Local Minima Problem Research Articles

Modified Artificial Potential Field for the Path Planning of Aircraft Swarms in Three-Dimensional Environments.

Path planning techniques are of major importance for the motion of autonomous systems. In addition, the chosen path, safety, and computational burden are essential for ensuring the successful application of such strategies in the presence of obstacles. In this context, this work introduces a modified potential field method that is capable of providing obstacle avoidance, as well as eliminating local minima problems and oscillations in the influence threshold of repulsive fields. A three-dimensional (3D) vortex field is introduced for this purpose so that each robot can choose the best direction of the vortex field rotation automatically and independently according to its position with respect to each object in the workspace. A scenario that addresses swarm flight with sequential cooperation and the pursuit of moving targets in dynamic environments is proposed. Experimental results are presented and thoroughly discussed using a Crazyflie 2.0 aircraft associated with the loco positioning system for state estimation. It is effectively demonstrated that the proposed algorithm can generate feasible paths while taking into account the aforementioned problems in real-time applications.

SECURITY APPLICATION OF NEURAL NETWORKS UNDER THE INSPECTION OF NONLINEAR DYNAMIC SYSTEMS

Based on the improved BP neural network, this paper establishes an adaptive online controlling model and adopts the model to optimize the controlling accuracies in discrete nonlinear dynamic systems and inverted pendulum systems. To avoid the local minimum problem of the BP neural network’s objective function in the training process, this paper proposes a neural network training method based on the quasi-Newton method (BFGS) optimization algorithm. Compared with other control methods, the neural network-based inverted pendulum control method proposed in this paper has higher control accuracy. Through the control simulation of its power system uses a discrete control method and the control of the inverted pendulum model system, this paper verifies the validity and good control has significantly improved the control method.

Reinforcement learning in optimization problems. Applications to geophysical data inversion

<abstract> <p>In this paper, we introduce a novel inversion methodology that combines the benefits offered by Reinforcement-Learning techniques with the advantages of the Epsilon-Greedy method for an expanded exploration of the model space. Among the various Reinforcement Learning approaches, we applied the set of algorithms included in the category of the Q-Learning methods. We show that the Temporal Difference algorithm offers an effective iterative approach that allows finding an optimal solution in geophysical inverse problems. Furthermore, the Epsilon-Greedy method properly coupled with the Reinforcement Learning workflow, allows expanding the exploration of the model-space, minimizing the misfit between observed and predicted responses and limiting the problem of local minima of the cost function. In order to prove the feasibility of our methodology, we tested it using synthetic geo-electric data and a seismic refraction data set available in the public domain.</p> </abstract>

Elastic Full Waveform Inversion Based on Full-Band Seismic Data Reconstructed by Dual Deconvolution

Affected by the low-frequency seismic data missing and multiple parameters coupling, elastic full waveform inversion is easy to fall into local minima. This paper attempts to solve the local minima problem from two aspects: low-frequency seismic data reconstruction and wave mode decomposition. First, by introducing the envelope into sparse constrained deconvolution, an envelope-based sparse constrained deconvolution method is proposed to overcome the problem caused by the phase shift and side lobes. However, the resolution of the envelope is insufficient to identify overlapping seismic events, which are generated by velocity models rich in thin layers. Therefore, sparse constrained deconvolution and envelope-based sparse constrained deconvolution are combined, and a dual deconvolution method is proposed: sparse constrained deconvolution is used to improve the resolution of the original seismic data, then envelope-based sparse constrained deconvolution is used to reconstruct high-precision reflection sequence. Convolve the reconstructed reflection sequence with the full-band source wavelet to obtain the full-band seismic data. Secondly, for the multi-parameter coupling problem, we use wave mode decomposition to obtain separated P- and S-wave. Finally, a multi-scale elastic full waveform inversion method based on dual deconvolution and wave mode decomposition is proposed. Numerical experiment results demonstrate the algorithm proposed in the article.

Local path planning for autonomous mobile robots by integrating modified dynamic‐window approach and improved follow the gap method

AbstractMobile robots need to automatically generate a safe, goal‐oriented, and fast collision‐free trajectory in real‐time during the movement in an indoor/outdoor environment. A planned trajectory must be adaptable and drivable with environmental changes where various static and moving obstacles may be present. The ultimate goal of a robot is to reach the destination without hitting any obstacles, therefore, a reactive local path planning algorithm is needed. In this paper, a novel local algorithm is proposed by integrating dynamic window approach (DWA) and improved follow the gap method (IFGM) to generate a collision‐free trajectory for a mobile robot which is capable to avoid any moving obstacles presenting in the surrounding environment. In this proposed method, first, a safety distance is maintained according to the relative position of obstacles and the robot. Moreover, find a feasible gap to direct the robot toward the desired goal. Besides, the heading angle is calculated to change the direction of the robot for avoiding collision with nearby obstacles. After that, calculate the appropriate velocity for the robot. Finally, a robust, safe, and goal‐directed trajectory is generated which does not suffer from global convergence and local minima problems. The performance and effectiveness of this proposed algorithm are evaluated by experimental results.

ESIMD: Epileptic seizure identification using metaheuristic deep learning technique

AbstractThe identification of epileptic seizure from electroencephalogram (EEG) segments is significant for seizure identification and classification. In epilepsy, the patients develop epileptic seizures. These lead to neurological disorders and abnormal brain activities. The manual identification of seizures is not very efficient. As the manual analysis of EEG data requires expert neurologists it is prone to inaccuracies. Therefore, automated methods for seizure identification are required. Deep learning methods have shown efficiency in the seizure classification problem. Many challenges are faced by the existing methods owing to the properties of the EEG signals like transiency, non‐stationary behaviour and presence of noise. Therefore, to overcome these challenges and design a highly efficient method an automated method based on deep learning and spotted hyena optimization (SHO) algorithm is proposed. The SHO algorithm is used to initialize the network as it avoids the local minima problem. Epileptic seizure identification using metaheuristic deep learning (ESIMD) is proposed in this paper which is a hybridization of spotted hyena and deep convolution network. The convolutional neural network used has two blocks, the first block is used for feature extraction and the second block for seizure classification. ESIMD is used for seizure detection and classification. The proposed algorithm can handle the complex and large number of features in EEG signals. The performance of the proposed is evaluated by applying it on EEG Bonn Dataset. The results are compared with 13 other conventional methods. The comparative study shows that ESIMD gives higher accuracy than the existing methods.

Hybrid generative regression-based deep intelligence to predict the risk of chronic disease

PurposeChronic diseases are considered as one of the serious concerns and threats to public health across the globe. Diseases such as chronic diabetes mellitus (CDM), cardio vasculardisease (CVD) and chronic kidney disease (CKD) are major chronic diseases responsible for millions of death. Each of these diseases is considered as a risk factor for the other two diseases. Therefore, noteworthy attention is being paid to reduce the risk of these diseases. A gigantic amount of medical data is generated in digital form from smart healthcare appliances in the current era. Although numerous machine learning (ML) algorithms are proposed for the early prediction of chronic diseases, these algorithmic models are neither generalized nor adaptive when the model is imposed on new disease datasets. Hence, these algorithms have to process a huge amount of disease data iteratively until the model converges. This limitation may make it difficult for ML models to fit and produce imprecise results. A single algorithm may not yield accurate results. Nonetheless, an ensemble of classifiers built from multiple models, that works based on a voting principle has been successfully applied to solve many classification tasks. The purpose of this paper is to make early prediction of chronic diseases using hybrid generative regression based deep intelligence network (HGRDIN) model.Design/methodology/approachIn the proposed paper generative regression (GR) model is used in combination with deep neural network (DNN) for the early prediction of chronic disease. The GR model will obtain prior knowledge about the labelled data by analyzing the correlation between features and class labels. Hence, the weight assignment process of DNN is influenced by the relationship between attributes rather than random assignment. The knowledge obtained through these processes is passed as input to the DNN network for further prediction. Since the inference about the input data instances is drawn at the DNN through the GR model, the model is named as hybrid generative regression-based deep intelligence network (HGRDIN).FindingsThe credibility of the implemented approach is rigorously validated using various parameters such as accuracy, precision, recall, F score and area under the curve (AUC) score. During the training phase, the proposed algorithm is constantly regularized using the elastic net regularization technique and also hyper-tuned using the various parameters such as momentum and learning rate to minimize the misprediction rate. The experimental results illustrate that the proposed approach predicted the chronic disease with a minimal error by avoiding the possible overfitting and local minima problems. The result obtained with the proposed approach is also compared with the various traditional approaches.Research limitations/implicationsUsually, the diagnostic data are multi-dimension in nature where the performance of the ML algorithm will degrade due to the data overfitting, curse of dimensionality issues. The result obtained through the experiment has achieved an average accuracy of 95%. Hence, analysis can be made further to improve predictive accuracy by overcoming the curse of dimensionality issues.Practical implicationsThe proposed ML model can mimic the behavior of the doctor's brain. These algorithms have the capability to replace clinical tasks. The accurate result obtained through the innovative algorithms can free the physician from the mundane care and practices so that the physician can focus more on the complex issues.Social implicationsUtilizing the proposed predictive model at the decision-making level for the early prediction of the disease is considered as a promising change towards the healthcare sector. The global burden of chronic disease can be reduced at an exceptional level through these approaches.Originality/valueIn the proposed HGRDIN model, the concept of transfer learning approach is used where the knowledge acquired through the GR process is applied on DNN that identified the possible relationship between the dependent and independent feature variables by mapping the chronic data instances to its corresponding target class before it is being passed as input to the DNN network. Hence, the result of the experiments illustrated that the proposed approach obtained superior performance in terms of various validation parameters than the existing conventional techniques.

Grade estimation using a hybrid method of back-propagation artificial neural network and particle swarm optimization with integrated samples coordinate and local variability

Grade estimation is a critical issue in mineral resource evaluation, being extensively investigated by data mining techniques. In this paper, a hybrid method composed of back-propagation artificial neural network (BPANN) and particle swarm optimization (PSO) algorithms is proposed to solve the grade estimation problem. The PSO algorithm is implemented to optimize the BPANN parameters by reducing the effects of a local minimum problem, which is one of the critical drawbacks of BPANN. The proposed BPANN-PSO algorithm is validated for Al2O3 grade estimation in one of Iran's largest Bauxite deposits. The performance of BPANN-PSO algorithm for grade estimation is compared with BPANN and ordinary kriging. The experimental results indicate that the BPANN-PSO model is more appropriate for estimating Al2O3 grade with a reasonable error.

Path Planning of a Mechanical Arm Based on an Improved Artificial Potential Field and a Rapid Expansion Random Tree Hybrid Algorithm

To improve the path planning efficiency of a robotic arm in three-dimensional space and improve the obstacle avoidance ability, this paper proposes an improved artificial potential field and rapid expansion random tree (APF-RRT) hybrid algorithm for the mechanical arm path planning method. The improved APF algorithm (I-APF) introduces a heuristic method based on the number of adjacent obstacles to escape from local minima, which solves the local minimum problem of the APF method and improves the search speed. The improved RRT algorithm (I-RRT) changes the selection method of the nearest neighbor node by introducing a triangular nearest neighbor node selection method, adopts an adaptive step and generates a virtual new node strategy to explore the path, and removes redundant path nodes generated by the RRT algorithm, which effectively improves the obstacle avoidance ability and efficiency of the algorithm. Bezier curves are used to fit the final generated path. Finally, an experimental analysis based on Python shows that the search time of the hybrid algorithm in a multi-obstacle environment is reduced to 2.8 s from 37.8 s (classic RRT algorithm), 10.1 s (RRT* algorithm), and 7.4 s (P_RRT* algorithm), and the success rate and efficiency of the search are both significantly improved. Furthermore, the hybrid algorithm is simulated in a robot operating system (ROS) using the UR5 mechanical arm, and the results prove the effectiveness and reliability of the hybrid algorithm.

Anti-collision zone division based hazard avoidance guidance for asteroid landing with constant thrust

Future asteroid landing and sample return missions will seek for landing sites with high scientific value, such as hazardous terrains, which means that the spacecraft needs the ability of autonomous hazard avoidance. Nowadays, the guidance algorithm based on artificial potential function plays an increasingly important role in hazard avoidance, but the local minimum problem makes that the spacecraft cannot reach the desired target landing point in some complex terrains. In this paper, a novel hazard avoidance guidance method which improves the traditional artificial potential function is developed. This method focuses on the impact zone analysis of hazards and defines anti-collision zone. In addition, a new repulsive potential function in logarithmic form is designed with continuity and fast numerical change rate in the anti-collision zone on this basis, and the problem of spacecraft falling into local minimum zone in complex terrains can be effectively avoided. Considering the practical application of constant thrust engine, the hazard avoidance control law with constant thrust sliding mode is designed to reduce switching frequency and fuel consumption. The performance of the proposed guidance law is verified through a set of simulations, as well as the global stability of the control system under uncertainty and perturbation conditions.

Absorption and Diffusion Enabled Ultrathin Broadband Metamaterial Absorber Designed by Deep Neural Network and PSO

With absorption and interference cancellation, lossy metamaterials can achieve broadband electromagnetic wave absorption. However, the design of such metamaterial absorbers (MMAs) is very complicate, because tremendous meta-atoms and their configuration parameters need to be determined. The conventional methods, such as parameter sweep and adjoint-based optimization, suffer from slow convergence and local minimum problem. In this letter, a deep neural network (DNN) is used to map the configuration parameters of a type of meta-atom onto its reflection coefficients. The DNN well predicts the reflection coefficients and is applied to design the MMA under the demand of −10 dB backscattering reduction (BSR) covering the microwave S to Ku bands with the smallest thickness. By globally searching the configuration parameter space using particle swarm optimization (PSO) algorithm, which automatically cooperates the absorption and phase cancelation (or diffusion) of meta-atoms, we obtain the optimized configuration of the meta-atoms and corresponding filling ratios. The designed MMA realizes −10 dB absorption bandwidth covering 2.2–18 GHz with the thickness only 4 mm, which is further verified by experiments. The performance of our absorber is better than other similar absorbers reported. Our letter provides a useful method for ultrathin broadband MMA design, which can also be applied to other functional devices based on metamaterials.

Artificial immune system training algorithm for a dendritic neuron model

Dendritic neuron model (DNM), which is a single neuron model with a plastic structure, has been applied to resolve various complicated problems. However, its main learning algorithm, namely the back-propagation (BP) algorithm, suffers from several shortages, such as slow convergence rate, being easy to fall into local minimum and over-fitting problems. That largely limits the performances of the DNM. To address this issue, another bio-inspired learning paradigm, namely the artificial immune system (AIS) is employed to train the weights and thresholds of the DNM, which is termed AISDNM. These two methods have advantages on different issues. Due to the powerful global search capability of the AIS, it is considered to be efficient in improving the performance of the DNM. To evaluate the performance of AISDNM, eight classification datasets and eight prediction problems are adopted in our experiments. The experimental results and statistical analysis confirm that the AISDNM can exhibit superior performance in terms of accuracy and convergence speed when compared with the multilayer perceptron (MLP), decision tree (DT), the support vector machine with the linear kernel (SVM-l), the support vector machine with the radial basis function kernel (SVM-r), the support vector machine with the polynomial kernel (SVM-p) and the conventional DNM. It can be concluded that the reasonable combination of two different bio-inspired learning paradigms is efficient. Furthermore, for the classification problems, empirical evidence also validates the AISDNM can delete superfluous synapses and dendrites to simplify its neural structure, then transform the simplified structure into a logic circuit classifier (LCC) which is suitable for hardware implementation. The process does not sacrifice accuracy but significantly improves the classification speed. Based on these results, both the AISDNM and the LCC can be regarded as effective machine learning techniques to solve practical problems.

Solving an inverse elliptic coefficient problem by convex non-linear semidefinite programming

Several applications in medical imaging and non-destructive material testing lead to inverse elliptic coefficient problems, where an unknown coefficient function in an elliptic PDE is to be determined from partial knowledge of its solutions. This is usually a highly non-linear ill-posed inverse problem, for which unique reconstructability results, stability estimates and global convergence of numerical methods are very hard to achieve. The aim of this note is to point out a new connection between inverse coefficient problems and semidefinite programming that may help addressing these challenges. We show that an inverse elliptic Robin transmission problem with finitely many measurements can be equivalently rewritten as a uniquely solvable convex non-linear semidefinite optimization problem. This allows to explicitly estimate the number of measurements that is required to achieve a desired resolution, to derive an error estimate for noisy data, and to overcome the problem of local minima that usually appears in optimization-based approaches for inverse coefficient problems.

Research on improved convolutional wavelet neural network

Artificial neural networks (ANN) which include deep learning neural networks (DNN) have problems such as the local minimal problem of Back propagation neural network (BPNN), the unstable problem of Radial basis function neural network (RBFNN) and the limited maximum precision problem of Convolutional neural network (CNN). Performance (training speed, precision, etc.) of BPNN, RBFNN and CNN are expected to be improved. Main works are as follows: Firstly, based on existing BPNN and RBFNN, Wavelet neural network (WNN) is implemented in order to get better performance for further improving CNN. WNN adopts the network structure of BPNN in order to get faster training speed. WNN adopts the wavelet function as an activation function, whose form is similar to the radial basis function of RBFNN, in order to solve the local minimum problem. Secondly, WNN-based Convolutional wavelet neural network (CWNN) method is proposed, in which the fully connected layers (FCL) of CNN is replaced by WNN. Thirdly, comparative simulations based on MNIST and CIFAR-10 datasets among the discussed methods of BPNN, RBFNN, CNN and CWNN are implemented and analyzed. Fourthly, the wavelet-based Convolutional Neural Network (WCNN) is proposed, where the wavelet transformation is adopted as the activation function in Convolutional Pool Neural Network (CPNN) of CNN. Fifthly, simulations based on CWNN are implemented and analyzed on the MNIST dataset. Effects are as follows: Firstly, WNN can solve the problems of BPNN and RBFNN and have better performance. Secondly, the proposed CWNN can reduce the mean square error and the error rate of CNN, which means CWNN has better maximum precision than CNN. Thirdly, the proposed WCNN can reduce the mean square error and the error rate of CWNN, which means WCNN has better maximum precision than CWNN.

Quantitative Performance Review of Wheeled Mobile Robot Path Planning Algorithms

Path planning evaluates and identifies an obstacle free path for a wheeled mobile robot (WMR) to traverse within its workspace. It emphasizes metric like, start and goal coordinate, static or dynamic workspace, static or dynamic obstacles, computational time and local minimum problem. Path planning play a significant role toward WMR effective traverse within it workspace like industrial, military, hospital, school and office. In this workspace, path planning is an optimal method to increase the productivity of WMR to achieve it specific task. Hence, in this paper, we present a review of path planning algorithms (classical algorithms, heuristics and intelligent algorithms, and machine learning algorithm) for mobile robot using statistical method. Regarding our objective, we use this statistical method to evaluate the success of these algorithms base on the following metrics: architecture (hybrid or standalone), algorithm sub-category (global or local or combine), workspace (static or dynamic), obstacle type (static or dynamic), number of obstacle (≤ 2, ≤ 5, > 5) and test workspace (virtual or real-world). Research materials are sourced from recognized databases where relevant research articles are obtained and analyzed. Result shows hybrid of machine learning approach with heuristic and intelligent algorithm has superior performance where they are applied compare to other hybrid. Also, in complex workspace Q-learning algorithm outperforms other algorithms. To conclude future research is discussed to provide reference for hybrid of Q-learning algorithm with Cuckoo Search, Shuffled Frog Leaping and Artificial Bee Colony algorithm to improve its performance in complex workspace.

Through-the-Wall Nonlinear SAR Imaging

An inverse scattering problem (ISP) for synthetic aperture radar (SAR) data in application to through-the-wall imaging is addressed. In contrast with the conventional algorithms of SAR imaging, which work with the linearized mathematical model based on the Born approximation, the fully nonlinear case is considered here. To avoid the local minima problem, the so-called “convexification” globally convergent inversion scheme is applied to approximate the distribution in the slant range (SR) plane of a function that is associated with the dielectric constant. It is demonstrated that this function estimates quite well both the value of the dielectric constant and the location of the target. The benchmark scene of this article comprises a homogeneous dielectric wall and different dielectric targets hidden behind it. The results comprise 2-D images of the SR dielectric constant of the scene of interest. Numerical results are obtained by the proposed inversion method for both the computationally simulated and experimental data. Our results show that the values, cross-range sizes, and locations of SR dielectric constants for targets hidden behind the wall are close to those of real targets. Numerical comparison with the solution of the linearized ISP provided by the Born approximation, commonly used in conventional SAR imaging, shows a significantly better accuracy of our results.

Multiscale phase inversion for vertical transverse isotropic media

ABSTRACTInanisotropy full waveform inversion, the pseudo‐acoustic approximation is widely used to reduce the computation cost. However, artefacts and inaccurate predictions of amplitudes by the pseudo‐acoustic approximation often result in slow convergence in the full waveform inversion iterations and inaccurate tomograms. To solve this problem, multiscale phase inversion methodology is extended to vertical transverse isotropic media. In multiscale phase inversion, the amplitude spectra of the predicted data are replaced by those of the recorded data to mitigate the amplitude mismatch problem. Moreover, multiscale phase inversion tends to avoid the local minimum problem of full waveform inversion by temporally integrating the traces several times. Numerical tests on synthetic data and field data demonstrate the superiority of this method compared to conventional multiscale full waveform inversion for vertical transverse isotropic media.

Revisiting non-convexity in topology optimization of compliance minimization problems

PurposeThis is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods.Design/methodology/approachStarting from the global optimum of the compliance minimization problem, the authors employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum and how the initial guess has some weight in determining the final optimum.FindingsThe non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application.Originality/valueIn this article, the authors present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. The authors put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.

Enhanced bat algorithm for COVID-19 short-term forecasting using optimized LSTM.

The highly infectious COVID-19 critically affected the world that has stuck millions of citizens in their homes to avoid possible spreading of the disease. Researchers in different fields are continually working to develop vaccines and prevention strategies. However, an accurate forecast of the outbreak can help control the pandemic until a vaccine is available. Several machine learning and deep learning-based approaches are available to forecast the confirmed cases, but they lack the optimized temporal component and nonlinearity. To enhance the current forecasting frameworks’ capability, we proposed optimized long short-term memory networks (LSTM) to forecast COVID-19 cases and reduce mean absolute error. For the optimization of LSTM, we applied bat algorithm. Furthermore, to tackle the premature convergence and local minima problem of BA, we proposed an enhanced variant of BA. The proposed version utilized Gaussian adaptive inertia weight to control the individual velocity in the entire swarm. In addition, we substitute random walk with the Gaussian walk to observe the local search mechanism. The proposed LSTM examines the personal best solution with the swarm’s local best and preserves the optimal solution by combining the Gaussian walk. To evaluate the optimized LSTM, we compared it with the non-optimal version of LSTM, recurrent neural network, gated recurrent units, and other recent state-of-the-art algorithms. The experimental results prove the superiority of the optimized LSTM over other recent algorithms by obtaining 99.52 % accuracy.

Analysis of seismic inversion with optimal transportation and softplus encoding

This paper is devoted to the theoretical and numerical investigation of the local minimum problem in an inverse boundary value problem. We provide a mathematical analysis for the objective function of the optimal transportation type in the context of seismic full waveform inversion. In particular, we prove that the gradient obtained using the adjoint-state method does not depend on the specific choice of the Kantorovich potentials. Moreover, our frequency analysis results show a decreasing sensitivity of the reconstruction as the data misfit is concentrated in the high-frequency part. This confirms previous observations in many numerical experiments. We also propose a new method using the softplus encoding, which maps the seismic data into probability measures and, therefore, the Wasserstein metric can be applied. The softplus encoding retains the convexity of the data misfit with respect to translations and provides a parameter to tune the landscape of the objective function. The effectiveness of the proposed method is demonstrated numerically on an inversion task with the benchmark Marmousi model.