Surface water sodium (Na+) concentration prediction using hybrid weighted exponential regression model with gradient-based optimization

Forecasting water quality indices using generalized ridge model, regularized weighted kernel ridge model, and optimized multivariate variational mode decomposition

Permeability index (PI) and magnesium absorption ratio (MAR) are both primary irrigation water quality indicators (IWQI) used to evaluate the efficacy of agricultural water supplies. This is considered a complex environmental issue to reliably forecast IWQI parameters without its appropriate time series and limited input sequences. Hence, this research develops an innovative hybrid intelligence framework for the first time to forecast the PI and MAR indices at the Karun River, Iran. The proposed framework includes a new hybrid machine learning (ML) model based on generalized ridge regression and kernel ridge regression with a regularized locally weighted (GRKR) method. This research developed an optimized multivariate variational mode decomposition (OMVMD) technique, optimized by the Runge-Kutta algorithm (RUN), to decompose the input variables. The light gradient boosting machine model (LGBM) is also implemented to select the influential input variables. The main contribution of the intelligence framework lies in developing a new hybrid ML model based on GRKR coupled with OMVMD. Five water quality parameters from the Karun River at two stations (Ahvaz and Molasani) over 40 years are used to forecast the PI and MAR indices monthly. Statistical metrics confirmed that the proposed OMVMD-GRKR model, concerning the best efficiency in the Ahvaz (R = 0.987, RMSE = 0.761, and U95% = 2.108) and Molasani (R = 0.963, RMSE = 1.379, and U95% = 3.828) stations, outperformed the OMVMD and simple-based methods such as ridge regression (Ridge), least squares support vector machine (LSSVM), deep random vector functional link (DRVFL), and deep extreme learning machine (DELM). For this reason, the suggested OMVMD-GRKR model serves as a valuable framework for predicting IWQI parameters.

A hybrid framework: singular value decomposition and kernel ridge regression optimized using mathematical-based fine-tuning for enhancing river water level forecasting

The precise monitoring and timely alerting of river water levels represent critical measures aimed at safeguarding the well-being and assets of residents in river basins. Achieving this objective necessitates the development of highly accurate river water level forecasts. Hence, a novel hybrid model is provided, incorporating singular value decomposition (SVD) in conjunction with kernel-based ridge regression (SKRidge), multivariate variational mode decomposition (MVMD), and the light gradient boosting machine (LGBM) as a feature selection method, along with the Runge-Kutta optimization (RUN) algorithm for parameter optimization. The L-SKRidge model combines the advantages of both the SKRidge and ridge regression techniques, resulting in a more robust and accurate forecasting tool. By incorporating the linear relationship and regularization techniques of ridge regression with the flexibility and adaptability of the SKRidge algorithm, the L-SKRidge model is able to capture complex patterns in the data while also preventing overfitting. The L-SKRidge method is applied to forecast water levels in the Brook and Dunk Rivers in Canada for two distinct time horizons, specifically one- and three days ahead. Statistical criteria and data visualization tools indicates that the L-SKRidge model has superior efficiency in both the Brook (achieving R = 0.970 and RMSE = 0.051) and Dunk (with R = 0.958 and RMSE = 0.039) Rivers, surpassing the performance of other hybrid and standalone frameworks. The results show that the L-SKRidge method has an acceptable ability to provide accurate water level predictions. This capability can be of significant use to academics and policymakers as they develop innovative approaches for hydraulic control and advance sustainable water resource management.

Enhanced NSGA-II algorithm based on novel hybrid crossover operator to optimise water supply and ecology of Fenhe reservoir operation

Reservoir-operation optimisation is a crucial aspect of water-resource development and sustainable water process management. This study addresses bi-objective optimisation problems by proposing a novel crossover evolution operator, known as the hybrid simulated binary and improved arithmetic crossover (SBAX) operator, based on the simulated binary cross (SBX) and arithmetic crossover operators, and applies it to the Non-dominated Sorting Genetic Algorithms-II (NSGA-II) algorithm to improve the algorithm. In particular, the arithmetic crossover operator can obtain an optimal solution more precisely within the solution space, whereas the SBX operator can explore a broader range of potential high-quality solutions. Considering the advantages of both operators, this study introduces an improved arithmetic operator to reduce the risk of local convergence inherent in conventional arithmetic operators. Subsequently, two strategies for the SBAX operator are discussed: SBX operator + new arithmetic operator and new arithmetic operator + SBX operator. The convergence of the bi-objective Pareto solution set is evaluated based on the generation and inverted generational distances. This method is used for the collaborative optimisation of the water supply and ecological operation of the Fenhe Reservoir, where its effectiveness is demonstrated. A comparative analysis of the bi-objective optimisation schemes obtained using different crossover operators indicates the following: (1) the NSGA-II algorithm based on the SBAX operator achieves a convergence efficiency that is 14.25-41.95% higher than that of the conventional NSGA-II algorithm; (2) the reservoir operation indices of the scheduling scheme derived from the NSGA-II algorithm based on the SBAX operator significantly outperform those obtained using the conventional NSGA-II algorithm. The optimal strategy reduces the annual average water abandonment by 11.2-14.52 million m3. This study provides a novel approach for bi-objective optimisation and sustainable reservoir management.

Shuffling-type gradient method with bandwidth-based step sizes for finite-sum optimization

Shuffling-type gradient method is a popular machine learning algorithm that solves finite-sum optimization problems by randomly shuffling samples during iterations. In this paper, we explore the convergence properties of shuffling-type gradient method under mild assumptions. Specifically, we employ the bandwidth-based step size strategy that covers both monotonic and non-monotonic step sizes, thereby providing a unified convergence guarantee in terms of step size. Additionally, we replace the lower bound assumption of the objective function with that of the loss function, thereby eliminating the restrictions on the variance and the second-order moment of stochastic gradient that are difficult to verify in practice. For non-convex objectives, we recover the last iteration convergence of shuffling-type gradient algorithm with a less cumbersome proof. Meanwhile, we also establish the convergence rate for the minimum iteration of gradient norms. Under the Polyak-Łojasiewicz (PL) condition, we prove that the function value of last iteration converges to the lower bound of the objective function. By selecting appropriate boundary functions, we further improve the previous sublinear convergence rate results. Overall, this paper contributes to the understanding of shuffling-type gradient method and its convergence properties, providing insights for optimizing finite-sum problems in machine learning. Finally, numerical experiments demonstrate the efficiency of shuffling-type gradient method with bandwidth-based step size and validate our theoretical results.

Surface water quality index forecasting using multivariate complementing approach reinforced with locally weighted linear regression model

River water quality management and monitoring are essential responsibilities for communities near rivers. Government decision-makers should monitor important quality factors like temperature, dissolved oxygen (DO), pH, and biochemical oxygen demand (BOD). Among water quality parameters, the BOD throughout 5 days is an important index that must be detected by devoting a significant amount of time and effort, which is a source of significant concern in both academic and commercial settings. The traditional experimental and statistical methods cannot give enough accuracy or solve the problem for a long time to detect something. This study used a unique hybrid model called MVMD-LWLR, which introduced an innovative method for forecasting BOD in the Klang River, Malaysia. The hybrid model combines a locally weighted linear regression (LWLR) model with a wavelet-based kernel function, along with multivariate variational mode decomposition (MVMD) for the decomposition of input variables. In addition, categorical boosting (Catboost) feature selection was used to discover and extract significant input variables. This combination of MVMD-LWLR and Catboost is the first use of such a complete model for predicting BOD levels in the given river environment. In addition, an optimization process was used to improve the performance of the model. This process utilized the gradient-based optimization (GBO) approach to fine-tune the parameters and better the overall accuracy of predicting BOD levels. To assess the robustness of the proposed method, we compared it to other popular models such as kernel ridge (KRidge) regression, LASSO, elastic net, and gaussian process regression (GPR). Several metrics, comprising root-mean-square error (RMSE), R (correlation coefficient), U95% (uncertainty coefficient at 95% level), and NSE (Nash-Sutcliffe efficiency), as well as visual interpretation, were used to evaluate the predictive efficacy of hybrid models. Extensive testing revealed that, in forecasting the BOD parameter, the MVMD-LWLR model outperformed its competitors. Consequently, for BOD forecasting, the suggested MVMD-LWLR optimized with the GBO algorithm yields encouraging and reliable results, with increased forecasting accuracy and minimal error.

Gradient-Based Optimizer (GBO): A Review, Theory, Variants, and Applications

This paper introduces a comprehensive survey of a new population-based algorithm so-called gradient-based optimizer (GBO) and analyzes its major features. GBO considers as one of the most effective optimization algorithm where it was utilized in different problems and domains, successfully. This review introduces set of related works of GBO where distributed into; GBO variants, GBO applications, and evaluate the efficiency of GBO compared with other metaheuristic algorithms. Finally, the conclusions concentrate on the existing work on GBO, showing its disadvantages, and propose future works. The review paper will be helpful for the researchers and practitioners of GBO belonging to a wide range of audiences from the domains of optimization, engineering, medical, data mining and clustering. As well, it is wealthy in research on health, environment and public safety. Also, it will aid those who are interested by providing them with potential future research.

Improved Fitness-Dependent Optimizer for Solving Economic Load Dispatch Problem

Economic load dispatch depicts a fundamental role in the operation of power systems, as it decreases the environmental load, minimizes the operating cost, and preserves energy resources. The optimal solution to economic load dispatch problems and various constraints can be obtained by evolving several evolutionary and swarm-based algorithms. The major drawback to swarm-based algorithms is premature convergence towards an optimal solution. Fitness-dependent optimizer is a novel optimization algorithm stimulated by the decision-making and reproductive process of bee swarming. Fitness-dependent optimizer (FDO) examines the search spaces based on the searching approach of particle swarm optimization. To calculate the pace, the fitness function is utilized to generate weights that direct the search agents in the phases of exploitation and exploration. In this research, the authors have used a fitness-dependent optimizer to solve the economic load dispatch problem by reducing fuel cost, emission allocation, and transmission loss. Moreover, the authors have enhanced a novel variant of the fitness-dependent optimizer, which incorporates novel population initialization techniques and dynamically employed sine maps to select the weight factor for the fitness-dependent optimizer. The enhanced population initialization approach incorporates a quasi-random Sabol sequence to generate the initial solution in the multidimensional search space. A standard 24-unit system is employed for experimental evaluation with different power demands. The empirical results obtained using the enhanced variant of the fitness-dependent optimizer demonstrate superior performance in terms of low transmission loss, low fuel cost, and low emission allocation compared to the conventional fitness-dependent optimizer. The experimental study obtained 7.94E−12, the lowest transmission loss using the enhanced fitness-dependent optimizer. Correspondingly, various standard estimations are used to prove the stability of the fitness-dependent optimizer in phases of exploitation and exploration.