Improved whale optimization algorithm and its application in vehicle structural crashworthiness

Combined Terrestrial Evapotranspiration Index prediction using a hybrid artificial intelligence paradigm integrated with relief algorithm-based feature selection

To address the shortcomings of the whale optimization algorithm (WOA) in terms of insufficient global search ability and slow convergence speed, a differential evolution chaotic whale optimization algorithm (DECWOA) is proposed in this paper. Firstly, the initial population is generated by introducing the Sine chaos theory at the beginning of the algorithm to increase the population diversity. Secondly, new adaptive inertia weights are introduced into the individual whale position update formula to lay the foundation for the global search and improve the optimization performance of the algorithm. Finally, the differential variance algorithm is fused to improve the global search speed and accuracy of the whale optimization algorithm. The impact of various improvement strategies on the performance of the algorithm is analyzed using different kinds of test functions that are randomly selected. The particle swarm optimization algorithm (PSO), butterfly optimization algorithm (BOA), WOA, chaotic feedback adaptive whale optimization algorithm (CFAWOA), and DECWOA algorithm are compared for the optimal search performance. Experimental simulations are performed using MATLAB software, and the results show that the improved whale optimization algorithm has a better global optimization-seeking capability. The improved whale optimization algorithm is applied to the distribution network fault location of IEEE-33 nodes, and the effectiveness and accuracy of the distribution network fault zone location based on the multistrategy improved whale optimization algorithm is verified.

Robust Lp-norm least squares support vector regression with feature selection

To address the problems of local optima and insufficient convergence accuracy in parameter identification of primary frequency regulation (PFR) for steam turbines, this paper proposed a hybrid identification method that integrated an Improved Bayesian Optimization (IBO) algorithm and an Improved Whale Optimization Algorithm (IWOA). By initializing the Bayesian parameter population using Tent chaotic mapping and the reverse learning strategy, employing a radial basis kernel function hyperparameter training mechanism based on the Adam optimizer and optimizing the Expected Improvement (EI) function using the Limited-memory Broyden–Fletcher– Goldfarb–Shanno with Bounds (L-BFGS-B) method, IBO was proposed to obtain the optimal candidate set with the smallest objective function value. By introducing a nonlinear convergence factor and the adaptive Levy flight perturbation strategy, IWOA was proposed to obtain locally optimized optimal solutions. By using the reverse-guided optimization mechanism and employing a fitness-oriented selection strategy, the optimal solution was chosen to complete the closed-loop process of reverse learning feedback. Nine standard test functions and the Proportional Integral Derivative (PID) parameter identification of the electro-hydraulic servo system in a 330 MW steam turbine were presented as examples. Compared with Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Bayesian Optimization (BO) and Particle Swarm Optimization-Grey Wolf Optimizer (PSO-GWO), the Improved Bayesian Optimization-Whale Optimization Algorithm (IBO-WOA) proposed in this paper has been validated to effectively avoid the problem of getting stuck in local optima during complex optimization and has high parameter recognition accuracy. Meanwhile, an Out-Of-Distribution (OOD) Test based on noise injection had demonstrated that IBO-WOA had good robustness. The time constant identification of the steam turbine were carried out using IBO-WOA under two experimental conditions, and the identification results were input into the PFR model. The simulated power curve can track the experimental measured curve well, proving that the parameter identification results obtained by IBO-WOA have high accuracy and can be used for the modeling and response characteristic analysis of the steam turbine PFR.

Towards locating time-varying indoor particle sources: Development of two multi-robot olfaction methods based on whale optimization algorithm

Variations in illumination lead to serious errors in the evaluation of chromatic aberration. We propose an illumination correction model based on the opposition‐based learning improved whale optimization algorithm for support vector regression optimization, named "OBL‐IWOA‐SVR." Because the initial population quality of the whale optimization algorithm has a significant impact on the solution speed and accuracy, the Opposition‐based learning strategy is adopted in this article to mix the original population and its opposite individuals and select the best as the new population, replacing the random initialization to generate a more suitable initial population. This increases the diversity of the population and thus overcomes the impact of the quality of the initial population on the algorithm performance. Secondly, the proposed algorithm adopts the adaptive weight and the convergence factor based on the variation of the cosine law to balance the algorithm's global exploration ability and local development ability and enhance the convergence accuracy. Finally, the algorithm utilizes good global searching ability to optimize the penalty factor and nuclear parameters and obtains the optimal support vector machine parameter combination to construct the illumination correction model OBL‐IWOA‐SVR accurately and robustly. Experimental results show that the illumination correction model proposed in this article is found superior to other models in significance analysis: the root mean square error of the proposed model is 0.0173, the smallest of all illumination correction models. Furthermore, the model exhibits good stability and high illumination estimation accuracy.

In this paper, we have used a novel initialization strategy to improve Whale optimization algorithm (WOA), which is named as The Improved Whale Optimization Algorithm (IWOA). To evaluate the capability of the algorithm in terms of efficiency and performance, we have implemented it to solve thermal economic multi-objective optimization problems of Plate Fin Heat Exchanger (PFHE). We have investigated the design problem with a single-objective as well as multi-objectives. In single-objective we have minimized the total cost and maximized the effectiveness of PFHE. In multi-objective, we have combined the total cost and effectiveness, with the help of design weights and a penalty parameter. The sensitivity of IWOA is checked towards the change in population sizes and the target prey numbers. The algorithm was stable in calculating the best values but was variative in number of functions evaluations. The performance of IWOA is compared with Genetic Algorithm (GA), Elitist-Jaya Algorithm (EJA), and modified-TLBO (Teaching Learning Based Optimization). Which show that IWOA has significantly improved the results. The suggested algorithm has less parameters to be set by designers. It converges to the required results quickly and is easy to implement. Similarly, all the experiments suggested that IWOA is applicable to design problems with complex objectives and highly non-linear constraints.

Dissolved oxygen directly affects the growth status of fishes in intensive aquaculture, thus we set up a prediction model to determine the future changing trend of dissolved oxygen. The dissolved oxygen prediction model we proposed was based on the least squares support vector regression (LSSVR) model with fruit fly optimization algorithm (FOA) to find optimal parameters (γ and σ) of LSSVR. Because these two parameters can significantly affect the performance of the LSSVR, we studied the other two parameter optimization methods the particle swarm optimization (PSO) algorithm, the genetic algorithm (GA) and immune genetic algorithm(IGA) to compare them with the FOA algorithm. The calculated mean absolute percentage errors of the results of the four prediction models were 0.35%, 1.3%, 2.03% and 1.33%, respectively. The FOA-LSSVR model has a higher prediction accuracy and more reliable performance than the other models. When the predicted values of dissolved oxygen fall below the safety level, the farmer can start an oxygen increasing machine in advance to maintain the safety of fishes. The prediction model was used in Yangzhong, Jiangsu province, China, and it performed well and helped farmers make decisions and reduce aquaculture risks.

The least square support vector regression (LSSVR) with the Gaussian kernel has two hyperparameters, sigma, $\sigma$, a bandwidth showing the spread of the kernel, and C, a regularization gauging the level of errors. In this paper, we want to systematically study how the hyperparameters are related to the LSSVR learning, thanks to the observation that the ergodic and stationary mean field game (MFG) implied hyperparameters are estimated based on the closed form solution given arbitrarily fixed bounded hyperparameters. Inversely, this closed form solution enables us to estimate MFG implied hyperparameters. The LSSVR with particle swarm optimization (LSSVR + PSO) allows a new way to estimate hyperparameters that doesn't involve cross-validations. The exact solvable MFG equivalent to our model has a stationary and ergodic solution of nonlinear Schr\"{o}dinger equation (NLS). The equilibrium solution of MFG is a pair of optimal action and the interaction density and this pair in NLS is the ergodic and stationary chemical potential and the interacting residual particle density, or $|\psi|^2$ in NLS. The ergodic solution of NLS ergodicises and stationarizes the LSSVR residual particles via the local interaction measure and we call this \emph{'the ergodic learning.'} As long as the non-zero volatility sigma and the non-zero mass ($\mu=1/C$) are bounded and the input and output data are required to have a non-degenerate support vector kernel, the input and output processes themselves don't need to be stationary, while all local interaction measures of the residual particles are ergodic. Depending on the (ergodic) learning classifications into condensed learning, intermediate learning and classical learning, based on theoretical temperatures, many candidate models for prediction are ergodically generated and the region of ergodicized and stationalized residuals via local interaction measure can be found for each hyperparameter pairs. As the C increases (or as we decrease the mass) or as the sigma increases, the volatility of learning increases. The learning tends to be more classical and less condensed. For each ergodic path generated as the ergodic solution to the MFG system, we profile the system response with respect to hyperparameters. Also, even in ergodic learning setting, phase transition behavior has been observed when PSO correctly keep the stationary energy conserved ergodically and stationarily. Lastly, it is shown that the zero crossing number of LSSVR $+$ PSO $=$ MFG is given by $E(N_0(T))=\frac{T}{2 \pi},$ given the data $\{(x_i, y_i)\}_{i=1}^T,$ x input, y output with $T>\tau^*=\sqrt{4 \pi} \Sigma^* \mu \sigma^2.$

A rising meta-heuristic swarm intelligent computation algorithm, the Whale optimization Algorithm (WOA), which has been proved competitive with other intelligent optimization algorithms in solving different optimization problems. To accelerate the convergence rate of WOA, this paper has proposed a new improved whale optimization algorithm, called Chaos Regulation Whale optimization Algorithm (CRWOA). The chaotic map generator composed with three kinds of chaotic maps has been used to initialize the population. Furthermore, Cauchy distribution and Gauss distribution are introduced to regulate the position in each iteration. To analyze the superiority of CRWOA further, ten single-objective benchmark test functions are chosen. Through the comparison and analysis of the optimal results, CRWOA is demonstrated superior in general. It has faster convergence speed and better results than the other algorithms when less iteration number, less population quantity and wider ranges of variables are set.

Soft sensors are becoming increasingly important in our world today as tools for inferring difficult-to-measure process variables to achieve good operational performance and economic benefits. Recent advancement in machine learning provides an opportunity to integrate machine learning models for soft sensing applications, such as Least Square Support Vector Regression (LSSVR) which copes well with nonlinear process data. However, the LSSVR model usually uses the radial basis function (RBF) kernel function for prediction, which has demonstrated its usefulness in numerous applications. Thus, this study extends the use of non-conventional kernel functions in the LSSVR model with a comparative study against widely used partial least square (PLS) and principal component regression (PCR) models, measured with root mean square error (RMSE), mean absolute error (MAE) and error of approximation (Ea) as the performance benchmark. Based on the empirical result from the case study of the penicillin fermentation process, the Ea of the multiquadric kernel (MQ) is lowered by 63.44% as compared to the RBF kernel for the prediction of penicillin concentration. Hence, the MQ kernel LSSVR has outperformed the RBF kernel LSSVR. The study serves as empirical evidence of LSSVR performance as a machine learning model in soft sensing applications and as reference material for further development of non-conventional kernels in LSSVR-based models because many other functions can be used as well in the hope to increase the prediction accuracy.

Prediction of dissolved oxygen content in river crab culture based on least squares support vector regression optimized by improved particle swarm optimization

In this study, an innovative approach that combines least square support vector regression (LSSVR) with uncertainty theory to enhance its performance in dealing with low-quality or imprecise data from real-world be proposed. The resulting model, called uncertain least square support vector regression (ULSSVR), incorporates chance constraints and simplified parameter selection, which are critical to handle imprecise observations. A numerical algorithm called the conjugate residual method (CR) is introduced to reduce the computational complexity of the model solution. The experimental results using both small and medium-sized datasets demonstrate the superior performance of ULSSVR in terms of prediction accuracy and generalization ability compared to other models such as uncertain support vector regression (USVR), uncertain linear lodel, uncertain polynomial model, and uncertain growth models. ULSSVR not only improves prediction accuracy by at least 28.49% but also demonstrates faster computational speed. Overall, ULSSVR presents a promising solution for data science and internet applications where dealing with imprecise and low-quality data is a common challenge.

An improved whale optimization algorithm with armed force program and strategic adjustment

In this paper, division algebras are proposed as an elegant basis upon which to extend support vector regression (SVR) to multidimensional targets. Using this framework, a multitarget SVR called epsilon(Z)-SVR is proposed based on an epsilon-insensitive loss function that is independent of the coordinate system or basis used. This is developed to dual form in a manner that is analogous to the standard epsilon-SVR. The epsilon(H)-SVR is compared and contrasted with the least-square SVR (LS-SVR), the Clifford SVR (C-SVR), and the multidimensional SVR (M-SVR). Three practical applications are considered: namely, 1) approximation of a complex-valued function; 2) chaotic time-series prediction in 3-D; and 3) communication channel equalization. Results show that the epsilon(H)-SVR performs significantly better than the C-SVR, the LS-SVR, and the M-SVR in terms of mean-squared error, outlier sensitivity, and support vector sparsity.