mechanism is developed to select better leaders. To improve the convergence of the algorithm, the bounce strategy is introduced in the IMOAVOA. The effectiveness of the proposed algorithm is verified by UF1-UF10, kursawe, Viennet2, Viennet3, ZDT1-ZDT6, DTLZ4, and DTLZ6 test functions with several multi-objective algorithms. The experimental results indicate that IMOAVOA outperforms the original algorithm and three other multi-objective algorithms in terms of the algorithm convergence, the Pareto front coverage, and the solution diversity. Finally, the proposed algorithm is tested in an application case of regenerative aluminum smelting process. The results show that the optimal parameters for the aluminum smelting process using the proposed algorithm can reduce the consumption while meeting the objective of furnace temperature.

Fuel Replenishment Problem of Heterogeneous Fleet in Initiative Distribution Mode

Petrol, a vital energy source for residents’ consumption and economically sustainable operation, generates substantial distribution demand. To reduce distribution costs, we propose a fuel replenishment problem using a heterogeneous fleet based on the initiative distribution mode. In this mode, the distribution center determines both the delivery orders of customers and the distribution plan. We develop a mathematical model with minimal operational costs, including transport, employment, and penalty costs. A Two-stage heuristic algorithm K-IBKA based on time-space clustering is proposed, which also combines the advantages of the butterfly optimization algorithm in quick convergence and hierarchical mutation strategy in population diversity. The results demonstrate that: (1) Heterogeneous truck distribution exhibits better cost advantages compared to homogeneous distribution, reducing total costs by 13.07%; (2) Compared to passive distribution mode, the total cost of the initiative distribution mode is reduced by 11.03% and 41.80%, respectively, through small and large-scale instances. (3) Compared with the unimproved BKA, ALNS, and GA, the total cost calculated by K-IBKA is reduced by 37.68%, 35.30%, and 27.26%, respectively, thus demonstrating the contribution of this work to reducing the cost of petrol distribution and achieving sustainable development of distribution.

Enhanced Diagnosis of Skin Cancer from Dermoscopic Images Using Alignment Optimized Convolutional Neural Networks and Grey Wolf Optimization

Skin cancer (SC) is a highly serious kind of cancer that, if not addressed swiftly, might result in the patient’s demise. Early detection of this condition allows for more effective therapy and prevents disease development. Deep Learning (DL) approaches may be used as an effective and efficient tool for SC detection (SCD). Several DL-based algorithms for automated SCD have been reported. However, more efficient models are needed to improve accuracy. As a result, this paper introduces a new strategy for SCD based on Grey Wolf optimization (GWO) methodologies and CNN. The proposed methodology has four stages: preprocessing, segmentation, feature extraction, and classification. The proposed method utilizes a Convolutional Neural Network (CNN) to extract features from Regions of Interest (ROIs). CNN is employed for feature categorization, whereas the GWO approach enhances accuracy by refining edge detection and segmentation. This technique utilizes a probabilistic model to accelerate the convergence of the GWO algorithm. Employing the GWO model to optimize the structure and weight vectors of CNNs can enhance diagnostic accuracy by a minimum of 5%, based on evaluation outcomes. The application of the proposed strategy and its performance comparison with other methods indicate that the proposed method with GWO predicted SC with an average accuracy of 95.11% and without GWO an Accuracy of 92.66%, respectively, enhancing accuracy by a minimum of 2.5% when we train our model with GWO.

A Novel Prescribed-Time Convergence Acceleration Algorithm with Time Rescaling

In machine learning, the processing of datasets is an unavoidable topic. One important approach to solving this problem is to design some corresponding algorithms so that they can eventually converge to the optimal solution of the optimization problem. Most existing acceleration algorithms exhibit asymptotic convergence. In order to ensure that the optimization problem converges to the optimal solution within the prescribed time, a novel prescribed-time convergence acceleration algorithm with time rescaling is presented in this paper. Two prescribed-time acceleration algorithms are constructed by introducing time rescaling, and the acceleration algorithms are used to solve unconstrained optimization problems and optimization problems containing equation constraints. Some important theorems are given, and the convergence of the acceleration algorithms is proven using the Lyapunov function method. Finally, we provide numerical simulations to verify the effectiveness and rationality of our theoretical results.

Two relaxed inertial forward-backward-forward algorithms for solving monotone inclusions and an application to compressed sensing

Abstract Two novel algorithms, which incorporate inertial terms and relaxation effects, are introduced to tackle a monotone inclusion problem. The weak and strong convergence of the algorithms are obtained under certain conditions, and the R-linear convergence for the first algorithm is demonstrated if the set-valued operator involved is strongly monotone in real Hilbert spaces. The proposed algorithms are applied to signal recovery problems and demonstrate improved performance compared to existing algorithms in the literature.

Strongly convergent two-step inertial algorithm for a class of bilevel variational inequalities

Strongly convergent two-step inertial algorithm for a class of bilevel variational inequalities

Event-based reinforcement learning algorithm for dynamic resource allocation in smart grid

In this paper, we propose a dynamic event-based distributed reinforcement learning algorithm to address the resource allocation problem in a smart grid. The main challenge lies in the presence of unknown resource transfer functions and cost functions. Our objective is to discover a set of resource allocation solutions that minimise the total cost functions over a specified period. Our approach involves re-constructing a new convex optimisation problem to facilitate the approximation of Q-values in the reinforcement learning training process. Additionally, to avoid continuous communication, we integrate an event-based distributed optimisation approach to approximate the action-value function. We support our methodology with theoretical proofs that establish the validity of the event-triggered conditions and demonstrate the algorithm's convergence. We further validate the algorithm's feasibility through an illustrative example involving output power allocation in a smart grid.

A Cascaded Duplex Organic Vertical Memory with Learning Rate Scheduling for Efficient Artificial Neural Network Training

AbstractLearning rate scheduling (LRS) is a critical factor influencing the performance of neural networks by accelerating the convergence of learning algorithms and enhancing the generalization capabilities. The escalating computational demands in artificial intelligence (AI) necessitate advanced hardware solutions capable of supporting neural network training with LRS. This not only requires linear and symmetric analog programming capabilities but also the precise adjustment of channel conductance to achieve tunable slope in weight update behaviors. Here, a cascaded duplex organic vertical memory is proposed with the coupling of ferroelectric polarization effect and Schottky gate control on the same semiconducting channel, exhibiting adjustable‐slope conductance update with high linearity and symmetry. Therefore, in the chest X‐ray image detection, a fast‐to‐slow LRS is used for a bi‐layer ANN training, achieving a rapid, stable convergence behavior within only 15 epochs and a high recognition accuracy. Moreover, the proposed LRS training is also suitable for the Mackey Glass prediction task using long short‐term memory networks. This work integrates LRS into synaptic devices, enabling efficient hardware implementation of neural networks and thus enhancing AI performance in practical applications.

An Improved Human Evolution Optimization Algorithm for Unmanned Aerial Vehicle 3D Trajectory Planning.

To address the challenges of slow convergence speed, poor convergence precision, and getting stuck in local optima for unmanned aerial vehicle (UAV) three-dimensional path planning, this paper proposes a path planning method based on an Improved Human Evolution Optimization Algorithm (IHEOA). First, a mathematical model is used to construct a three-dimensional terrain environment, and a multi-constraint path cost model is established, framing path planning as a multidimensional function optimization problem. Second, recognizing the sensitivity of population diversity to Logistic Chaotic Mapping in a traditional Human Evolution Optimization Algorithm (HEOA), an opposition-based learning strategy is employed to uniformly initialize the population distribution, thereby enhancing the algorithm's global optimization capability. Additionally, a guidance factor strategy is introduced into the leader role during the development stage, providing clear directionality for the search process, which increases the probability of selecting optimal paths and accelerates the convergence speed. Furthermore, in the loser update strategy, an adaptive t-distribution perturbation strategy is utilized for its small mutation amplitude, which enhances the local search capability and robustness of the algorithm. Evaluations using 12 standard test functions demonstrate that these improvement strategies effectively enhance convergence precision and algorithm stability, with the IHEOA, which integrates multiple strategies, performing particularly well. Experimental comparative research on three different terrain environments and five traditional algorithms shows that the IHEOA not only exhibits excellent performance in terms of convergence speed and precision but also generates superior paths while demonstrating exceptional global optimization capability and robustness in complex environments. These results validate the significant advantages of the proposed improved algorithm in effectively addressing UAV path planning challenges.

A generalized projection estimation algorithm

Given a linear regression model in discrete-time containing a vector of p constant uncertain parameters, this paper addresses the problem of designing an exponentially convergent parameter estimation algorithm, even when the regressor vector is not persistently exciting (not even in a finite time interval). On the basis of the definition of lack of persistency of excitation of order q for the regressor vector, 0≤q≤p (which coincides with the classical definition of persistency of excitation when q=0), a generalized projection estimation algorithm is proposed which guarantees global exponential convergence of the parameter estimation error and allows for the on-line computation of the order q of the lack of persistency of excitation. When the lack of persistency of excitation is of order zero, global exponential convergence to zero of the parameter estimation error is obtained, recovering a well-known result and the projection estimation algorithm as a special case.

A transactive energy cooperation scheduling for hydrogen-based community microgrid with refueling preferences of hydrogen vehicles

Hydrogen, as a high specific energy green carrier, is promising for power generation and transportation. This paper proposes a transactive energy cooperation framework for an end-user-oriented hydrogen-based community microgrid considering refueling preferences of hydrogen vehicles (HVs) and industrial hydrogen demand to minimize social cost. In this framework, an aggregator obtains stacking profits in both the electricity and hydrogen markets through flexible interconversion, storage, and interaction of electricity and hydrogen. For resident users, the refueling preferences of HVs are analyzed to reduce cost through demand response (DR). A novel energy density-weighted asymmetric Nash bargaining (DANB) method is designed to fairly assess the combined contribution, considering both electricity and hydrogen bargaining metrics for end-users. An alternating optimization procedure with the adaptive alternating direction method of multipliers (ADMM) algorithm is designed to solve the mixed-integer linear programming (MILP) problem in the social operation cost minimization process. Comparison results show the algorithm convergence advantage, the cost-effectiveness and scalability of the cooperation framework, as well as the rationality of the DANB and the flexibility of HVs in DR. Besides, the optimal configuration of the battery, the hydrogen tank, and the electrolyzer in the framework is explored, alongside the economic feasibility of electricity-hydrogen-electricity technology.

A Sequential Calibration Approach to Address Challenges of Repeated Calibration of a COVID-19 Model.

Mathematical models served a critical role in COVID-19 decision making throughout the pandemic. Model calibration is an essential, but often computationally burdensome, step in model development that provides estimates for difficult-to-measure parameters and establishes an up-to-date modeling platform for scenario analysis. In the evolving COVID-19 pandemic, frequent recalibration was necessary to provide ongoing support to decision makers. In this study, we address the computational challenges of frequent recalibration with a new calibration approach. We calibrated and recalibrated an age-stratified dynamic compartmental model of COVID-19 in Minnesota to statewide COVID-19 cumulative mortality and prevalent age-specific hospitalizations from March 22, 2020 through August 20, 2021. This period was divided into 10 calibration periods, reflecting significant changes in policies, messaging, and/or epidemiological conditions in Minnesota. When recalibrating the model from one period to the next, we employed a sequential calibration approach that leveraged calibration results from previous periods and adjusted only parameters most relevant to the calibration target data of the new calibration period to improve computational efficiency. We compared computational burden and performance of the sequential calibration approach to a more traditional calibration method, in which all parameters were readjusted with each recalibration. Both calibration methods identified parameter sets closely reproducing prevalent hospitalizations and cumulative deaths over time. By the last calibration period, both approaches converged to similar parameter values. However, the sequential calibration approach identified parameter sets that more tightly fit calibration targets and required substantially less computation time than traditional calibration. Sequential calibration is an efficient approach to maintaining up-to-date models with evolving, time-varying parameters and potentially identifies better-fitting parameter sets than traditional calibration. This study used a sequential calibration approach, which takes advantage of previous calibration results to reduce the number of parameters to be estimated in each round of calibration, improving computational efficiency and algorithm convergence to best-fitting parameter values.Both sequential and traditional calibration approaches were able to identify parameter sets that closely reproduced calibration targets. However, the sequential calibration approach generated parameter sets that yielded tighter fits and was less computationally burdensome.Sequential calibration is an efficient approach to maintaining up-to-date models with evolving, time-varying parameters.

Modern Free-Derivative Numerical Optimization of Approximate Algorithms Convergence and Neutrosophic Convergence

The aim of this study is to compare common and previously used numerical algorithms for nonlinear problems under different conditions. This study proposes a parallel implementation of two free derivative optimization methods, Powell's method and Nelder-Mead's method, combined with two restart strategies to achieve a global search. In terms of total time, the Powell method converges faster than the Nelder-Mead method. The final function value obtained by the Powell method is slightly lower. Both are optimization techniques used to find the minimum of an objective function in multidimensional space, without requiring derivatives. Also, we extend our results to apply to some neutrosophic non-linear problems under different neutrosophic-based conditions with many examples that explain the validity of our approach.

Joint Task Offloading and Resource Allocation in Mobile Edge Computing-Enabled Medical Vehicular Networks

In medical vehicular networks, medical vehicles can serve as efficient mobile medical service points to provide necessary and critical medical services for patients while in motion. The delay requirement is very vital for medical services to guarantee service quality and save the lives of patients. Mobile Edge Computing (MEC), as an emerging network paradigm, enables the computation extensive tasks to be offloaded to edge servers, efficiently reducing the delay and bandwidth demands. MEC technology is a promising solution to provide high-quality medical services for users in medical vehicular networks. However, task offloading and resource allocation incurs additional service delay and energy consumption, affecting the overall service performance and Quality of Experience (QoE) of users. Thus, realizing the optimal task offloading and resource allocation in MEC-enabled medical vehicular networks, to reduce task completion time and energy consumption, becomes a potential challenge. To address the challenge, we investigate the joint task offloading and resource allocation problem in MEC-enabled medical vehicular networks to improve the QoE of users. Considering the resource requirements and QoS constraint, we formulate a multi-objective optimization model, with the target of average task completion time and average energy consumption minimization. On this basis, we propose a MOEAD-based task offloading and resource allocation (IMO) algorithm to solve it. Furthermore, in order to obtain the optimal solution and speed up the algorithm convergence, we design a greedy strategy-based population initialization algorithm. The extensive simulations demonstrate that compared to existing algorithms, our proposed IMO algorithm can obtain a smaller average completion time, and achieve better tradeoff between task completion time and energy consumption.

On the convergence of generalized kernel-based interpolation by greedy data selection algorithms

We analyze the convergence of generalized kernel-based interpolation methods. This is done under minimalistic assumptions on both the kernel and the target function. On these grounds, we further prove convergence of popular greedy data selection algorithms for totally bounded sets of sampling functionals. Supporting numerical results concerning computerized tomography are provided for illustration.

Models and methods for forming service packages for solving of the problem of designing services in information systems of providers

Today, in the telecommunications industry, service is one of the fundamental concepts. Building a service architecture is a key stage in the service life cycle. Information systems of telecommunications providers are designed, implemented and supported by IT companies based on the End-to-End model. This requires the IT company to solve a number of complex problems. In these conditions, building a service architecture, implementing and providing a service are divided into subproblems. Solutions to subproblems must be integrated to determine the coordinated activities of both the IT company and the provider. In this case, it is necessary to take into account the goals of IT companies, providers and their customers in such a way that it is beneficial to all parties. One of such subproblems is the formation of service packages that the IT company offers to providers. The article proposes formal models for the subproblem of forming service packages that allow taking into account the interests of the IT company and providers. These are multi-criteria nonlinear mathematical programming models. To solve the subproblem of forming service packages, a two-stage algorithm and a modified version of the guided genetic algorithm are proposed. The use of these methods allows us to take into account the interests of the IT company and providers. Also, such important factors that affect the formation of packages as the base price of the service, service dependency, discount system, resource and other constraints of the IT company and providers are taken into account. The two-stage algorithm at the first stage uses classical algorithms for solving the knapsack problem, and at the second stage implements a compromise scheme to improve the solution. The second of the proposed methods uses three types of tools in combination. The first tool controls the convergence of the genetic algorithm. The second tool determines the choice of the best solutions taking into account the features of the multi-criteria problem. The third tool allows to obtain the best solutions to the optimization problem with the simultaneous choice of a discount strategy. Experimental studies have confirmed the effectiveness of the proposed methods. Their ability to form the basis of the technology of forming service packages as a component of the platform for supporting the life cycle of services is also confirmed.

Classical pressure profile prediction using a hybrid form of artificial neural network algorithm applied to building drainage systems

Classical pressure profile data for building drainage systems (BDS) represent a temporal snapshot of the pressure regime within the system following an event such as a water discharge from an appliance, and therefore can be an indicator of system performance. This research describes, for the first time, a method of predicting the pressure profile using FF(Feed Forward -PSO(Particle Swarm Optimization) artificial neural network (ANN) algorithm. The ANN model was validated against two sets of data: the first from a dedicated 32-storey building drainage experimental test rig at the National Lift Tower (NLT) test facility in Northampton, UK, and the second set of data from a validated numerical model, AIRNET. Both data sets were used to assess the FF- PSO-ANN Model. Calculation errors were minimized by refining weight vectors with a PSO scheme. The convergence of the PSO algorithm was managed through adjusted inertia weights, population size, damping factor, and acceleration coefficients. A generic prediction model was developed using a database of similar building drainage types and configurations. This algorithm refines and trains the ANN model, enhancing its applicability across various applications. The study confirms that the FF-PSO ANN model effectively predicts BDS pressure profile data and system performance. Practical application The ANN model presented develops a new approach with which to assess performance of a BDS at design stage. The model is based on the philosophy of a natural search algorithm which helps to attain global optimisation by refining the weight vectors. It is envisaged that this model can form a part of the assessment of designs at an early stage and provide useful information on the performance of the system. The in-built learning of the model allows accuracy to be improved as the database of existing pressure profiles increases, thus making the tool more relevant with time.