This paper presents a Fourier-enhanced dynamic sequence-to-sequence latent graph neural network (Seq2SeqLatentGNN), a deep learning architecture for multi-node spatiotemporal forecasting in hydroelectric reservoir systems. The model integrates three key components: (i) a custom Fourier layer that analyzes global temporal patterns through frequency-domain transformations, (ii) a latent correlation graph convolutional network that infers relational structures between monitoring stations without requiring predefined adjacency matrices, and (iii) an attention-based sequence-to-sequence model that processes temporal dependencies while enabling multi-step forecasting. The architecture simultaneously learns graph structure and forecasting tasks, adapting to changing spatial relationships between reservoir nodes. The proposed architecture was evaluated using a comprehensive dataset derived from 19 interconnected hydroelectric reservoirs located in southern Brazil. The dataset encompasses multiple years of high-resolution (hourly) measurements, including reservoir water levels, inflow and outflow rates, precipitation records, and energy production metrics. Experimental results demonstrate that Seq2SeqLatentGNN achieves superior performance compared to conventional statistical models and contemporary machine learning methods, as measured by standard error metrics. Analysis of the learned latent correlations reveals meaningful spatial dependencies that align with hydrological principles. The model exhibits consistent performance across varying temporal patterns, adapts to regime transitions, and captures both periodic and nonstationary dynamics. The proposed architecture contributes to spatiotemporal forecasting by combining spectral processing, dynamic graph learning, and sequence modeling in a unified framework applicable to systems with evolving connectivity patterns. • Fourier layer captures global temporal patterns in reservoir systems. • Latent graph convolution uncovers dynamic spatial relationships. • Attention model processes temporal dependencies for multi-step forecasts. • Seq2SeqLatentGNN outperforms ML models on hydroelectric data.

Alzheimer's disease (AD), a neurodegenerative disorder, progressively impairs memory and cognitive functions.Magnetic resonance imaging (MRI) is used as AD diagnosis and progress monitoring method.Convolutional Neural Network (CNN) is a data-driven deep learning model containing layers transforming data input using convolution filters.The goal of this paper is to present an analysis of the CNN architectures for classifying AD diagnoses using functional brain MRI scans acquired by the experimental dataset from the Alzheimer's Disease Neuroimaging Initiative (ADNI).Results show CNNs variants such as InceptionV3 and In-ceptionResNetV2 as powerful computational tools for developing predictive neuroimaging biomarkers in AD diagnosis applications, with accuracy above 70%.

Random vector functional link networks (RVFLNs) simplify supervised learning to a purely linear issue that can be conducted by computing the Moore-Penrose pseudoinverse, eliminating the need to optimize the input to hidden layer weights and biases. This paper proposes a RVFLN approach enhanced through feature engineering pipeline using nonlinear transformations and Predictive Permutation Feature Selection method leveraging Markov blanket concepts combined with hyperparameter optimization using a tree-structured Parzen estimator. The optimized RVFLN hyperparameters include activation function type, number of nodes, regularization term, dropout rate, and feature inclusion/exclusion. This paper aims to enhance the accuracy of predictive modeling for carbon monoxide (CO) and nitrogen oxide (NOx) emissions in a gas turbine through the proposed RVFLN approach. Overall, the proposed RVFLN offered an effective tool for predicting gas turbine emissions considering the coefficient of determination (R2) for a 5-fold cross-validation scheme. For the CO emissions modeling, the RVFLN achieved the highest performance, with a test R2of 0.710 and a validation R2of 0.708. This was followed by the competitive performance of eXtreme Gradient Boosting and Random Forest (RF), which also demonstrated strong predictive capabilities, albeit slightly lower than RVFLN. For NOxemissions modeling, RVFLN delivered the best performance, achieving a test R2of 0.756 and a validation R2of 0.864. RF followed closely with a test R2of 0.729, while Ridge also demonstrated competitive results, attaining a test R2of 0.684 along with the shortest computation time. In contrast, LASSO (Least Absolute Shrinkage and Selection Operator) and ElasticNet underperformed significantly, with test R2values of 0.362 and 0.371, respectively.

This study proposes hybrid machine learning (ML) models to predict the daily urban water consumption scenario in a neighborhood Brazilian city. The framework evaluates various signal decomposition modes, including empirical wavelet transform (EWT), complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), seasonal-trend decomposition (STL) using LOESS (LOcally Estimated Scatterplot Smoothing), and variational mode decomposition (VMD), to prepare the dataset. The decomposed data are combined with different ML models such as Bayesian regularized neural networks (BRNN), extreme learning machines (ELM), k-nearest neighbor (KNN), multilayer perceptron neural network (MLP), support vector regression with linear kernel function (SVRL), and support vector regression with radial basis function kernel (SVRR) for daily short- and long-term forecasting. The CEEMDAN-SVRL and VMD-SVRL hybrid models are found to have the best results in terms of statistical metrics and performance criteria, significantly improving the prediction accuracy and the stability of the results. The study demonstrates the potential of ML frameworks to improve water resource planning and management by accurately predicting water consumption scenarios. The results indicated that the VMD-SVRL model exhibited relatively better performance in most scenarios.

For the mechanical system to keep running as efficiently, safely, and effectively as feasible, the level-bearing vibration (LBV) in the car is required to be appropriately estimated. In light of recent regression progress, the broad learning system (BLS) models with mathematical proof of the universal approximation property are an alternative regression with origins in pseudo-inverse theory and compressed sensing. By utilizing a horizontal structure with feature nodes and enhancement nodes, BLS models provide options for deep learning to capture complex patterns. To address the limitations of single BLS in terms of generalization ability and robustness to noise, this study proposes an optimized ensemble of BLS models in bagging and stacking schemes for the LBV estimation dataset, measured at frequencies of 300 Hz and 1800 Hz. The LBV dataset is derived from simulations involving a lithium polymer cell model (ePLB C020) in an electric vehicle similar to the Nissan Leaf EV. The proposed BLS models are configured with 5-fold cross-validation scheme splitted into training (60%), validation (20%), and testing (20%) sets. Its hyperparameter tuning is based on a tree-structured Parzen estimator with an objective function given by minimization of the root mean square error (RMSE) of the validation set. Overall, the proposed ensemble BLS approaches offered an effective tool for LB estimation. The stacking BLS achieved the highest coefficient of determination (R2) train, validation, and test with 0.872, 0.821, and 0.815, respectively, followed by bagging BLS, eXtreme gradient boosting, and adaptive boosting. The results and comparison studies demonstrate ensemble BLS approaches exhibit better prediction accuracy and better fitting in data trends.

A comparison of proportional-integral-derivative (PID) controller tuning for a 2x2 Multiple-Input Multiple-Output (MIMO) water treatment plant model is presented. The PID tuning procedures are based on Multi-Objective Grey Wolf Optimizer (MOGWO) and Multi-Objective Grouped Grey Wolf Optimizer (MOGGWO) are performed under two different initial conditions. The tuning procedure is structured as a multi-objective optimization problem with four objective functions, the integral time-squared error is minimized in each output response, and the integral of the control actions is minimized in each input. MOGWO is a metaheuristic based on the hunting behavior of grey wolves, following the hierarchy and leadership procedures that these animals have, while the proposed MOGGWO is a new version proposed in this study with two different groups with different functionalities. The performance was analyzed by 50 runs based on statistical metrics. MOGGWO can find more local minima since its Pareto front is more dispersed than that found by MOGWO.

This work presents a performance comparison between the newly developed Manta Ray Foraging Optimization (MRFO) and two different variants created for tuning a decentralized fractional order proportional-integral-derivative (FOPID) controller for a multiple-input multiple-output (MIMO) application. The application consists of a ball mill pulverizing system to pulverize coal and maximize fuel efficiency. MRFO and its applications have the task of finding the optimal controller variable values to control the system's temperature and pressure. The MRFO is a metaheuristic based on the behavior of manta rays, and although it shows efficient performance it may be improved through the use of techniques which generate new variants of the algorithm. Two techniques were used in the de-velopment of new variants: Quantum mechanics and opposition-based learning. The three different versions of MRFO were used to minimize a custom fitness function which is a combination of the integral time squared error (ITSE) and the overshoot of the system response. Simulations were carried using Simulink and Matlab softwares. For analyzing the performances, statistical measures such as minimum, maximum, best, mean, median, and standard deviation of the fitness function over 50 runs were used. Additionally, the different variants were also compared for minimizing 10 benchmark functions. The results show that the use of the previously mentioned techniques improve the performance of the original MRFO in optimizing the FOPID to control the ball mill pulverizing system.

The wind energy forecast is an useful tool for wind farm production planning, and operation, facilitating decision making in terms of maintenance, electricity market clearing, and load sharing.This study proposes a cooperative ensemble learning model, using time series preprocessing, multi-objective optimization, and artificial intelligence to forecast wind energy generation in two wind farms in Brazil.Multi-objective optimization is employed to combine variational mode decompositionbased components of a model with bootstrap aggregation (bagging) and extreme learning machine models.Forecasting accuracy is evaluated through the root mean squared error, mean absolute error, mean absolute percentage error, and Diebold-Mariano hypothesis test.The empirical results suggest that proposed ensemble learning model achieved better forecasting performance than bootstrap stacking, machine learning, artificial neural networks, and statistical models, with values of approximately 12.76%, 25.25%, 31.91%, and 34.76%, respectively, in terms of root mean squared errors reduction for out-of-sample forecasting.

Forecasts can help in the decision-making process. Epidemiological forecasts are no different, they can help to evaluate the scenario and possible direction of disease spread, for guiding possible interventions. In this work, Echo State Networks (ESNs) are evaluated for COVID-19 (Coronavirus Disease 2019) cases and deaths forecasting ten days ahead. The chosen locations for the experiment are five states in Brazil, namely Sao Paulo (SP), Bahia (BA), Minas Gerais (MG), Rio de Janeiro (RJ), and Ceara (CE), the states with the most COVID-19 cases as of December 31, 2020. The results are evaluated using performance indexes RMSE (Root-mean-square error), MAE (Mean absolute error), and MAPE (Mean absolute percentage error). Results are compared with a common forecasting technique called ARIMA (Autoregressive Integrated Moving Average). The error signals are compared using Wilcoxon Signed-Rank Test, to evaluate the difference statistically. ESNs presented overall good results for a ten day horizon forecast regarding used performance metrics, but for the number of cases, ARIMA outperformed ESNs regarding RMSE, MAE, and MAPE in all but one state. For the number of deaths however, ESNs outperformed ARIMA in most states when the MAE is taken into account. ESNs are shown to be a solid forecasting model when compared with ARIMA, presenting comparable results and in some cases outperforming it.

Water consumption forecasting is essential for the development of efficient cities planning. Due to the non-linearities and relations of the water consumption with different factors the developing of an accurate forecasting system is challenging. This paper proposes a seasonal, trend and multiobjective ensemble learning model to forecast multi-step-ahead (one, two, and three-month-ahead) water consumption for two cities of Paraná state in Brazil. The proposed data analysis uses seasonal and trend decomposition using Loess (STL) to split the original data into the seasonal, trend, and residual components. In the next stage, the machine learning models named Support Vector Regression and Ridge Regression as well as the stochastic approach Gaussian Processes model are employed to train and predict the STL components. The previous components are weighted integrated to compose a heterogeneous ensemble learning of components obtaining the final forecasts. The elitist Non-Dominated Sorting Genetic Algorithm – version II (NSGA-II) is adopted to obtain the weights assigned to the components. The best model has better generalization out-of-sample considering the root mean squared error, mean absolute error, and mean absolute percentage error criteria in respect to minimization problem. Through developed comparisons, results showed that combining STL and multi-objective optimization with a heterogeneous ensemble learning can achieve high forecasting accuracy in comparison with some models. The framework proposed in this paper is effective to obtain reliable water consumption forecasting and can support and help future decision.

Alternative energy sources are becoming more and more common around the world. In order to reduce environmental pollution and CO2emissions, in addition to being an ideal solution to overcome the energy crisis. In this context, power energy stands out, as it is the most abundant and most widely available natural resource on the entire planet. Due to the high level of uncertainty of the factors that directly interfere in the generation of solar power, such as temperature and solar radiation, make predictions of solar power with high precision is a challenge. Thus, the objective of this article is to develop a forecasting model, through time series, that makes it possible to predict the production of power energy, using a database collected in a photovoltaic plant in Uruguay. For the development of the proposal, models (base-learners), pre-processing techniques and models (meta-learners) used in the Stacking-Ensemble Learnig (STACK) method were used, which were compared using the measurements of performance Relative Root Mean Square Error (RRMSE), Symmetric Mean Absolute Percentage Error (sMAPE) and Determination Coefficient (R2) in addition to statistical tests. In the end, it can be concluded that the combination Correlation Matrix (CORR) and Language Model (LM), from Layer-0 obtained the best results, in the three performance measures and the combination of models (base-learners) and pre-processing techniques (Layer-0) presented the best results when compared to Layer-1, obtaining satisfactory values in all performance measures.

The development of accurate models to forecast electricity energy prices is a challenge due to the number of factors which can affect this commodity. In this paper, a hybrid multi-stage approach is proposed to forecast multi-stepahead (one, two and three-month-ahead) Brazilian commercial and residential electricity energy prices. The proposed data analysis combines the pre-processing named complementary ensemble empirical mode decomposition (CEEMD) in the first stage coupled with the coyote optimization algorithm (COA) to define the CEEMD's hyperparameters, aiming to deal with time series non-linearities and enhance the model's performance. On the next stage, four machine learning models named extreme learning machine, Gaussian process, gradient boosting machine, and relevance vector machine are employed to train and predict the CEEMD's components. Finally, in the final stage, the results of the previous step are directly integrated to compose a heterogeneous ensemble learning of components to obtain the final forecasts. In this case, a grid of models is obtained. The best model is one that has better generalization out-of-sample. Through developed comparisons, results showed that combining COA-CEEMD with a heterogeneous ensemble learning can develop accurate forecasts. The modeling developed in this paper is promising and can support decision making in electricity energy price forecasting.

Bitcoin is the leading currency in the cryptocurrency market capturing attention worldwide. Forecasting the Bitcoin price as accurate as possible is essential, but due to its high volatility this task is challenging. Many researchers try, through the years, to develop efficient models for predicting the Bitcoin price using several different data-driven approaches. The objective of this paper is to develop a novel decomposition-ensemble learning model that combines Variational Mode Decomposition (VMD) and Stacking-ensemble learning (STACK) with machine learning algorithms to forecast the Bitcoin price multi-step ahead. The algorithms are k-Nearest Neighbors, Support Vector Regression with Linear kernel, Feed-forward Artificial Neural Network with single-layer perceptron, Generalized Linear Model, and Cubist. Correlation matrix (CORR), principal component analysis (PCA), and Box-Cox transformation (BOXCOX) were used as data preprocessing techniques. Estimating the performance of the proposed models (namely VMD-STACK-CORR, VMD-STACK-PCA, and VMD-STACK-BOXCOX) using relative root mean square error, symmetric mean absolute percentage error, and absolute percentage error measures, defined that for one-day-ahead forecast VMD-STAK-BOXCOX model presented the better performance, and for two and three-days-ahead forecast VMD-STACK-CORR model was chosen, compared to VMD, STACK, and machine learning algorithms models' performance. Diebold-Mariano statistical test was conducted to evaluate a reduction in forecasting errors. Therefore, the proposed models (VMD-STACK-CORR, VMD-STACK-PCA, and VMD-STACK-BOXCOX) indeed forecast accurately Bitcoin price and outperformed the compared models (VMD, STACK, and machine learning models).

Metaheuristics of the natural computing field have been proposed as an alternative to mathematical optimization approaches to address non convex problems involving large search spaces. In recent years a new optimization metaheuristic algorithm was proposed called Wind Driven Optimization (WDO). WDO is a stochastic nature-inspired paradigm based on atmospheric motion. In this paper, a modified version of WDO is proposed and evaluated, based on Lévy flights (or Lévy motions) to tune its control parameters, called Lévy WDO (LWDO). Lévy flight or anomalous diffusion process is a random walk characterized by Markov chain in which the step-lengths have a probability distribution that is heavy-tailed. To evaluate the multiobjective optimization performance of the WDO and the proposed LWDO, a benchmark for optimizing of a safety isolating transformer is adopted. In this paper, the transformer design optimization is treated as a multiobjective problem, with the aim to minimize both the total mass (iron and copper materials) and losses taking into consideration design constraints. Simulation results testify that the multiobjective LWDO is a promising approach for multiobjective optimization as it outperforms the WDO in multiobjective version and the classical NSGA-II (Non-dominated Sorting Genetic Algorithm, version II).

Time series forecasting plays a key role in many areas of science, finance and engineering, mainly for the estimation of trend or seasonality of a variable under observation, aiming to serve as basis for future purchase decisions, choice of design parameters or maintenance schedule. Artificial Neural Networks (ANNs) have proven to be suitable in linear or nonlinear functions mapping. However, the ANNs, implemented in its most simplistic form, tend to have a loss in overall performance. This work aims to obtain a prediction model for a short-term load problem through the usage of wavenets ensemble, which is an ANN approach capable in combining the best characteristics of each ensemble component, in order to achieve a higher overall performance. We adopted the usage of bootstrapping, cross-validation and the inputs decimation approaches for the ensemble construction. For the components selection, `constructive' and `no selection' methods were applied. Finally, the combination is held though simple average, mode or stacked generalization. The results show that it is possible to improve the generalization ability through effective committees depending on the methods used to construct the ensemble. The total relative improvement achieved in respect to the naive model, was over 95%, regardless the number of sub wavenets, and for the best component, the relative improvement was 93.91% using five wavenets. We conclude that the most frequent and effective set, but not always with the lower MSE (Mean Squared Error), was using constructive bagging with simple average.

Simulated annealing (SA) is a solo-search algorithm, trying to simulate the cooling process of molten metals through annealing to find the optimum solution in an optimization problem. SA selects a feasible starting solution, produces a new solution at the vicinity of it, and makes a decision by some rules to move to the new solution or not. However, the results found by SA depend on the selection of the starting point and the decisions SA makes. In this paper, in order to ameliorate the drawbacks of the algorithm, a population-based simulated annealing (PSA) algorithm is proposed. PSA uses the population's ability to seek different parts of the search space, thus hedging against bad luck in the initial solution or the decisions. A set of benchmark functions was used in order to evaluate the performance of PSA algorithm. Simulation results accentuate the superior capability of PSA in comparison with the other optimization algorithms.

Nature-inspired algorithms of the swarm intelligence field perform powerfully and efficiently in solving global optimization problems. Inspired by nature, these metaheuristic algorithms have obtained promising performance over continuous domains of optimization problems. Recently, a new swarm intelligence approach called firefly algorithm (FA) has emerged. The FA is a stochastic paradigm based on the idealized behavior of the flashing characteristics of fireflies. However, to achieve good performance with FA, the tuning of control parameters is essential as its performance is sensitive to the choice of the randomization parameter (α) setting. This paper introduces a FA approach combined with chaotic sequences generated by Zaslavskii map (FACZ) to tune the randomization parameter. Simulations of Loney's solenoid benchmark problem examine the effectiveness of the conventional FA and the proposed FACZ algorithms. Simulation results and comparisons with the FACZ demonstrated that the performance of the FA is promising in the Loney's solenoid case.

The reliability-redundancy allocation problem can be approached as a mixed-integer programming problem. It has been solved by using optimization techniques such as dynamic programming, integer programming, and mixed-integer nonlinear programming. On the other hand, a broad class of meta-heuristics has been developed for reliability-redundancy optimization. Recently, a new meta-heuristics called firefly algorithm (FA) algorithm has emerged. The FA is a stochastic metaheuristic approach based on the idealized behavior of the flashing characteristics of fireflies. In FA, the flashing light can be formulated in such a way that it is associated with the objective function to be optimized, which makes it possible to formulate the firefly algorithm. This paper introduces a modified FA approach combined with chaotic sequences (FAC) applied to reliability-redundancy optimization. In this context, an example of mixed integer programming in reliability-redundancy design of an overspeed protection system for a gas turbine is evaluated. In this application domain, FAC was found to outperform the previously best-known solutions available.

Among the existing meta-heuristic optimization algorithms, a well-known branch is the differential evolution (DE). DE is a powerful population-based algorithm of evolutionary computation field designed for solving global optimization problems which only has a few control parameters. With an eye to improve the performance of DE, in this paper, a DE approach combined with a cultural algorithm technique based on normative knowledge (NDE) is investigated to estimate the heat transfer coefficient during freezing treatment by inverse analysis. Numerical results for inverse heat transfer problem demonstrate the applicability and efficiency of the NDE algorithm. In this application, NDE approach outperforms a classical DE approach in terms of quality of solution.

The Harmony Search (HS) algorithm was originally conceptualized using the musical improvisation process of searching for a perfect state of harmony. The HS algorithm uses a random search, which is based on random selection, memory consideration, and pitch adjusting. This paper proposes a modified HS approach combined with differential evolution and chaotic sequences to solve the economic load dispatch problem of thermal generators with the valve-point effect. The proposed modified HS algorithm was validated in a power economic problem comprised by 10 generating units with valve-point effects and multiple fuels for a load demand of 2500 MW. Simulation results and performance analysis show that the modified HS algorithm presented promising results when compared with results of other optimization methods reported in recent literature.

In this paper a Modified Differential Evolution (MDE) is proposed and its performance for solving the inverse heat transfer problem is compared with Genetic Algorithm with Floating-point representation (GAF) and classical Differential Evolution (DE). The inverse analysis of heat transfer has some practical applications, for example, the estimation of radioactive and thermal properties, such as the conductivity of material with and without the temperatures dependence of diffusive processes. The inverse problems are usually formulated as optimization problems and the main objective becomes the minimization of a cost function. MDE adapts a concept originally proposed in particle swarm optimization design for the dynamic adaptation of mutation factor. Using a piecewise function for apparent thermal conductivity as a function of the temperature data, the heat transfer equation is able to estimate the unknown variables of the inverse problem. The variables that provide the beast least squares fit between the experimental and predicted time-temperatures curves were obtained. Numerical results for inverse heat transfer problem demonstrated the applicability and efficiency of the MDE algorithm. In this application, MDE approach outperforms the GAF and DE best solutions.

The particle swarm optimization (PSO) algorithm is a member of the wide category of swarm intelligence methods for solving global optimization problems. Its basic idea is the simulation of simplified animal social behaviors such as fish schooling and bird flocking. PSO algorithms are attracting attentions in recent years, due to their ability of keeping good balance between convergence and diversity maintenance. Several attempts have been made to improve the performance of the original PSO algorithm. In this paper, a modified version of the original PSO based on Cauchy distribution and dynamic adaptation of inertia factor, named modified PSO (MPSO), is proposed. to estimate the unknown variables of an inverse heat transfer problem. To validate the optimization performance of the proposed MPSO, an inverse heat transfer problem is illustrated and the algorithm has to estimate its unknown variables. The results testify that the MPSO can perform well in an inverse heat transfer problem.

The reliability-redundancy allocation problem can be approached as a mixed-integer programming problem. It has been solved by using optimization techniques such as dynamic programming, integer programming, and mixed-integer nonlinear programming. On the other hand, a broad class of meta-heuristics has been developed for reliability-redundancy optimization. Recently, a new meta-heuristics called harmony search (HS) algorithm has emerged. HS was conceptualized using an analogy with music improvisation process where music players improvise the pitches of their instruments to obtain better harmony. This paper introduces a modified HS approach combined with an operator of differential evolution — a paradigm of evolutionary computation — to solve optimization problems in reliability engineering. In this context, an example of mixed integer programming in reliability-redundancy design of an over-speed protection system for a gas turbine is evaluated. In this application domain, HS was found to outperform the previously best-known solutions available.

A new class of meta-heuristics called SOMA (Self-Organizing Migrating Algorithm) was proposed in recent literature. SOMA works on a population of potential solutions called specimen and it is based on the self-organizing behavior of groups of individuals in a “social environment”. This paper proposes a modified SOMA approach to solving the economic load dispatch problem of thermal generators with the valve-point effect. To show the performance of the proposed modified SOMA algorithm based on fundamentals of normative knowledge in cultural algorithms, which was applied to test the power economic problem comprised 10 generating units with valve-point effects and multiple fuels for the load demands of 2400 MW. Simulation results show that the classical and modified SOMA algorithms are efficient and have good convergence property when compared with results of other optimization methods reported in the literature.

Differential evolution (DE) is a powerful population-based algorithm of evolutionary computation field designed for solving global optimization problems. The potentialities of DE are its simple structure, easy use, convergence speed and robustness. However, the control parameters and learning strategies involved in DE are highly dependent on the problems under consideration. Choosing suitable parameter values requires also previous experience of the user. Despite its crucial importance, there is no consistent methodology for determining the control parameters of a DE. In this paper, different DE approaches combined with a cultural algorithm technique based on normative and situational knowledge are proposed as alternative methods to solving the economic load dispatch problem of thermal generators with valve-point effect. The DE approaches are validated for a test system consisting of 13 thermal generators whose nonsmooth fuel cost function takes into account the valve-point loading effects. Numerical results indicate that performance of the cultural DE present best results when compared with previous optimization approaches in solving load dispatch problems with the valve-point effect.

Particle swarm optimization (PSO) is a population-based stochastic optimization technique, originally developed by Eberhart and Kennedy, inspired by simulation of a social psychological metaphor instead of the survival of the fittest individual. In PSO, the system (swarm) is initialized with a population of random solutions (particles) and searches for optima using cognitive and social factors by updating generations. PSO has been successfully applied to a wide range of applications, mainly in solving continuous nonlinear optimization problems. Based on the PSO and chaos theories, this paper discusses the use of a chaotic PSO approach hybridized with an implicit filtering (IF) technique to optimize performance of economic dispatch problems. The chaotic PSO with chaos sequences is the global optimizer and the IF is used to fine-tune the chaotic PSO run in sequential manner. The hybrid methodology is validated for a test system consisting of 13 thermal units whose incremental fuel cost function takes into account the valve-point loading effects.

Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm driven by the simulation of a social psychological metaphor instead of the survival of the fittest individual. Based on the swarm intelligence theory, this paper discusses the use of PSO approaches using an operator and based on the Gaussian probability distribution function as a population space of a cultural algorithm, called cultural Gaussian PSO (GPSO-CA). Cultural algorithms are mechanisms that incorporate domain knowledge obtained during the evolutionary process, which increase the efficiency of the search process. These approaches are employed in a well-studied continuous optimization problem of mechanical engineering design.

Particle swarm optimization (PSO) is a population-based swarm intelligence algorithm driven by the simulation of a social psychological metaphor instead of the survival of the fittest individual. Based on the swarm intelligence theory, this paper discusses the use of PSO with a Quasi-Newton (QN) local search method. The PSO is used to produce good potential solutions, and the QN is used to fine-tune of final solution of PSO. The hybrid methodology is validated for a test system consisting of 13 thermal units whose incremental fuel cost function takes into account the valve-point loading effects.