Adaptive Step Size Research Articles

Alpha evolution: An efficient evolutionary algorithm with evolution path adaptation and matrix generation

Metaheuristics involve information extraction and utilization processes to generate more promising solutions. However, the background of excessive metaphor has led to ambiguity in the computational process. To solve this problem, this paper proposes a novel evolutionary algorithm called alpha evolution (AE). It updates the solution using the alpha operator with the adaptive base vector and the random and adaptive step sizes. First, sample candidate solutions to construct the evolution matrix. Estimate the population state through diagonal or weighted operations of the evolution matrix. To enhance the correlation of estimates for each generation, two evolution paths accumulate the estimate results and achieve the base vector adaptation. Second, the composite differential operation constructs the adaptive step size to estimate the problem gradient, which is used to accelerate the convergence of AE. Finally, the attenuation factor alpha adaptively adjusts the random step size generated based on search space to balance exploration and exploitation. AE was comprehensively verified regarding its search bias, invariance, scalability, parameter sensitivity, search behavior, qualitative indicators, exploration and exploitation, convergence, statistics, and complexity. In numerical simulation, AE was compared with 106 algorithms on the CEC’17 benchmark announced at the 2017 congress on evolutionary computation (CEC). Furthermore, AE was applied to solve multiple sequence alignment and engineering design problems. The evidence shows that AE is competitive in exploration and exploitation, convergence speed and accuracy, avoiding local optima, applicability, and reliability. The source code of AE is publicly available at https://github.com/tsingke/AlphaEvolution.

Enhancing the Transferability of Adversarial Patch via Alternating Minimization

Adversarial patches, a type of adversarial example, pose serious security threats to deep neural networks (DNNs) by inducing erroneous outputs. Existing gradient stabilization methods aim to stabilize the optimization direction of adversarial examples through accumulating gradient momentum to enhance attack transferability on black-box models. However, they are not fully effective for adversarial patches. The accumulated momentum during optimization often misaligns with the optimization direction, reducing their efficacy in black-box scenarios. We introduce an optimization method called Alternating Minimization for Adversarial Patch (AMAP). This method decomposes the original AP into multiple sub-patches and utilizes their update direction to stabilize the optimization of the original AP. Additionally, we propose an adaptive step size optimization method that accelerates convergence and boosts the attack performance. In face recognition tasks, AMAP outperforms baseline methods by a remarkable 5.21% and exceeds the second-best method by 1.4%. Furthermore, AMAP demonstrates practical feasibility in the physical domain, highlighting its potential for robust computer security testing applications.

Hybrid vibration isolator based on piezoelectric actuator and metal rubber and its adaptive control method

To achieve vibration isolation across the entire working frequency range, this paper proposes a novel hybrid vibration isolator combining metal rubber and piezoelectric actuators, along with an adaptive active control algorithm. The passive isolation system allows for manual adjustment of stiffness and damping based on the preload, overcoming the issue of fixed stiffness and damping in traditional passive isolation units. For the active isolation system, an improved Filtered-x Normalized Least Mean Squares with adaptive step size active control algorithm is proposed, overcoming the problem of narrow frequency range applicability in traditional active control algorithms. A hybrid model of electromechanical coupling and hysteresis for the piezoelectric actuator is developed for the secondary path in the algorithm. Experimental results confirm that the hybrid isolator possesses vibration isolation capabilities within the 5–500 Hz working frequency range, with vibration suppression at the first and second resonance frequencies improved by 98.9% and 92.2%, respectively, compared to the passive system. Additionally, the hybrid isolator effectively suppresses complex multifrequency signals and demonstrates robustness and adaptability. This research provides advanced technological means to address complex vibration problems, and establishes both theoretical and practical foundations for multi-degree-of-freedom vibration isolation.

[formula omitted]-adaptive discontinuous Galerkin solution of transonic viscous flows with variable time step-size

The discontinuous Galerkin methods demonstrated to be well suited for scale resolving simulations of complex configurations, characterized by different fluid dynamics phenomena, such as transition, separation, shock/boundary layer interaction. Unfortunately, solvers based on these methods cannot yet reach the computational efficiency of well-established standard solvers, e.g., based on finite volume methods. To reduce the computational cost and the memory footprint, while not spoiling the accuracy, different approaches were investigated, which act on the spatial or the temporal discretization, and on the linear algebra. The above approaches have been extensively investigated, but rarely considering their mutual interactions. In this work, a p-adaptation algorithm is coupled with a time step-size adaptation algorithm to mitigate robustness issues arising after each adaptation cycle, probably related to the projection of the old solution on the new polynomial orders distribution. Moreover, this strategy is able to control the transient phase before each adaptation cycle, and can handle also the presence of initial steady solution, when the mesh is too coarse and the polynomial degree has not yet compensated for the lack of spatial accuracy. The effectiveness and accuracy of the proposed algorithm are demonstrated on transonic viscous flows with shock-wave/boundary-layer interaction.

An efficient ADAM-type algorithm with finite elements discretization technique for random elliptic optimal control problems

We consider an optimal control problem governed by an elliptic partial differential equation (PDE) with random coefficient, and introduce an efficient numerical method for the problem under concern. Based on a finite element discretization of the constraint PDE and objective functional, an ADAM-type iteration scheme is proposed to compute the approximated optimal control, which equips the stochastic gradient iteration with modified momentum acceleration and adaptive step size. We provide theoretical bounds on both the discretization and iteration error of the proposed numerical method. Our method is tested on two examples, and the numerical results show the efficiency and performance of the method.

An Inertial Relaxed CQ Algorithm with Two Adaptive Step Sizes and Its Application for Signal Recovery

An Inertial Relaxed CQ Algorithm with Two Adaptive Step Sizes and Its Application for Signal Recovery

A new adaptive Perturb & Observe controller via robust approach for PV grid-connected

Given the importance of renewable energies, several countries are integrating these energies into their energy strategies, such as their connections to the grid, in particular photovoltaic energy. In this paper, a PV grid-connected system in a two-stage configuration is studied. In this configuration, an improvement to a control MPPT is proposed. To achieve this, we propose a novel concept for MPPT control that consists of generating an adaptive step size for P&O control that is based on sliding mode control in order to minimise ripple phenomena and chattering phenomena. The proposed control approach was then tested using MATLAB/Simulink simulations under varying irradiation conditions. We compared this approach to the conventional P&O method as well as the adaptive step size of P&O and hybrid P&O-sliding mode control. The results of the test indicate that the proposed control strategy significantly minimises the two phenomena and improves overall efficiency.

An improved P&O-based DC-link voltage control algorithm for standalone PV systems with adaptive step-size and operating point determination strategy

ABSTRACT An improved DC-Link voltage controller (IPOVR), which is built upon the perturb & observe-based voltage regulator (POVR), is proposed in this paper. The aim is to achieve the best balance between tracking time and steady-state oscillation while maintaining good tracking accuracy. This is achieved by implementing a dynamic step-size (∆D) changing strategy and operating region detection technique. Quick tracking time is produced with large initial ∆D, and low steady-state oscillation is obtained through continuous ∆D reduction. Additionally, through the operating region determination technique, the IPOVR operates over a much wider range, typically with lower PV current (IPV), which helps in reducing the losses of the system. It is found that the IPOVR has the lowest steady-state ripple and the highest tracking accuracy, which are averaged at 0.44% and 99.98%, respectively. In terms of tracking time, the IPOVR is averaged at 0.15 s, which is only 0.07 s slower compared to the POVR with high ∆D but is 0.19 s faster than the POVR with low ∆D. Furthermore, the IPOVR recorded higher efficiencies under all tested conditions compared to the POVR. The IPOVR is also demonstrated to be working decently when being connected to a multilevel inverter to generate AC power.

Adaptive Bregman–Kaczmarz: an approach to solve linear inverse problems with independent noise exactly

We consider the block Bregman–Kaczmarz method for finite dimensional linear inverse problems. The block Bregman–Kaczmarz method uses blocks of the linear system and performs iterative steps with these blocks only. We assume a noise model that we call independent noise, i.e. each time the method performs a step for some block, one obtains a noisy sample of the respective part of the right-hand side which is contaminated with new noise that is independent of all previous steps of the method. One can view these noise models as making a fresh noisy measurement of the respective block each time it is used. In this framework, we are able to show that a well-chosen adaptive stepsize of the block Bregman–Kaczmarz method is able to converge to the exact solution of the linear inverse problem. The plain form of this adaptive stepsize relies on unknown quantities (like the Bregman distance to the solution), but we show a way how these quantities can be estimated purely from given data. We illustrate the finding in numerical experiments and confirm that these heuristic estimates lead to effective stepsizes.

Research on Path Planning of a Mining Inspection Robot in an Unstructured Environment Based on an Improved Rapidly Exploring Random Tree Algorithm

To ensure the safe production of mines, the intelligent trend of underground mining operations is gradually advancing. However, the operational environment of subterranean mining is intricate, making the conventional path-planning algorithm used by mining inspection robots frequently inadequate for real requirements. To safeguard the mining inspection robot, targeting the problem of low search efficiency and path redundancy in the path planning of the existing rapidly exploring random tree (RRT) algorithm in the narrow and complex unstructured environment, a path-planning algorithm combining improved RRT and a probabilistic road map (PRM) is proposed. Initially, the target area is efficiently searched according to the fan-shaped goal orientation strategy and the adaptive step size expansion strategy. Subsequently, the PRM algorithm and the improved RRT algorithm are combined to reduce the redundant points of the planning path. Ultimately, considering the kinematics of the vehicle, the path is optimized by the third-order Bessel curve. The experimental simulation results show that the proposed path-planning algorithm has a higher success rate, smoother path, and shorter path length than other algorithms in complex underground mining environments, which proves the effectiveness of the proposed algorithm.

A Golden Ratio Algorithm With Backward Inertial Step For Variational Inequalities

In this paper we study the convergence analysis of a Golden Ratio Algorithm with a backward inertial step and a fully adaptive step size procedure for the purpose of approximating solutions of variational inequalities in Hilbert spaces. We present a weak convergence result when the operator is quasi-monotone and locally Lipschitz continuous, and a strong convergence result in the setting of strong pseudo-monotonicity. Our algorithm features one operator evaluation and one projection computation at the current iteration. We recover interesting algorithms in the literature, for instance, the Golden Ratio Algorithm. Numerical experiments were conducted to validate the theoretical convergence analysis.

Adaptive step size quantized simulation method for gas–electricity integrated energy systems

Gas–electricity integrated energy systems (GE-IES) offers a promising solution for enhancing energy efficiency and accommodating renewable energy sources. Accurate dynamic simulation is essential for optimizing and controlling GE-IES. However, the presence of various local controllers introduces prominent discrete characteristics, posing challenges for the dynamic simulation of the GE-IES. This paper investigates the dynamic simulation method in GE-IES with discrete characteristics. Firstly, we propose an adaptive step size simulation method based on quantized state system theory. This method maintains the event-driven characteristics of the quantized state integration algorithms, while enhancing computational speed through adaptive step size adjustments. Secondly, we establish an event-driven simulation framework that facilitates interactions of different subsystems during the dynamic simulation, improving the compatibility with various models and solving algorithms. Finally, we validate the accuracy, efficiency, and scalability of the proposed method and the framework using two typical GE-IES cases with different scales. Simulation results demonstrate the effectiveness on the dynamic simulation of GE-IES and highlight the feasibility of natural gas networks in consuming and storing surplus renewable energy.

Subgradient-projection-based stable phase-retrieval algorithm for X-ray ptychography.

X-ray ptychography is a lensless imaging technique that visualizes the nano-structure of a thick specimen which cannot be observed with an electron microscope. It reconstructs a complex-valued refractive index of the specimen from observed diffraction patterns. This reconstruction problem is called phase retrieval (PR). For further improvement in the imaging capability, including expansion of the depth of field, various PR algorithms have been proposed. Since a high-quality PR method is built upon a base PR algorithm such as ePIE, developing a well performing base PR algorithm is important. This paper proposes an improved iterative algorithm named CRISP. It exploits subgradient projection which allows adaptive step size and can be expected to avoid yielding a poor image. The proposed algorithm was compared with ePIE, which is a simple and fast-convergence algorithm, and its modified algorithm, rPIE. The experiments confirmed that the proposed method improved the reconstruction performance for both simulation and real data.

Research on Unmanned Vehicle Path Planning Based on the Fusion of an Improved Rapidly Exploring Random Tree Algorithm and an Improved Dynamic Window Approach Algorithm

Aiming at the problem that the traditional rapidly exploring random tree (RRT) algorithm only considers the global path of unmanned vehicles in a static environment, which has the limitation of not being able to avoid unknown dynamic obstacles in real time, and that the traditional dynamic window approach (DWA) algorithm is prone to fall into a local optimum during local path planning, this paper proposes a path planning method for unmanned vehicles that integrates improved RRT and DWA algorithms. The RRT algorithm is improved by introducing strategies such as target-biased random sampling, adaptive step size, and adaptive radius node screening, which enhance the efficiency and safety of path planning. The global path key points generated by the improved RRT algorithm are used as the subtarget points of the DWA algorithm, and the DWA algorithm is optimized through the design of an adaptive evaluation function weighting method based on real-time obstacle distances to achieve more reasonable local path planning. Through simulation experiments, the fusion algorithm shows promising results in a variety of typical static and dynamic mixed driving scenarios, can effectively plan a path that meets the driving requirements of an unmanned vehicle, avoids unknown dynamic obstacles, and shows higher path optimization efficiency and driving stability in complex environments, which provides strong support for an unmanned vehicle’s path planning in complex environments.

Embedded exponential Runge–Kutta–Nyström methods for highly oscillatory Hamiltonian systems

Exponential/extended Runge–Kutta–Nyström (ERKN) methods have been validated by numerous theoretical and numerical results to be more efficient and suitable than classical Runge–Kutta–Nyström (RKN) methods in dealing with highly oscillatory Hamiltonian systems. Once numerical solutions are required to achieve a prescribed local error tolerance for practical problems, the embedded ERKN pairs with adaptive stepsize are needed. Given the higher efficiency of high-order methods than low-order methods, this paper focuses on high-order embedded ERKN pairs. Using the particular mapping from RKN methods into ERKN methods, we establish an approach to constructing high-order embedded ERKN pairs. By diagonalizing the frequency matrix, an implementation algorithm with less calculation amount than the direct calculation procedure is proposed for high-dimensional problems. In addition, the dispersion and dissipation of the ERKN pairs ERKN4(3) and ERKN8(6) are analyzed. Furthermore, the application of ERKN pairs to an important highly oscillatory problem, i.e., the wave equation prescribed with different boundary conditions is discussed. For the periodic boundary condition, a special implementation algorithm incorporated with FFT techniques is presented, which decreases the calculation amount in one time step from O(N2) to O(Nlog⁡N). Finally, numerical results with the FPU problem, the Klein–Gordon equation in the nonrelativistic limit regime, and a two-dimensional wave equation demonstrate the superiority of ERKN pairs over classical RKN pairs.

Research on Autonomous Vehicle Path Planning Algorithm Based on Improved RRT* Algorithm and Artificial Potential Field Method.

For the RRT* algorithm, there are problems such as greater randomness, longer time consumption, more redundant nodes, and inability to perform local obstacle avoidance when encountering unknown obstacles in the path planning process of autonomous vehicles. And the artificial potential field method (APF) applied to autonomous vehicles is prone to problems such as local optimality, unreachable targets, and inapplicability to global scenarios. A fusion algorithm combining the improved RRT* algorithm and the improved artificial potential field method is proposed. First of all, for the RRT* algorithm, the concept of the artificial potential field and probability sampling optimization strategy are introduced, and the adaptive step size is designed according to the road curvature. The path post-processing of the planned global path is carried out to reduce the redundant nodes of the generated path, enhance the purpose of sampling, solve the problem where oscillation may occur when expanding near the target point, reduce the randomness of RRT* node sampling, and improve the efficiency of path generation. Secondly, for the artificial potential field method, by designing obstacle avoidance constraints, adding a road boundary repulsion potential field, and optimizing the repulsion function and safety ellipse, the problem of unreachable targets can be solved, unnecessary steering in the path can be reduced, and the safety of the planned path can be improved. In the face of U-shaped obstacles, virtual gravity points are generated to solve the local minimum problem and improve the passing performance of the obstacles. Finally, the fusion algorithm, which combines the improved RRT* algorithm and the improved artificial potential field method, is designed. The former first plans the global path, extracts the path node as the temporary target point of the latter, guides the vehicle to drive, and avoids local obstacles through the improved artificial potential field method when encountered with unknown obstacles, and then smooths the path planned by the fusion algorithm, making the path satisfy the vehicle kinematic constraints. The simulation results in the different road scenes show that the method proposed in this paper can quickly plan a smooth path that is more stable, more accurate, and suitable for vehicle driving.

An accelerated inexact Newton-type regularizing algorithm for ill-posed operator equations

We propose and analyze a new iterative regularization approach, called IN-SETPG, for efficiently solving nonlinear ill-posed operator equations in the Hilbert-space setting. IN-SETPG consists of an outer iteration and an inner iteration. The outer iteration is terminated by the discrepancy principle and consists of an inexact Newton regularization method, while the inner iteration is performed by a sequential subspace optimization method based on the two-point gradient iteration. The key idea behind IN-SETPG is that, unlike the standard Landweber method, it uses multiple search directions per iteration in combination with an adaptive step size in order to reduce the total number of iterations. The regularization property of IN-SETPG has been established, i.e., the iterate converges to a solution of the nonlinear problem with exact data when the noise level tends to zero. Various numerical experiments are presented to demonstrate that, compared with the original inexact Newton iteration, IN-SETPG can achieve better reconstruction results and remarkable acceleration.

A Binary Artificial Rabbit Optimization Algorithm for Improved Cognitive Radio Spectrum Allocation

A binary artificial rabbit optimization algorithm is proposed to maximize the cognitive radio (CR) network performance and fairness among users by addressing the issue of low spectrum resource utilization during the CR spectrum allocation process. Building upon the graph coloring spectrum allocation model, Sigmoid is introduced to transform the algorithm solution space. Incorporating the Lévy flight strategy for adaptive step size adjustment enhances the algorithm’s flexibility and convergence accuracy. Moreover, a selective opposition strategy based on Spearman’s coefficient is integrated into the algorithm to improve population diversity and convergence accuracy through reverse learning. Applying the binary artificial rabbit optimization algorithm to the CR spectrum allocation problem in the same CR network environment, we compare network efficiency and inter-user fairness through simulation experiments with the artificial rabbits optimization algorithm seagull optimization algorithm and particle swarm optimization algorithms. The experimental results show that the binary artificial rabbit optimization algorithm has higher convergence performance and global exploration ability, improves the overall network efficiency and user fairness of CR networks, and alleviates the problem of low spectrum resource utilization.

Mathematical Model and Statistical Assessment of Non Linear Scheduling Optimization in Cloud Environment using Improved Cuckoo Search Algorithm

The scheduling optimization subject is indeed one of the most effective solutions in cloud system area to ensure the high systems performance and resource usage. The novelty presented in this study is a mathematical model that draws on an Improved Cuckoo Search Algorithm as a scheduling non-linear optimizer for the cloud computing environment. The model under consideration takes into account the underlying complications as well as the varying nature of the use of cloud resources, primarily addressing the latency issue with priority given to the increase of the throughput. Improved Cuckoo Search (ICS) Algorithm, developed on 'cuckoo search' algorithm, uses adaptive step size and probabilistic switching, which, in turn, ensure that the solution space is both being properly examined and exploited. The applications’ utilization of the scheduling mathematical model is based on an elaborately designed theoretical background representing the task as a non-linear optimization problem that meets all the specific constraints and objectives important in cloud computing. Statistical reassessment involves the comparison of the proposed model with standard benchmarks. The proposed model superiority is evident in terms of convergence speed, solution quality and robustness against diverse workloads, as shown in varied tests. The findings of this research contributes to the field by deriving a specialized tool commonly used by the cloud service provider in designing resource scheduling, enhancing the service delivery and operational efficiency.

Research on Intelligent Ship Route Planning Based on the Adaptive Step Size Informed-RRT* Algorithm

Research on Intelligent Ship Route Planning Based on the Adaptive Step Size Informed-RRT* Algorithm