Convergence Of Algorithm Research Articles

Efficient Modelisation for Complex Geometries of Tumor Growth via Thermo-Elastic Diffusion Partial Differential Equations and Artificial Neural Networks

<p dir="ltr"><span>The availability of high quality image data urges the development of new conceptual techniques to realise cancer accurate prognostic and treatment. In this study we propose a boundary value problem to model tumor elasticity impacting various types of mechanical stresses on cancer cell properties, assuming isotropic and inhomogeneous condition. We show the solution of this multiscale model expressed by PDE is numerically approximated by means of an Artificial Neural Network Architecture based on generalised Fourier decomposition. The connective key step is the use of the Laplace Neural Operator, which contributes to an efficient algorithm convergence rate. While further research of this model may address critical points on machine learning optimality checks, this framework is a rational development for oncologic medical prognosis and therapy. </span></p><div><span><br /></span></div>

Convergence Analysis for Differentially Private Federated Averaging in Heterogeneous Settings

Federated learning (FL) has emerged as a prominent approach for distributed machine learning, enabling collaborative model training while preserving data privacy. However, the presence of non-i.i.d. data and the need for robust privacy protection introduce significant challenges in theoretically analyzing the performance of FL algorithms. In this paper, we present novel theoretical analysis on typical differentially private federated averaging (DP-FedAvg) by judiciously considering the impact of non-i.i.d. data on convergence and privacy guarantees. Our contributions are threefold: (i) We introduce a theoretical framework for analyzing the convergence of DP-FedAvg algorithm by considering different client sampling and data sampling strategies, privacy amplification and non-i.i.d. data. (ii) We explore the privacy–utility tradeoff and demonstrate how client strategies interact with differential privacy to affect learning performance. (iii) We provide extensive experimental validation using real-world datasets to verify our theoretical findings.

Multichannel Parallel Mode Order Converter for On‐Chip Reconfigurable PDM‐MDM Transmission

AbstractThe increasing demand for communication capacity has led to extensive exploration of hybrid multiplexing technologies that combine multiple wavelengths, modes, and polarization. Nevertheless, designing mode converters for hybrid multiplexing remains challenging. Reconfigurable and scalable multichannel parallel mode converters offer an attractive solution for efficient mode switching with a small footprint. In this paper, a compact and high‐performance dual‐polarization multichannel parallel mode order converter based on metamaterials is proposed, which consists of two components. One of the components is the flexible and compact multimode beam splitter designed by the rapidly convergent variable step size binary search algorithm. The other component is the dual‐polarization phase shifter that maximizes the feature size of the non‐subwavelength structure, significantly reducing the adverse effects of over‐etching. The experimental results demonstrate that the insertion loss of each mode is below 1.96 dB, while the crosstalk of each input mode is lower than −13.4 dB. The feasibility of high‐speed transmission is demonstrated by transmitting 30 GBuad 16‐quadrature amplitude modulation (QAM) signals on the device. This device is believed to be the first dual‐polarization multichannel parallel mode converter reported to date. This innovative device holds great potential for enhancing communication capacity in reconfigurable and scalable hybrid multiplexed transmission systems.

Adaptive Kalman filter-based time synchronization algorithm for civil aviation communication

Abstract The traditional synchronization algorithms often struggle to meet the stringent requirements of civil aviation communication. This paper proposes an adaptive time synchronization algorithm based on Kalman filtering (KF) to enhance the synchronization performance of civil aviation communication systems. Firstly, a dynamic clock model is established considering the characteristics of civil aviation communication, with clock offset and drift as state variables. Moreover, a step-by-step detection strategy is employed to adaptively adjust the detection range based on the statistical characteristics of synchronization errors, thereby improving the algorithm's robustness and convergence speed. To evaluate the algorithm's performance, a civil aviation communication system-level simulation platform is built based on ICAO standards, and various typical scenarios, such as take-off, landing, and cruising, are designed. Simulation results demonstrate that the proposed algorithm achieves significant improvements in synchronization accuracy, convergence speed, and robustness compared to classical synchronization algorithms based on phase-locked loops (PLL) and early late gates (ELD).

An improved golden jackal optimization - hybrid kernel extreme learning machine approach for fault diagnosis of chillers

Abstract In the context of the dual carbon target, it is particularly important to reduce energy consumption and carbon emissions in the building sector. Chillers, as the main source of energy consumption in building equipment, will significantly exacerbate the building's energy consumption in the event of a failure. In order to improve the detection rate of early chiller failure, an improved golden jackal optimization algorithm (IGJO)-hybrid kernel extremum learning machine (HKELM) chiller fault diagnosis model is proposed. Firstly, to address the problem of slow convergence speed and easy to fall into local optimization of the golden jackal algorithm (GJO), we introduce four strategies, namely, improved sine chaotic mapping, simplex method, fusion of golden sinusoidal formula and Cauchy's variant, and put forward the IGJO algorithm to improve the algorithm's convergence speed and global optimization ability; and then, we use the fast optimization search of the hyperparameters combinations of the HKELM using the IGJO, to build a data-driven model for chiller failure detection; and finally, we use the data-driven model of ASEAN to construct a data-driven model of HKELM. The data-driven model is then used to construct a data-driven model for chiller fault detection; finally, the performance of the proposed model is simulated using ASHRAE 1043-RP. The results show that the accuracy of the proposed IGJO-HKELM model for chiller fault diagnosis reaches 99.83%, which is an obvious advantage compared with other algorithms.

Bi-Objective Integrated Scheduling of Job Shop Problems and Material Handling Robots with Setup Time

This work investigates the bi-objective integrated scheduling of job shop problems and material handling robots with setup time. The objective is to minimize the maximum completion time and the mean of earliness and tardiness simultaneously. First, a mathematical model is established to describe the problems. Then, different meta-heuristics and their variants are developed to solve the problems, including genetic algorithms, particle swarm optimization, and artificial bee colonies. To improve the performance of algorithms, seven local search operators are proposed. Moreover, two reinforcement learning algorithms, Q-learning and SARSA, are designed to help the algorithm select appropriate local search operators during iterations, further improving the convergence of algorithms. Finally, based on 82 benchmark cases with different scales, the effectiveness of the suggested algorithms is evaluated by comprehensive numerical experiments. The experimental results and discussions show that the genetic algorithm with SARSA is more competitive than its peers.

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.

Multi-Timescale Battery-Charging Optimization for Electric Heavy-Duty Truck Battery-Swapping Stations, Considering Source–Load–Storage Uncertainty

With the widespread adoption of renewable energy sources like wind power and photovoltaic (PV) power, uncertainties in the renewable energy output and the battery-swapping demand for electric heavy-duty trucks make it challenging for battery-swapping stations to optimize battery-charging management centrally. Uncoordinated large-scale charging behavior can increase operation costs for battery-swapping stations and even affect the stability of the power grid. To mitigate this, this paper proposes a multi-timescale battery-charging optimization for electric heavy-duty truck battery-swapping stations, taking into account the source–load–storage uncertainty. First, a model incorporating uncertainties in renewable energy output, time-of-use pricing, and grid load fluctuations is developed for the battery-swapping station. Second, based on day-ahead and intra-day timescales, the optimization problem for battery-charging strategies at battery-swapping stations is decomposed into day-ahead and intra-day optimization problems. We propose a day-ahead charging strategy optimization algorithm based on intra-day optimization feedback information-gap decision theory (IGDT) and an improved grasshopper algorithm for intra-day charging strategy optimization. The key contributions include the following: (1) the development of a battery-charging model for electric heavy-duty truck battery-swapping stations that accounts for the uncertainty in the power output of energy sources, loads, and storage; (2) the proposal of a day-ahead battery-charging optimization algorithm based on intra-day-optimization feedback information-gap decision theory (IGDT), which allows for dynamic adjustment of risk preferences; (3) the proposal of an intra-day battery-charging optimization algorithm based on an improved grasshopper optimization algorithm, which enhances algorithm convergence speed and stability, avoiding local optima. Finally, simulation comparisons confirm the success of the proposed approach. The simulation results demonstrate that the proposed method reduces charging costs by 4.26% and 6.03% compared with the two baseline algorithms, respectively, and improves grid stability, highlighting its effectiveness for managing battery-swapping stations under uncertainty.

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.

Application of Discrete Event Simulation to Enhance the Efficiency of the Ant Colony Optimization Algorithm

The application of the Ant Colony Optimization (ACO) algorithm to solve the the Traveling Salesman Problem (TSP) has been extensively studied by scientists worldwide. However, implementing the algorithm faces challenges due to the randomness in the departure and movement times of ants, as well as the limitations of computer hardware. These factors reduce the algorithm's convergence ability and overall effectiveness. This paper proposes an approach to implement the algorithm by utilizing discrete event simulation (DES). Artificial ants are modeled to depart and move completely randomly, closely mimicking the behavior of natural ants. This approach accelerates the algorithm's convergence, minimizes the likelihood of falling into local optima, and enhances overall performance. The simulation results clearly demonstrate the advantages of this method.