Local Minima Problem Research Articles

An adaptive neuro-fuzzy with nonlinear PID controller design for electric vehicles

In this work, an adaptive neuro-fuzzy (ANF) with a nonlinear proportional integral derivative (NLPID) controller (ANF-NLPID) has been proposed to solve the speed-tracking problem in electric vehicles (EVs) with brushless DC motor (BLDC). The ANF-NLPID controller eliminates the external disturbances caused by environmental or internal issues and uncertainties caused by parameter variations that lead to insufficient speed-tracking performance and increased energy consumption in EVs. An improved particle swarm optimization based on the chaos theory (IPSO-CT) algorithm is introduced to obtain the parameters of the fuzzy logic controller membership function and nonlinear PID controller and present the optimal performance for the EV. Employing the chaos technique with PSO helps to prevent the system from being trapped in the local minimum or optimum problem. The performance of the IPSO-CT algorithm is tested using a numerical comparison with other existing works. The outstanding performance of the ANF-NLPID controller has been evaluated by measuring the speed-tracking performance for the new European driving cycle (NEDC) and circular trajectories. Three case studies have been presented based on measuring the ANF-NLPID controller performance without disturbances, with disturbances, with disturbances, and uncertainties effects, respectively. Furthermore, the ANF-NLPID controller has been employed in different EV models to study the performance of this type of controller. Each of the three cases includes other existing works along with the ANF-NLPID controller to provide an insightful comparison using statistical functions to obtain each controller’s overall objective function value. The other existing works are fuzzy fractional order PID (Fuzzy FOPID), fuzzy integer order PID (Fuzzy IOPID), and integer order PID (IOPID) controllers. A sensitivity analysis has been conducted to test the proposed controller’s ability to present high speed-tracking performance while changing the disturbances and uncertainty rates. The results demonstrate that the ANF-NLPID controller is superior in speed-tracking control regulation for the new European cycle drive (NEDC) and circular speed trajectories and overcomes the external disturbances and uncertainties problem with low error results. In the end, the results reveal that the ANF-NLPID controller is more efficient than the fuzzy FOPID, fuzzy IOPID, and IOPID controllers in each case.

Real Aperture Radar Angular Super-Resolution Imaging Using Modified Smoothed L0 Norm with a Regularization Strategy

Restricted by the ill-posed antenna measurement matrix, the conventional smoothed L0 norm algorithm (SL0) fails to enable direct real aperture radar angular super-resolution imaging. This paper proposes a modified smoothed L0 norm (MSL0) algorithm to address this issue. First, as the pseudo-inverse of the ill-posed antenna measurement matrix is required to set the initial values and calculate the gradient projection, a regularization strategy is employed to relax the ill-posedness. Based on the regularization strategy, the proposed MSL0 algorithm can avoid noise amplification when faced with the ill-posed antenna measurement matrix of real aperture radar. Additionally, to prevent local minima problems, we introduce a hard thresholding operator, based on which the proposed MSL0 algorithm can accurately reconstruct sparse targets. Simulations and experimental results verify the performance of the proposed MSL0 algorithm.

Adaptive Control of an Inverted Pendulum by a Reinforcement Learningbased LQR Method

Inverted pendulums constitute one of the popular systems for benchmarking control algorithms. Several methods have been proposed for the control of this system, the majority of which rely on the availability of a mathematical model. However, deriving a mathematical model using physical parameters or system identification techniques requires manual effort. Moreover, the designed controllers may perform poorly if system parameters change. To mitigate these problems, recently, some studies used Reinforcement Learning (RL) based approaches for the control of inverted pendulum systems. Unfortunately, these methods suffer from slow convergence and local minimum problems. Moreover, they may require hyperparameter tuning which complicates the design process significantly. To alleviate these problems, the present study proposes an LQR-based RL method for adaptive balancing control of an inverted pendulum. As shown by numerical experiments, the algorithm stabilizes the system very fast without requiring a mathematical model or extensive hyperparameter tuning. In addition, it can adapt to parametric changes online.

New modified Bat algorithm for blind speech enhancement in time domain

We address the speech enhancement problem for dual convolutif mixed channel by viewing it in a blind separation sources setting. One widely used technique to separate mixed signals is to apply adaptive filtering, the challenge is to identify an unknown finite impulse response. traditionally we apply a gradient-based algorithm to adapt filter coefficients. However, such algorithm often suffers from premature convergence ,when using large filters and non-stationary inputs , leading to the so-called local minimum problem , which affects the quality of enhanced signals significatively .one alternative to overcome this problem is to apply a population-based metaheuristic algorithms in which filter coefficients are adapted iteratively by minimizing a cost function .But even with this metaheuristic based solution, local minimum problem at large filters still exists. In order to avoid local minima and improve the chance to reach the global solution, we propose in this paper, a novel algorithm called a modified bat algorithm to render the search process efficiently by enhancing its capability of exploration and exploitation. Several experiments under different noise types are carried out using our proposed modified bat algorithm in comparison with some of the popular state-of-the-art algorithms. The enhanced signals obtained by each algorithm at the separation process outputs, show good behavior and superiority of our proposed algorithm. In terms of system misalignment, as well as a segmental signal-to-noise ratio.

Learn to Rotate: Part Orientation for Reducing Support Volume via Generalizable Reinforcement Learning

In design for additive manufacturing, an essential task is to determine the optimal build orientation of a part according to one or multiple factors. Heuristic search is used by the most part orientation methods to select the optimal orientation from a large solution space. Search algorithms occasionally converge towards the local optimum and waste considerable time on trial and error. The above issues could be addressed if there was an intelligent agent that knew the optimal search/rotation path for a given 3D model. A straightforward method to construct such an agent is reinforcement learning (RL). By adopting this idea, the time-consuming online searches in existing part orientation methods will be moved to the offline learning stage, potentially improving part orientation performance. This is a challenging research problem because the goal is to build an agent capable of rotating arbitrary 3D models, whereas RL agents frequently struggle to generalize in new scenarios. Therefore, this paper suggests a generalizable reinforcement learning (GRL) framework to train the agent, and a GPU-accelerated GRL benchmark to support the training, testing, and comparison of part orientation approaches. Experimental results demonstrate that the proposed part orientation method on average outperforms others in terms of effectiveness and efficiency. It is proved to have the potential to solve the local minima problems raised in the existing approaches, to swiftly discover the global (sub-)optimal solution (i.e. on average 2.62x to 229.00x faster than the random search algorithm), and to generalize beyond the environment in which it was trained.

Models and methods of learning neural networks with differentiated activation functions

Analysis of the literature made it clear that the problem associated with improving the performance and acceleration of ANN learning is quite actual, as ANNs are used every day in more and more industries. The concepts of finding more profitable activation functions have been outlined a lot, but changing their behavior as a result of learning is a fresh look at the problem. The aim of the study is to find new models of optimization tasks for the formulated prob-lem and effective methods for their implementation, which would improve the quality of ANN training, in particular by overcoming the problem of local minima. A studied of models and methods for training neural networks using an extended vector of varying parameters is conducted. The training problem is formulated as a continuous mul-tidimensional unconditional optimization problem. The extended vector of varying parameters implies that it includes some parameters of activation functions in addition to weight coeffi-cients. The introduction of additional varying parameters does not change the architecture of a neural network, but makes it impossible to use the back propagation method. A number of gradient methods have been used to solve optimization problems. Different formulations of optimization problems and methods for their solution have been investigated according to ac-curacy and efficiency criteria. The analysis of the results of numerical experiments allowed us to conclude that it is expedient to expand the vector of varying parameters in the tasks of training ANNs with con-tinuous and differentiated activation functions. Despite the increase in the dimensionality of the optimization problem, the efficiency of the new formulation is higher than the generalized one. According to the authors, this is due to the fact that a significant share of computational costs in the generalized formulation falls on attempts to leave the neighborhood of local min-ima, while increasing the dimensionality of the solution space allows this to be done with much lower costs.

A real‐time fuzzy motion planning system for unmanned aerial vehicles in dynamic 3D environments

This paper presents a new fuzzy potential system to plan the motion of Unmanned Aerial Vehicles (UAVs) in dynamic 3D Space. The system consists of two fuzzy subsystems representing the attractive model and the repulsive model of virtual forces in 3D. The attractive model will generate the attractive force required to pull the UAV in a smooth and optimized trajectory to land softly on a moving or stationary target. The repulsive model will generate the required repulsive force to avoid stationary or moving obstacles in 3D Space. The attractive fuzzy inference system takes the relative position and relative velocity between UAV and the target in the x, y, and z directions as inputs. It generates the required attractive force in the x, y, and z directions. The repulsive fuzzy inference system takes the relative position between UAV and obstacle in the xyz directions as input. Fuzzy associative memory (FAM) models the inputs and generates the required repulsive force in the x, y, and z directions. As a result, the UAV is considered to be moving under the influence of fuzzy virtual attractive and repulsive forces simultaneously. Accordingly, it will be able to change both its altitude and projected planner position concurrently and resolves the local minima problem if occurred. On the other hand, many classical models in dynamic environments require several additional inputs, such as the relative position and relative velocity, which increase the requirement on the measurement system to localize the moving objects in the 3D Space. Several experiments were performed and discussed to verify the robustness and effectiveness of the proposed motion planner with real-time implementations. The system performance was validated using three robotics platforms, two quadcopter drones, and one ground robot. The position and orientation of each robot were defined using a motion capture system with 6 opti-track cameras. The motion planning system produces a quadcopter drone's efficient and accurate low-frequency trajectory. The generated trajectory allows the drone to track the ground robot and avoid collision effectively with the second drone in the vicinity.

Using Differential Evolution to avoid local minima in Variational Quantum Algorithms

Variational Quantum Algorithms (VQAs) are among the most promising NISQ-era algorithms for harnessing quantum computing in diverse fields. However, the underlying optimization processes within these algorithms usually deal with local minima and barren plateau problems, preventing them from scaling efficiently. Our goal in this paper is to study alternative optimization methods that can avoid or reduce the effect of these problems. To this end, we propose to apply the Differential Evolution (DE) algorithm to VQAs optimizations. Our hypothesis is that DE is resilient to vanishing gradients and local minima for two main reasons: (1) it does not depend on gradients, and (2) its mutation and recombination schemes allow DE to continue evolving even in these cases. To demonstrate the performance of our approach, first, we use a robust local minima problem to compare state-of-the-art local optimizers (SLSQP, COBYLA, L-BFGS-B and SPSA) against DE using the Variational Quantum Eigensolver algorithm. Our results show that DE always outperforms local optimizers. In particular, in exact simulations of a 1D Ising chain with 14 qubits, DE achieves the ground state with a 100% success rate, while local optimizers only exhibit around 40%. We also show that combining DE with local optimizers increases the accuracy of the energy estimation once avoiding local minima. Finally, we demonstrate how our results can be extended to more complex problems by studying DE performance in a 1D Hubbard model.

Path planning algorithm based on Improved Artificial Potential Field method

The domain of research and development concerning mobile robot obstacle avoidance continues to remain an active area of interest. Artificial potential fields (APF) are a common and effective method for obstacle avoidance path planning, where the robot is guided to the target location by a simulated environmental potential field. Traditional artificial potential field methods tend to trap robots in local minima, impeding their ability to reach the goal. This research endeavours to introduce a new approach, the Improved Artificial Potential Field (IAPF) algorithm, which incorporates the A-star method in constructing the artificial potential field. This technique more effectively addresses the issue of path planning for mobile robots, thereby avoiding local minimum solutions. Through simulation experiments in different scenarios, the feasibility of the IAPF algorithm of this paper is verified. The results show that, compared with the traditional APF method, the IAPF algorithm can solve problem of local minimum and plan a sensible path.

Improved artificial potential field to solve the problem of local minimum

The artificial potential field approach is a traditional method that is frequently used for local path planning, but in order for it to be successful, it requires more than unreachable target sites, local minimums, and oscillation difficulties. An enhanced method that is based on discretized sampling was presented as a potential solution to these issues as a result of this information. In the first place, a decision must be made regarding whether or not to enter the local minimum mark. In order to free ourselves from the confines of the local minimum, we subsequently devised a motion that was perpendicular to the direction in which the object was being moved. In the end, a regression search is carried out in order to further hone in on the correct path. The results of the simulation show that this method is capable of efficiently handling the local minimum problem and providing appropriate paths, as demonstrated by a comparison between the conventional method and the enhanced method.

Improving the artificial potential field by A-star to solve the local minima problem

This paper discusses the method for artificial potential field in traditional sense. It is based on the algorithm with the planning of physics that guides a robot along a gradient toward a target endpoint by applying forces with gravitation and repulse within a robot environment. The article proposes to improve the potential field method by incorporating the A-star algorithm for the improvement of path planning in accuracy and efficiency. The A-star algorithm uses a cost function to measure the goodness of a node and finds the optimal path totally and thoroughly through heuristic search. The proposed method uses the A-star algorithm to generate the optimal path, which takes potential field and its method as basis, thus repeating the process until the robot reaches the end point. By combining the A-star algorithm and the method based on artificial potential field, the robot's driving route is made more reasonable, and thus testing and verifying how the method works through an experiment with simulation.

Improved MTAPF method for autonomous vehicles

Path planning has evolved into one of the most crucial critical studies with the introduction of numerous autonomous vehicles. The artificial potential field approach is being used by many intelligent vehicles to plan their paths, and a variety of autonomous vehicles may avoid barriers depending on their own conditions and the movement of the obstacles. The design of dynamic real-time paths frequently makes use of artificial potential field (APF) techniques. The issue of local minima and unattainable targets in the APF approach is addressed in this study with a better solution. The global optimum path is first determined using the heuristic A-STAR path algorithm in this work, which is combined with the artificial potential field approach. The global optimal path is then divided into many sub-goals to form a sequence. The artificial potential field approach is then used to produce these targets' final routes sequentially, considerably lowering the likelihood that many unmanned vehicles may simultaneously enter a local minimum. The method could avoid the local minima problem and plan a viable path is supported by simulation results.

Spacecraft environmental path planning method based on improved artificial potential field

Spacecraft is the primary means of transportation for human exploration of outer space. With the advancement of science and technology, existing space exploration can no longer satisfy people's desire to explore, in the future, further and deeper space exploration is the goal of development. And the safety of spacecraft navigation in space requires the development of a path planning system. Although there have been many kinds of methods for path planning at this stage, all of them have their strengths and specialize in planning directions, but they also have defects. Based on this, this study improves the traditional artificial potential field method, by adjusting its repulsive field calculation and combining it with the RRT algorithm. The improved method can avoid the local minimum problem of the traditional artificial potential field and generate paths to meet the requirements of spacecraft. The effectiveness of the algorithm is verified by simulation experimental results.

Kinetics and mechanism of nonisothermal crystallization of biobased poly(hexamethylene 2,5-furan dicarboxylate)

Biobased poly(hexamethylene 2,5-furan dicarboxylate) (PHF) was synthesized by the two-stage melt polycondensation method (transesterification and polycondensation) in a glass batch reactor. The nonisothermal crystallization from the melt and from the glass was studied by means of Differential Scanning Calorimetry, Fast Scanning Calorimetry and advanced kinetic analysis. It is shown that changes in the crystallization regime occurs at certain temperatures and that the end of the crystallization presents some deviation from what is predicted by the Hoffman-Lauritzen's theory of growth rate. A method is presented that allows the determination of the equilibrium melting temperature, the infinite glass transition temperature, the temperature at maximum of the growth rate, and accurate simulation of crystallization rate curves. An equation is proposed for modelling the crystallization process using a methodology that avoid the problem of local minima occurring when too many parameters must be determined simultaneously.

Disturbance rejection controller design based on adaptive nonlinear FOPID controller and chaotic WOA with a neuro-fuzzy approximation for URV robot

This paper presents an adaptive neuro-fuzzy-based nonlinear fractional order proportional integral derivative (ANF-NLFOPID) controller to stabilize six degrees of freedom (6-DOF) underwater robotic vehicle (URV). Generally, the stability of the URV system is jammed due to internal and external variations related to unknown uncertainties and disturbances in the URV model, which lead to trajectory tracking problems. Thus, to solve unknown uncertainties and disturbances problems, an ANF network is proposed to estimate unknown uncertainties and disturbances. At the same time, an NLFOPID controller is proposed to minimize the error effect generated by the variation of the URV model parameters. Considering the unknown and unpredictable behavior of the URV system in the presence of uncertainties and disturbances, the ANF-NLFOPID controller parameters are tuned continuously using an improved whale optimization algorithm based on chaotic theory (IWOA-CT). The main working principle of the IWOA-CT is to solve the local minimum (optimum) problem and achieve the global optimum points to deliver the best parameter values for the ANF-NLFOPID controller. A simulation and experimental results are conducted to measure the performance of the ANF-NLFOPID controller compared to other existing works. MATLAB software is used to simulate four trajectory tracking cases, where the first case proved the superiority of the ANF-NLFOPID controller by 52.559%, 70.028%, and 73.83%, the second case shows that the ANF-NLFOPID improves the trajectory tracking performance by 34.399%, 46.094%, and 59.143%, the third case demonstrates the effectiveness of the ANF-NLFOPID controller by 41.922%, 51.205%, and 62.252%, and the fourth case shows that the ANF-NLFOPID enhance the overall trajectory tracking efficiency by 29.356%, 38.413%, and 44.795% compared to adaptive neural network-based nonlinear FOPID (ANNFOPID), adaptive fuzzy-based nonlinear PID (AFNLPID), and disturbance rejection based on adaptive neural network (DR-ANN) controllers respectively. In the end, the experimental results were conducted using a real-world URV model and showed that the ANF-NLFOPID controller presents superior in solving trajectory tracking problems compared to the ANNFOPID controller.

Path planning of unmanned surface vehicle based on artificial potential field approach considering virtual target points

Aiming at the local minimum problem and target unreachable problems in the path planning of unmanned surface vehicle (USV), a path planning algorithm of USV considering virtual target point is proposed. For the target unreachable problem, a repulsive force potential field function is created. According to the measured distance between the target and the obstacle, the repulsive force of the target is zero, so that the USV can reach the target point. For the local minimum problem, the local minimum caused by various obstacles is analyzed, simulated annealing (SA) and artificial potential field approach (APFA) are combined to solve the minimum point problem caused by general obstacles. For the local minimum problem caused by special U-shaped obstacles, a virtual target point algorithm (VTPA) is established to solve this problem. The simulation results prove that this algorithm solves the problem of long path caused by too large repulsive force. Compared with Dual-Tree Rapidly exploring Random Tree (DT-RRT) algorithm, the efficiency of this algorithm has been significantly improved. Algorithm running time was reduced by 33.4%. Path length was reduced by 17.8%. Not only the time is saved, but also the path planning is optimized, so that the speed of the algorithm is accelerated.

Improved Nelder-Mead algorithm for output voltage control of a synchronous generator

It is known that the standard Nelder-Mead algorithm (NMA) is subject to the problem of local minimum. This paper proposes an improved Nelder-Mead algorithm (INMA) based on dynamically varying the reflection, expansion, contraction and the shrinkage coefficients, following a cosine function. Dynamical coefficients intensify the search space exploration and also increase the ability of quickly finding the optimal solution. Firstly, the effectiveness and validity of this approach are confirmed by using some benchmark functions. Secondly, the approach is also verified by applying it for tuning a Proportional–Integral–Derivative (PID) controller used to regulate the voltage of a synchronous generator (SG) under different loading conditions. The PID controller parameters are obtained by a minimisation of the quadratic output error between the reference and the SG output voltage calculated from the adopted model. A comparison is established between INMA, standard NMA, genetic algorithm (GA) and particle swarm optimisation (PSO). The Obtained results show that the INMA has a better performance compared to other algorithms.

An intellectual optimization of k-anonymity model for efficient privacy preservation in cloud platform

Concerns of security as well as privacy are the chief obstacles which have prevented the public cloud’s extensive adoption in Intel IT as well as across the industry. Generally, IT organizations are quite reluctant to store sensitive as well as valuable data in infrastructures which are out of their control. The technique of anonymization is employed by enterprises to raise the security of the public cloud’s data whilst facilitating the data’s analysis as well as application. The procedure of data anonymization will modify how the data is either employed or published in such a way that it will prevent the key information’s identification. The privacy issues are addressed using k-anonymity. However, the issue of selecting the variables for anonymization and suppression of variables without the loss of knowledge is an optimization problem. To address the selection of variables for anonymization and suppression, metaheuristic algorithms are used. Diverse research groups have successfully utilized the River Formation Dynamics (RFD) metaheuristic to handle numerous problems of discrete combinatorial optimization. Even so, this metaheuristic has never been adapted for use in domains of continuous optimization. To mitigate the local minima problem, hybridization of the algorithms is proposed. In this work, a modified K-Anonymity technique’s proposal has been given by using the Modified Hill Climbing (MHC) optimization, the RFD-MHC optimization, the RFD-PSO optimization, the RFD-MHC suppression as well as the RFD-PSO suppression. Furthermore, proposal for a suppression technique has also been given in this work. Experiments demonstrated that the RFD-PSO optimization has higher classification accuracy in the range of 6.73% to 8.55% when compared to manual K-anonymization. The work has also given better trade off for security analysis and data utility effectiveness.

Modified Backpropagation Algorithm with Multiplicative Calculus in Neural Networks

Backpropagation is one of the most widely used algorithms for training feedforward deep neural networks. The algorithm requires a differentiable activation function and it performs computations of the gradient proceeding backwards through the feedforward deep neural network from the last layer through to the first layer. In order to calculate the gradient at a specific layer, the gradients of all layers are combined via the chain rule of calculus. One of the biggest disadvantages of the backpropagation is that it requires a large amount of training time. To overcome this issue, this paper proposes a modified backpropagation algorithm with multiplicative calculus. Multiplicative calculus provides an alternative to the classical calculus and it defines new kinds of derivative and integral forms in multiplicative form rather than addition and subtraction forms. The performance analyzes are discussed in various case studies and the results are given comparatively with classical backpropagation algorithm. It is found that the proposed modified backpropagation algorithm converges in less time to the solution and thus provides fast training in the given case studies. It is also shown that the proposed algorithm avoids the local minima problem.

A real-time local path planning algorithm for the wave glider based on time-stamped collision detection and improved artificial potential field

The local path planning technology of wave gliders (WGs) is faced with two inherent difficulties: the impact of the complex marine environment on the path and the weak maneuverability. In this paper, a fusion algorithm based on the time-stamped collision detection (TCD) and the environmental improved artificial potential field (EAPF) is proposed to solve the above problems, which combines the dynamic model of the WG to guide it by generating a desired heading output. The improved APF (IAPF) is developed to solve the problems of local minimum and target unreachability. The influence of the complex marine environment on the WG is considered during dynamic obstacle avoidance, and the proposed EAPF improves the maneuverability of the WG with the help of environmental field, while reducing the impact of the environment on the path. For dynamic obstacle prediction, different dynamic obstacle models are used, and the TCD is proposed to predict the collision risk between WG and dynamic obstacles to adapt to the weak maneuverability of the WG. The simulation results show that the proposed TCD-EAPF can realize the early avoidance of dynamic obstacles and improve the maneuverability of the WG in obstacle avoidance.