Nonlinear Function Optimization Research Articles

Optimization Techniques in the Localization Problem: A Survey on Recent Advances

Optimization is a mathematical discipline or tool suitable for minimizing or maximizing a function. It has been largely used in every scientific field to solve problems where it is necessary to find a local or global optimum. In the engineering field of localization, optimization has been adopted too, and in the literature, there are several proposals and applications that have been presented. In the first part of this article, the optimization problem is presented by considering the subject from a purely theoretical point of view and both single objective (SO) optimization and multi-objective (MO) optimization problems are defined. Additionally, it is reported how local and global optimization problems can be tackled differently, and the main characteristics of the related algorithms are outlined. In the second part of the article, extensive research about local and global localization algorithms is reported and some optimization methods for local and global optimum algorithms, such as the Gauss–Newton method, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and so on, are presented; for each of them, the main concept on which the algorithm is based, the mathematical model, and an example of the application proposed in the literature for localization purposes are reported. Among all investigated methods, the metaheuristic algorithms, which do not exploit gradient information, are the most suitable to solve localization problems due to their flexibility and capability in solving non-convex and non-linear optimization functions.

An Evaluation Model for Node Influence Based on Heuristic Spatiotemporal Features.

The accurate assessment of node influence is of vital significance for enhancing system stability. Given the structural redundancy problem triggered by the network topology deviation when an empirical network is copied, as well as the dynamic characteristics of the empirical network itself, it is difficult for traditional static assessment methods to effectively capture the dynamic evolution of node influence. Therefore, we propose a heuristic-based spatiotemporal feature node influence assessment model (HEIST). First, the zero-model method is applied to optimize the network-copying process and reduce the noise interference caused by network structure redundancy. Second, the copied network is divided into subnets, and feature modeling is performed to enhance the node influence differentiation. Third, node influence is quantified based on the spatiotemporal depth-perception module, which has a built-in local and global two-layer structure. At the local level, a graph convolutional neural network (GCN) is used to improve the spatial perception of node influence; it fuses the feature changes of the nodes in the subnetwork variation, combining this method with a long- and short-term memory network (LSTM) to enhance its ability to capture the depth evolution of node influence and improve the robustness of the assessment. Finally, a heuristic assessment algorithm is used to jointly optimize the influence strength of the nodes at different stages and quantify the node influence via a nonlinear optimization function. The experiments show that the Kendall coefficients exceed 90% in multiple datasets, proving that the model has good generalization performance in empirical networks.

Exploring the Performance of Whale Optimization Algorithm on Rosenbrock's Function

Optimization of complex and nonlinear functions is essential across various domains, from engineering and finance to artificial intelligence and machine learning. Rosenbrock's function stands as a fundamental benchmark for evaluating optimization algorithms due to its highly nonlinear and multimodal nature. Among the multitude of optimization algorithms, the Whale Optimization Algorithm (WOA) has garnered attention for its inspiration from the social behavior of humpback whales. However, its performance on Rosenbrock's function remains relatively unexplored. This paper aims to investigate the effectiveness of the WOA specifically on Rosenbrock's function through rigorous experimentation and analysis. By evaluating convergence speed, solution accuracy, and robustness, this study sheds light on WOA's behavior when confronted with the challenges posed by Rosenbrock's function. Comparative analysis with other optimization algorithms further elucidates WOA's adaptability and scalability. The findings contribute valuable insights for selecting suitable optimization algorithms in real-world applications and advance understanding of optimization algorithms' behavior in challenging landscapes.

A Particle Swarm Optimised Independence Estimator for Blind Source Separation of Neurophysiological Time Series.

The decomposition of neurophysiological recordings into their constituent neural sources is of major importance to a diverse range of neuroscientific fields and neuroengineering applications. The advent of high density electrode probes and arrays has driven a major need for novel semi-automated and automated blind source separation methodologies that take advantage of the increased spatial resolution and coverage these new devices offer. Independent component analysis (ICA) offers a principled theoretical framework for such algorithms, but implementation inefficiencies often drive poor performance in practice, particularly for sparse sources. Here we observe that the use of a single non-linear optimization function to identify spiking sources with ICA often has a detrimental effect that precludes the recovery and correct separation of all spiking sources in the signal. We go on to propose a projection-pursuit ICA algorithm designed specifically for spiking sources, which uses a particle swarm methodology to adaptively traverse a polynomial family of non-linearities approximating the asymmetric cumulants of the sources. We robustly prove state-of-the-art decomposition performance on recordings from high density intramuscular probes and demonstrate how the particle swarm quickly finds optimal contrast non-linearities across a range of neurophysiological datasets.

LiDAR-assisted accuracy improvement strategy for binocular visual measurement.

The measurement model of binocular vision is inaccurate when the measurement distance is much different from the calibration distance, which affects its practicality. To tackle this challenge, we proposed what we believe to be a novel LiDAR-assisted accuracy improvement strategy for binocular visual measurement. First, the 3D points cloud and 2D images were aligned by the Perspective-n-Point (PNP) algorithm to realize calibration between LiDAR and binocular camera. Then, we established a nonlinear optimization function and proposed a depth-optimization strategy to lessen the error of binocular depth. Finally, the size measurement model of binocular vision based on the optimized depth is built to verify the effectiveness of our strategy. The experimental results show that our strategy can improve the depth accuracy compared to three stereo matching methods. The mean error of binocular visual measurement decreased from 33.46% to 1.70% at different distances. This paper provides an effective strategy for improving the measurement accuracy of binocular vision at different distances.

Predictive longitudinal following control for ship platoon considering diesel engine driven propeller reversal

To realize synchronous movement of ship platoons, a cooperative Longitudinal Following Control (LFC) method based on Model Predictive Control (MPC) considering the diesel engine driven propeller reversal is studied. To describe the complex process of diesel engine driven propeller rotation, we propose a diesel engine driven propeller rotation model with taking engine fuel injection signal as an input and rotation speed as an output, and the rotation direction switching logic is expressed with a function. Then, a unified LFC predictive model is proposed in combination of the propeller rotation model, propeller propulsion model and ship following model. An objective function considering multiple constraints, energy consumption, and platoon performance is designed, and a dynamic optimization problem is solved with a nonlinear optimization function, where a discrete process (rotation direction switching) and a continuous process motion control are handled simultaneously. Four cases have been studies in simulation experiments with a standard container ship and 12K98ME diesel engine. The results show that the proposed MPC based LFC considering the Propeller Reversal (MPC-LFC-PR) can effectively achieve the ship platooning control in comparison of the MPC based LFC Not considering the Propeller Reversal (MPC-LFC-NPR) and the Proportional–Integral Derivative based LFC considering the Propeller Reversal (PID-LFC-PR).

Development of The Steepest Descent Method for Unconstrained Optimization of Nonlinear Function

The q-gradient method used a Yuan step size for odd steps, and geometric recursion as an even step size (q-GY). This study aimed to accelerate convergence to a minimum point by minimizing the number of iterations, by dilating the parameter q to the independent variable and then comparing the results with three algorithms namely, the classical steepest descent (SD) method, steepest descent method with Yuan Steps (SDY), and q-gradient method with geometric recursion (q-G). The numerical results were presented in tables and graphs. The study used Rosenbrock function f(x)=〖(1-x_1)〗^2+100〖(x_2-〖x_1〗^2)〗^2 and determined μ=1,σ_0=0.5,β=0.999, the starting point (x_0) with a uniform distribution on the interval x_0= (-2.048, 2.048) in R^2, with 49 starting points (x_0) executed using the Python online compiler on a 64bit core i3 laptop. The maximum number of iterations was 58,679. Using tolerance limits as stopping criteria is 10-4 and the inequality 〖f(x〗^*)>f to get numerical results. q-GY method down ward movement towards the minimum point was better than the SD and SDY methods while the numerical results of the Rosenbrock function showed good enough performance to increase convergence to the minimum point

A Sampling-Based Unfixed Orientation Search Method for Dual Manipulator Cooperative Manufacturing.

The case of dual manipulators with shared workspace, asynchronous manufacturing tasks, and independent objects is named a dual manipulator cooperative manufacturing system, which requires collision-free path planning as a vital issue in terms of safety and efficiency. This paper combines the mathematical modeling method with the time sampling method in the classification of robot path-planning algorithms. Through this attempt we can achieve an optimal local search path during each sampling period interval. Our strategy is to build the corresponding non-linear optimization functions set based on the motion characteristics of the dual manipulator system. In this way, the path-planning problem can be turned into a purely mathematical problem of solving the non-linear optimization programming equations set. The spatial geometric analysis is used to linearize the predicted dual-manipulator minimum distance equation, thus linearizing the non-linear optimization equations set. Finally, this system of linear optimization equations will be mapped directly into a virtual Euclidean space and then solved intuitively using the spatial geometry theory. By simulation and comparing with the previous strategies, we find that the planning results of the newly proposed planning strategy are smoother and have shorter deviations as well as a higher algorithmic efficiency in terms of spatial geometric properties.

A Hybrid Adaptive Control Architecture for Grid-Connected Inverter With Optimal Policy Generation

A nonlinear optimization-based hybrid control architecture for grid-connected inverters is presented in this article. The proposed control approach augments the existing inverter control with an identification-based adaptive control architecture. Grid dynamics are first represented as energy signals at the inverter terminals using the concept of an energy function. The nonlinear optimization function will act on this dynamic energy signal and derive an optimal control gain for the augmented hybrid control architecture. The optimization function derived in this work considers both the state energy and controller effect. The proposed architecture developed considering the nonlinearities in the system ensures excellent performance during high-frequency grid dynamics. Based on validation on a real power grid, it was observed that the proposed architecture provides better control accuracy (more than 20%) when compared to static PI controller acting alone.

Appropriate Operating Policy for a Reservoir System Based on Inflow States (Mosul Reservoir as a Case Study)

The present study has focused on the selection of appropriate operating policies for a reservoir system to maximize the hydropower generation through the derivation of operation rule curves for different states of the inflow into the reservoir. And in order to accomplish this task, 30 years of monthly observed inflow has been used and arranged into five intervals with lower and upper values of each interval. The Genetic Algorithms techniques were implemented to obtain the optimal operating policies for each of the proposed five categories of inflow. Furthermore, and in order to alleviate the adverse effects of trapping in local maxima, a hybrid method is suggested making use of the built-in functions of optimization available in the Matlab software. The non-linear optimization function used the values of the variables obtained by GA's as initial solutions required by the optimization process to reach global solutions. One of the main objectives of the current study was to build a simple mechanism to select the most appropriate operating policy which is compatible with the nature of the inflow state entering the reservoir during a certain period of time. Consequently, a simulation model was conducted using SIMULINK technique to mimic the Mosul reservoir system which is selected as a case study to test the proposed method. The results reveal an improvement by 10 % of hydropower generation over that produced over the 30 years of real operation using the current method.

Machine‐learning‐based methods for output‐only structural modal identification

In this study, we propose a machine-learning-based approach to identify the modal parameters of the output-only data for structural health monitoring (SHM) that makes full use of the characteristic of independence of modal responses and the principle of machine learning. By taking advantage of the independence feature of each mode, we use the principle of unsupervised learning, making the training process of the deep neural network becomes the process of modal separation. A self-coding deep neural network is designed to identify the structural modal parameters from the vibration data of structures. The mixture signals, that is, the structural response data, are used as the input of the neural network. Then we use a complex loss function to restrict the training process of the neural network, making the output of the third layer the modal responses we want, and the weights of the last two layers are mode shapes. The deep neural network is essentially a nonlinear objective function optimization problem. A novel loss function is proposed to constrain the independent feature with consideration of uncorrelation and non-Gaussianity to restrict the designed neural network to obtain the structural modal parameters. A numerical example of a simple structure and an example of actual SHM data from a cable-stayed bridge are presented to illustrate the modal parameter identification ability of the proposed approach. The results show the approach's good capability in blindly extracting modal information from system responses.

An advanced hybrid algorithm for nonlinear function optimization with real world applications

SummaryThis article presents an advanced hybrid algorithm (haDEPSO) for nonlinear constrained function optimization problem. It consists of the advised advanced differential evolution, that is, aDE (wherein a novel mutation, crossover, and selection strategy is introduced, to avoid premature convergence) and particle swarm optimization, namely, aPSO (in which novel gradually varying parameters is utilized, to escape stagnation). The proposed haDEPSO achieve better results as aDE and aPSO provides diverse convergence characteristic to the solution space. Moreover, in haDEPSO distinct population is merged with other in a predefined way, to balance between exploration and exploitation. Efficiency of the proposed hybrid haDEPSO along with its integrating component aDE and aPSO are inspected on IEEE CEC'2006 constrained benchmark functions and IEEE CEC'2011 real world problems. According to the comparison results, the proposed methods achieved better results than traditional DE and PSO with their hybrids as well as over many state‐of‐the‐art algorithms.

Application of Data Envelopment and Internet of Things Technology for Asset Value Evaluation

Assets are an essential part of an enterprise’s production and an indispensable economic entity for production and operation. The valuation of assets is one such area that has received significant attention in recent years. However, there exist numerous issues from various perspectives. These issues require us to study and explore them further. This article discusses the role of Internet of Things (IoT) and data envelopment methods to improve and develop asset evaluation. Based on the concept of asset evaluation, this paper designs an asset evaluation framework using the IoT. This framework can provide an all-weather and no-delay preparation basis for the asset appraisal work. Moreover, this paper uses data envelopment and particle swarm optimization (PSO) algorithm to clean and reclassify asset data. The objective of this algorithm is to solve the nonlinear function optimization problems associated with asset value evaluation. Finally, we verify the effectiveness and practicability of the model by comparing experimental simulation and manual evaluation.

Parameter identification of nonlinear systems with time-delay from time-domain data

The present paper develops an enhanced response sensitivity approach for parameter identification of nonlinear time-delay systems from the time-domain data. Accurate and rapid identification of the time-delay system’s parameters is the key to achieve effective control and synchronization, especially for the delay parameters. The work of this paper is mainly threefold. Firstly, taking a general nonlinear time-delay system as the investigated object, the characteristics of the nonlinear time-delay system are introduced, and the response sensitivity analysis with respect to the system parameters is derived. Then, the problem of parameter identification is modeled as a nonlinear least-squares optimization function. To this end, a novel iteration-based approach is developed to solve such problem, and the ill-posed situation is tackled by Tikhonov regularization. Besides, the trust-region constraint is implemented to enhance the convergence of the algorithm. Finally, the feasibility of the proposed approach is verified by two numerical examples and a real electronic circuit experiment. The results proved that the proposed approach can identify parameters of nonlinear time-delay systems accurately, robustly and effectively.

An improved parameter identification method of redundant manipulator

To achieve more accurate simulation and control in the use of the manipulator, it is necessary to establish an accurate dynamic model of the redundant manipulator. The research of this article focuses on the dynamic parameter identification method of the redundant manipulator. In the study, the spinor theory is applied to the Newton–Euler dynamic equation, the Coulomb + viscous friction model is adopted, and the minimum parameter set is obtained by linearization derivation. The parameter identification of the manipulator is realized using the method of offline identification of the measured current, and the coefficient of the excitation trajectory is optimized using the nonlinear optimization function. Finally, the parameter set with high accuracy is obtained, and the motion trajectory of each joint can be obtained. The scheme has high accuracy and can meet the needs of practical application. To verify the accuracy and reliability of this method, we have carried out experiments on a service robot “Walker” and obtained the desired results.

The semi-obnoxious minisum circle location problem with Euclidean norm

‎The objective of the classical version of the minisum circle location problem is finding a circle $C$ in the plane such that the sum of the weighted distances from the circumference of $C$ to a set of given points is minimized‎, ‎where every point has a positive weight‎. ‎In this paper‎, ‎we investigate the semi-obnoxious case‎, ‎where every existing facility has either a positive or negative weight‎. ‎The distances are measured by the Euclidean norm‎. ‎Therefore‎, ‎the problem has a nonlinear objective function and global nonlinear optimization methods are required to solve this problem‎. ‎Some properties of the semi-obnoxious minisum circle location problem with Euclidean norm are discussed‎. ‎Then a cuckoo optimization algorithm is presented for finding the solution of this problem‎.

Search of Non-circular Slip Surface Based on Improved FOA

The determination of the most critical non-circular slip surface can be attributed to the optimization of complex non-linear multi-peak function due to its numerous control variables and large amount of calculation. It is a trend in recent years to apply intelligent optimization algorithm into slope stability analysis. Considering that the standard Fruit fly Optimization Algorithm (FOA) is prone to fall into local extremum, the improved Fruit fly Optimization Algorithm is obtained by incorporating the standard FOA with the simulated annealing idea. In order to improve the search efficiency, a fixed step size is adjusted to an adaptive step size, and a double tier search strategy is proposed to be applied: the potential non-circular slip surface is obtained from the outer layer, and the factor of safety along the potential slip surface is calculated step by step from the inner layer. The improved FOA is applied to a slope with weak interlayer. The feasibility, superiority and efficiency of the improved algorithm are proved by comparing its answers to the judges'. Different inter-slice force functions, various initial values of Fs and λ are assumed, and the results show that these parameters could hardly affect final solution for safety factor.

Strawberry algorithm and its newly evolved variant for pattern nulling in an antenna array

In this article attempt has been made for the first time to apply the reported strawberry optimization technique to antenna array synthesis problem. The algorithm is further modified by reinforcing it with adaptive values for the two key parameters known as runner length and root length embedded in the mathematical expression governing the movement of the mother plant from one position to another in the search space to locate the optimum solution. The case studies cited here refer to linear and circular array configurations. The design constraints are limited to minimizing the side lobe level and restricting the first null beam width, which play significant roles in antenna array performances. The important features which greatly influence in achieving the said objectives are either placement of antenna elements or amplitudes of excitations of these elements or both. And the recently reported nature inspired metaheuristic optimization algorithms have addressed to these antenna problems quite effectively and the application of the strawberry algorithm for the first time and the unraveling of a new algorithm known as reduced step size strawberry algorithm (rss-SBA) a variant of the existing SBA have shown quite exciting results thus opening avenues for these techniques to be the potential contenders in the race of authenticating their positions in the domain of nonlinear function optimization.

Task Scheduling Problem of Double-Deep Multi-Tier Shuttle Warehousing Systems

Double-deep multi-tier shuttle warehousing systems (DMSWS) have been increasingly applied for store-and-retrieval stock-keeping unit tasks, with the advantage of a reduced number of aisles and improved space utilization. Scheduling different devices for retrieval tasks to increase system efficiency is an important concern. In this paper, a Pareto optimization model of task operations based on the cycle time and carbon emissions is presented. The impact of the rearrangement operation is considered in this model. The cycle time model is converted into a flow-shop scheduling model with parallel machines by analyzing the retrieval operation process. Moreover, the carbon emissions of the shuttle in the waiting process, the carbon emissions of the lift during the free process, and the carbon emissions of the retrieval operation are considered in the carbon emissions model, which can help us to evaluate the carbon emissions of the equipment more comprehensively during the entire retrieval task process. The elitist non-dominated sorting genetic algorithm II (NSGA-II) is adopted to solve the non-linear multi-objective optimization function. Finally, a real case is adopted to illustrate the findings of this study. The results show that this method can reduce carbon emissions and improve system efficiency. In addition, it also help managers to reduce operational costs and improve the utilization of shuttles.

Local Wavenumber Method for Delamination Characterization in Composites With Sparse Representation of Lamb Waves.

This article presents a quantitative Lamb wave detection method for delamination characterization in composite laminates using local wavenumber features. In contrast to the conventional Fourier transform-based methods, the improved sparse reconstruction method is efficient and able to evaluate the spatial wavenumbers of Lamb waves with limited measurements. To improve the feasibility of the sparse reconstruction method, the analytical solution of the local wavenumbers to the compressed sensing (CS) formulation with considering structural discontinuity is firstly investigated. The estimated wavenumber values for the spatial window located on healthy and damaged regions simultaneously are governed by a nonlinear optimization function. Benefiting from revealing the evolution of local wavenumber slopes, a delamination characterization method is proposed to accurately determine the damage location and depth by wavenumber banalization. Subsequently, the performance of the proposed method on local wavenumber estimation and damage quantification is verified by the simulation data. The parameters are discussed in order to improve the algorithm stability. Finally, the experimental investigation was conducted on a quasi-isotropic carbon fiber reinforced polymer (CFRP) laminate with an induced delamination. Lamb wave was generated and scanned by the Nd:YAG laser spot with spatial intervals of 2 mm. The results verify the sparse reconstruction method for delamination characterization, which shows value of reducing labor cost and testing time.