Gradient-based Optimization Research Articles

Chaotic gradient based optimization with fuzzy temporal optimized CNN for heart failure prediction

Heart failure is a leading cause of premature death, especially among individuals with a sedentary lifestyle. Early and accurate detection is essential to prevent the progression of this situation. However, many existing prediction systems failed to detect early and accurately, also taking more time to detect. To address these issues, we propose an advanced heart failure detection model that combines one-dimensional chaotic maps and a Gradient-Based Optimizer (GBO) called Chaotic Gradient-Based Optimizer (CGBO). This approach improves feature selection by effectively selecting the most crucial features related to the risk of heart failure. Additionally, we introduce the Fuzzy Temporal Optimized Convolutional Neural Network (FTOCNN) classifier that incorporates CGBO and fuzzy temporal rules to enhance detection accuracy. The proposed model is evaluated using the UCI heart dataset and Electronic Health Records (EHRs) and its performance is assessed through statistical measures, classification metrics, and a Wilcoxon rank-sum p-test. Furthermore, a tenfold cross-validation process ensures a comprehensive evaluation and the proposed method outperforms different Machine Learning (ML) / Deep Learning (DL) classifiers. The experimental findings reveal that CGBO significantly improves the predictive performance of the FTOCNN classifier by achieving 94% accuracy in EHR and enhances the reliability of heart failure detection compared to existing systems.

Maximum Stress Minimization via Data-Driven Multifidelity Topology Design

Abstract The maximum stress minimization problem is among the most important topics for structural design. The conventional gradient-based topology optimization methods require transforming the original problem into a pseudo-problem by relaxation techniques. Since their parameters significantly influence optimization, accurately solving the maximum stress minimization problem without using relaxation techniques is expected to achieve extreme performance. This paper focuses on this challenge and investigates whether designs with more avoided stress concentrations can be obtained by solving the original maximum stress minimization problem without relaxation techniques, compared to the solutions obtained by gradient-based topology optimization. We employ data-driven multifidelity topology design (MFTD), a gradient-free topology optimization based on evolutionary algorithms. The basic framework involves generating candidate solutions by solving a low-fidelity optimization problem, evaluating these solutions through high-fidelity forward analysis, and iteratively updating them using a deep generative model without sensitivity analysis. In this study, data-driven MFTD incorporates the optimized designs obtained by solving a gradient-based topology optimization problem with the p-norm stress measure in the initial solutions and solves the original maximum stress minimization problem based on a high-fidelity analysis with a body-fitted mesh. We demonstrate the effectiveness of our proposed approach through the benchmark of L-bracket. As a result of solving the original maximum stress minimization problem with data-driven MFTD, a volume reduction of up to 22.6% was achieved under the same maximum stress value, compared to the initial solution.

Improving flood-prone areas mapping using geospatial artificial intelligence (GeoAI): A non-parametric algorithm enhanced by math-based metaheuristic algorithms.

Flooding presents substantial dangers to human lives and infrastructure, underscoring the need to map flood-prone areas to implement effective mitigation measures precisely. Although machine learning algorithms have made great strides, their accuracy in flood susceptibility mapping (FSM) remains limited due to data dependence, interpretability, and explainability issues, overfitting, generalization difficulties, and hyperparameter tuning. This study suggests combining the Decision Tree (DT) algorithm with advanced, math-based metaheuristic optimization algorithms to address these limitations. In this study, the FSM was prepared using a combination of the DT non-parametric algorithm and three math-based metaheuristic optimization algorithms, including the gradient-based optimizer (GBO), chaos game optimization (CGO), and arithmetic optimization algorithm (AOA). Four models were developed and compared for modeling and mapping: the basic DT, DT-AOA, DT-GBO, and DT-CGO. The DT-CGO model stood out on the training set, achieving the lowest root mean square error (RMSE) of 0.17. It was closely followed by DT-AOA (0.19), DT-GBO (0.2), and DT (0.201). In terms of mean absolute error (MAE), the DT-CGO model exhibited the lowest value of 0.06, followed by DT-AOA (0.07), DT-GBO (0.079), and the basic DT model (0.08). When considering the coefficient of determination (R2), the DT-CGO model achieved the highest value of 0.871, followed by DT-AOA (0.853), DT-GBO (0.84), and DT (0.838). The enhanced models performed superior over the test set's basic DT model. The area under the curve (AUC) values validated the enhanced models' efficacy, with the DT-CGO model achieving the highest AUC of 0.978, followed by DT-AOA (0.974), DT-GBO (0.967), and DT (0.958). The findings emphasize the importance of accurate flood-prone area identification and provide valuable insights for policymakers to develop robust flood mitigation strategies.

Adaptive Nesterov momentum method for solving ill-posed inverse problems

Abstract Nesterov’s acceleration strategy is renowned in speeding up the convergence of gradient-based optimization algorithms and has been crucial in developing fast first order methods for well-posed convex optimization problems. Although Nesterov’s accelerated gradient method has been adapted as an iterative regularization method for solving ill-posed inverse problems, no general convergence theory is available except for some special instances. In this paper, we develop an adaptive Nesterov momentum method for solving ill-posed inverse problems in Banach spaces, where the step-sizes and momentum coefficients are chosen through adaptive procedures with explicit formulas. Additionally, uniform convex regularization functions are incorporated to detect the features of sought solutions. Under standard conditions, we establish the regularization property of our method when terminated by the discrepancy principle. Various numerical experiments demonstrate that our method outperforms the Landweber-type method in terms of the required number of iterations and the computational time.

Arch bridge damage detection using vibration data and gradient-based optimizer algorithm

Arch bridge damage detection using vibration data and gradient-based optimizer algorithm

Gradient-based structural optimization of a wind turbine blade root section including high-cycle fatigue constraints

Under the modern design paradigm of wind turbines, the continuous drive towards lower costs through longer blades is raising serious challenges in design, and structural optimization is key to solving the problems effectively. This article focuses on the challenging structural optimization of wind turbine blade root sections, which is scarcely treated in the literature owing to the complex and computationally expensive critical criteria, i.e. buckling, static failure and fatigue damage. The root is parametrized with 1894 thickness design variables and, to solve such an optimization problem efficiently, an adjoint gradient-based framework is proposed, which includes all the criteria mentioned for twelve load cases. Fatigue is notoriously difficult owing to its highly nonlinear behaviour, and its inclusion in the adjoint optimization framework for wind turbine blade optimization is a novelty. The resulting optimization behaviour, laminate layup and structural response are all illustrated, showing many active constraints at convergence, and a significant reduction in mass.

An information gap decision theory and improved gradient-based optimizer for robust optimization of renewable energy systems in distribution network

In this paper, a robust fuzzy multi-objective framework is performed to optimize the dispersed and hybrid renewable photovoltaic-wind energy resources in a radial distribution network considering uncertainties of renewable generation and network demand. A novel multi-objective improved gradient-based optimizer (MOIGBO) enhanced with Rosenbrock’s direct rotational technique to overcome premature convergence is proposed to determine the problem optimal decision variables. The deterministic optimization framework without uncertainty minimizes active energy loss, unmet customer energy, and renewable generation costs. The study also examines the impact of dispersed and hybrid renewable resources on solving the problem. In the robust optimization framework considering the deterministic obtained results, the focus is on determining the maximum uncertainty radius (MUR) of renewable resource generation and network demand based on the uncertainty risk. The MURs and system robustness are optimally determined using information gap decision theory (IGDT) and the MOIGBO, considering various uncertainty budgets under worst-case scenarios. The deterministic results indicate that the MOIGBO effectively balances the objectives and identifies the final solution within the Pareto front, according to fuzzy decision-making. The results also reveal that the dispersed case yields better objective values than the hybrid case. Furthermore, the MOIGBO outperforms MOGBO and multi-objective particle swarm optimization (MOPSO) in improving distribution network operations. The robust results show that maximum system robustness is achieved at 30% uncertainty risk due to forecasting errors, with MUR values of 0.54% for resource production and 12.56% for load demand.

Kinematic Synthesis of a Serial Manipulator Using Gradient-Based Optimization on Lie Groups

Kinematic Synthesis of a Serial Manipulator Using Gradient-Based Optimization on Lie Groups

Intelligent Joint Optimization of Deployment and Task Scheduling for Mobile Users in Multi‐UAV‐Assisted MEC System

Mobile edge computing (MEC) servers integrated with multi‐unmanned aerial vehicles (multi‐UAVs) present a new system the multi‐UAV‐assisted MEC system. This system relies on the mobility of the UAVs to reduce the transmission distance between the servers and mobile users, thereby enhancing service quality and minimizing the overall energy consumption. Achieving optimal UAV deployment and precise task scheduling is crucial for improved coverage and service quality in this system. This problem is framed as a nonconvex optimization problem known as joint task scheduling and deployment optimization. Recently, an optimization technique based on a dual‐layer framework: Upper layer optimization and lower layer optimization have been proposed to tackle this problem and achieved superior performance compared to the alternative methods. In this framework, the lower layer was responsible for task scheduling optimization, while the upper layer was designed to assist in optimizing UAV deployment and thus achieving improved coverage and enhanced task scheduling for mobile users, thereby minimizing the total energy consumption. However, further refinement of upper layer optimization is needed to improve the deployment process. In this study, the upper layer undergoes enhancement through key modifications: First, random selection of the solutions is replaced with sequential selection to maintain the unique characteristics of each individual throughout the optimization process, fostering both exploration and exploitation. Second, a selection of recently reported metaheuristic algorithms, such as spider wasp optimizer (SWO), generalized normal distribution optimization (GNDO), and gradient‐based optimizer (GBO), are adapted to optimize UAV deployments. Both improved upper layer and lower layer optimization led to the development of novel, more effective optimization approaches, including IToGBOTaS, IToGNDOTaS, and IToSWOTaS. These techniques are evaluated using nine instances with a variety of mobile tasks ranging from 100 to 900 to test their stability and then compared to different optimization techniques to measure their effectiveness. This comparison is based on several statistical information to determine the superiority and difference between their outcomes. The results reveal that IToGBOTaS and IToSWOTaS exhibit slightly superior performance compared to all other algorithms, showcasing their competitiveness and efficacy in addressing the optimization challenges of the multi‐UAV‐assisted MEC system.

Equivalent plate formulation of Double–Double laminates for the gradient-based design optimization of composite structures

Equivalent plate formulation of Double–Double laminates for the gradient-based design optimization of composite structures

A novel gradient-based discrete time-delayed optimization algorithm for optimal control problems with Caputo–Fabrizio fractional derivative

A novel gradient-based discrete time-delayed optimization algorithm for optimal control problems with Caputo–Fabrizio fractional derivative

Optimizing Wind farm layout using a one-by-one replacement mechanism-incorporated gradient-based optimizer

Optimizing Wind farm layout using a one-by-one replacement mechanism-incorporated gradient-based optimizer

Gradient-Based Optimization of Coherent Distributed Arrays

Gradient-Based Optimization of Coherent Distributed Arrays

Distributed Conflict Detection and Optimal Four-Dimensional Trajectory Resolution Leveraging Polynomial-Based Methods

This paper presents a methodology for distributed conflict detection and resolution of aircraft following time-dependent flight paths. We use parametric fifth-order polynomial splines to define the full, time-based paths of aircraft. This representation can be exploited to rapidly detect conflicts and calculate optimal resolution solutions that minimize deviations from the original path. Conflicts are identified using a Sturm sequencing procedure and resolutions are found using gradient-based optimization techniques. Simulations show the locally optimal resolution of complex multi-aircraft conflicts and large-scale scenarios. Also, a method of fitting the flight- path model to data sets is presented and flight-path trajectories are shown to accurately represent commercial aircraft trajectories from collected automatic dependent surveillance-broadcast data sets.

A competitive learning approach for specialized models: An approach to modelling complex physical systems with distinct functional regimes

Complex systems in science and engineering sometimes exhibit behaviour that changes across different regimes. Traditional global models struggle to capture the full range of this complex behaviour, limiting their ability to accurately represent the system. In response to this challenge, we propose a competitive learning approach for obtaining localized data-based models of physical systems. The primary idea behind the proposed approach is to employ dynamic loss functions for a set of models that are trained concurrently on the data. Each model competes for each observation during training, allowing for the identification of distinct functional regimes within the dataset. To demonstrate the effectiveness of the learning approach, we coupled it with various regression methods that employ gradient-based optimizers for training. The proposed approach was tested on various problems involving model discovery and function approximation, demonstrating its ability to successfully identify functional regimes, discover true governing equations and reduce test errors.

PSP-GEN: Stochastic inversion of the Process-Structure-Property chain in materials design through deep, generative probabilistic modeling

Inverse material design is a cornerstone challenge in materials science, with significant applications across many industries. Traditional approaches that invert the structure–property (SP) linkage to identify microstructures with targeted properties often overlook the feasibility of production processes, leading to microstructures that may not be manufacturable. Achieving both desired properties and a realizable manufacturing procedure necessitates inverting the entire Process-Structure-Property (PSP) chain. However, this task is fraught with challenges, including stochasticity along the whole modeling chain, the high dimensionality of microstructures and process parameters, and the inherent ill-posedness of the inverse problem. This paper proposes a novel framework, named PSP-GEN, for the goal-oriented material design that effectively addresses these challenges by modeling the entire PSP chain with a deep generative model. It employs two sets of continuous, microstructure- and property-aware, latent variables, the first of which provides a lower-dimensional representation that captures the stochastic aspects of microstructure generation, while the second is a direct link to processing parameters. This structured, low-dimensional embedding not only simplifies the handling of high-dimensional microstructure data but also facilitates the application of gradient-based optimization techniques. The effectiveness and efficiency of this method are demonstrated in the inverse design of two-phase materials, where the objective is to design microstructures with target effective permeability. We compare state-of-the-art alternatives in challenging settings involving limited training data, target property regions for which no training data is available, and design tasks where the process parameters and microstructures have high-dimensional representations.

Development of a novel modeling framework based on weighted kernel extreme learning machine and ridge regression for streamflow forecasting

A precise streamflow forecast is crucial in hydrology for flood alerts, water quantity and quality management, and disaster preparedness. Machine learning (ML) techniques are commonly employed for hydrological prediction; however, they still face certain drawbacks, such as the need to optimize the appropriate predictors, the ability of the models to generalize across different time horizons, and the analysis of high-dimensional time series. This research aims to address these specific drawbacks by developing a novel framework for streamflow forecasting. Specifically, a hybrid ML model, WKELM-R, is developed to predict streamflow based on daily discharge and precipitation. The model combines ridge regression (RR), locally weighted linear regression (LWLR), and kernel extreme learning machine (KELM) to enhance multi-step-ahead predictions by accounting for both linear and nonlinear characteristics. In data preprocessing, this study applies multivariate variational mode decomposition (MVMD) for decomposition to handle non-stationarity and complexity, Boruta-XGBoost for feature selection to select the optimal inputs and decrease the dimension, and gradient-based optimizer (GBO) for adjustment of model parameters to overcome the need to optimize the appropriate predictors. To demonstrate the ability to handle real-world conditions and different time horizons, WKELM-R was applied to a watershed in North Dakota, USA to forecast discharge for three different time horizons. The results were compared with those from the existing standalone and hybrid models by multi-criteria decision-making (MCDM), demonstrating the efficacy and unique capabilities of the new hybrid model in streamflow forecasting (for the testing level at t + 3: R = 0.992, RMSE = 0.426, NSE = 0.983; at t + 7: R = 0.997, RMSE = 0.249, NSE = 0.994; at t + 14: R = 0.996, RMSE = 0.304, NSE = 0.991).

Topology optimization of metagratings using the advanced slime mold algorithm combined with a gradient-based method: the chimera of uniqueness of the optimal solution

In this paper, we discuss the use of a metaheuristic (MH) gradient-free optimization method, specifically, the slime mold algorithm (SMA), combined with a gradient-based method to topologically optimize metagratings. In the proposed method, the gradient-based optimization method is applied to a set of initial geometries with only a few iterations. Then, the resulting pre-refined set of designs is used to initialize an enhanced version of the SMA. At the end of each iteration, the gradient of the figure of merit is used again to generate two new individuals from the best current solution. The numerical results show that our approach outperforms the original SMA, the gradient-based method, and other state-of-the-art optimization methods.

Investigating Tidal Stream Turbine Array Performance Considering Effects of Number of Turbines, Array Layouts, and Yaw Angles

The performance of a tidal stream turbine array can be affected by numerous factors. Investigating the connection between array power production and these factors will be helpful in improving the development of tidal stream energy. This study investigates the impact of array layout, turbine number, and yaw angles on turbine array performance using an open-source coastal ocean modelling system. The results show that the total power output of the turbine array rises with the number of turbines. Under realistic conditions, there are not many differences in power output between aligned and staggered turbine array configurations. By extending the distance between the turbines, the array power output can be improved in both layouts. It appears that considering each turbine’s yaw angle can improve array power generation, since the downstream turbines will greatly benefit from the steering wake of the upstream turbines. Furthermore, using a gradient-based optimization algorithm to simultaneously adjust the yaw angles and turbine positions will boost the turbine array’s efficiency more than just optimizing the turbine position alone.

A Novel Spherical Shortest Path Planning Method for UAVs

As a central subdivision of the low-altitude economy industry, industrial and consumer drones have broad market application prospects and are becoming the primary focus of the low-altitude economy; however, with increasing aircraft density, effective planning of reasonable flight paths and avoiding conflicts between flight paths have become critical issues in UAV clustering. Current UAV path planning often concentrates on 2D and 3D realistic scenes, which do not meet the actual requirements of realistic spherical paths. This paper has proposed a Gradient-Based Optimization algorithm based on the State Transition function (STGBO) to address the spherical path planning problem for UAV clusters. The state transition function is applied on the scale of medium and high-dimensional cities, balancing the stability and efficiency of the algorithm. Through evolution and comparisons with many mainstream meta-heuristic algorithms, STGBO has demonstrated superior performance and effectiveness in solving Medium-Altitude Unmanned Aerial Vehicle (MUAV) path planning problems on three-dimensional spherical surfaces, contributing to the development of the low-altitude economy.