Differential Evolution Optimization Research Articles

Research on Active Disturbance Rejection Control of Small Modular Reactor Once-Through Steam Generator Based on Differential Evolution Optimization Algorithm

The pressure control of once-through steam generator (OTSG) is critical for the operation and safety of small modular reactors. However, the dynamics of the OTSG are quite nonlinear, time varying, and uncertain. Classical control methods face significant challenges in keeping the pressure within acceptable limits in an environment with frequent load variations and multiple sources of external disturbances. In this paper, a robust control strategy based on active disturbance rejection control (ADRC) optimized by the differential evolution (DE) algorithm is proposed to satisfy the requirements of steam pressure control in an optimum and efficient way. First, a lumped parameter model for the OTSG is developed based on the notion of moving boundaries and linearized to introduce a transfer function model for control design purposes. Then a feedforward cascade control system based on an ADRC controller and a proportional integral differential (PID) controller is designed, which mainly consists of a pressure ADRC controller, a feedwater PID controller, and a feedforward compensator. To improve the pressure control performance and parameter tuning efficiency of the OTSG control system, a DE algorithm is applied to optimize the ADRC parameters, and the frequency domain and time domain characteristics are compared with particle swarm optimization and the genetic algorithm. Transient simulation experiments were used to evaluate the control performance at 100%, 50%, and 25% power levels, respectively. Moreover, a performance robustness criterion is proposed to demonstrate the robust stability of the ADRC, and the robustness metric is compared with that of the PID control schemes. The simulation results show that DE-ADRC control strategy has better set point tracking, interference rejection, and robust stability than DE-PID control strategy.

Retraction Note: Fuzzy-entropic approach on chest X-ray region of interest segmentation-heart position shifting using differential evolution optimization and multi-level segmentation technique with cloud computing

Retraction Note: Fuzzy-entropic approach on chest X-ray region of interest segmentation-heart position shifting using differential evolution optimization and multi-level segmentation technique with cloud computing

Joint Optimization Algorithm for Latency-Energy and Privacy Combining Discrete Differential Evolution and Convex Optimization

A privacy protection task offloading algorithm combining discrete differential evolution and convex optimization is proposed to resolve the new position privacy leakage problem for mobile terminal due to transferring tasks to multiple edge servers for computation via wireless networks. First, the privacy cost of offloading decision is defined for the characteristics of the position privacy problem combined with the standard deviation theory. Second, the objective problem is modeled as a joint optimization of position privacy protection, offloading decision and transmission power, and the total cost of task offloading is an optimization objective. Finally, to handle the objective problem efficiently, offloading decision variable is decoupled from the transmission power variable to decrease the computational complexity of the problem; the discrete differential evolution algorithm is designed to accumulate the approximate optimal offloading decision, and the optimal transmission power is efficiently solved by variable substitution method and subgradient method. Simulations reveal that the algorithm has excellent convergence; it improves the position privacy protection level of mobile terminal and reduces the total cost of task offloading while maintaining lower energy consumption and latency.

Energy-aware virtual machine placement based on a holistic thermal model for cloud data centers

As energy-intensive infrastructures, data centers (DCs) have become a pressing challenge for managers due to their significant energy consumption and carbon emissions. Information technology (IT) and cooling systems contribute the most to energy consumption. Energy-aware virtual machine (VM) scheduling methods have been widely demonstrated to reduce energy consumption and operating costs in DCs. However, as realistic DCs exhibit complex power and thermodynamic behaviors, existing works cannot provide efficient measures to optimize computing and cooling power consumption simultaneously. To overcome this challenge, we construct a holistic thermal model (including CPU and server inlet thermal models) to accurately represent the non-uniform, dynamic thermal environment. Subsequently, this work proposes a thermal model-based energy-aware VM placement method (TEVP) to minimize the holistic energy consumption of the DCs, considering resource and thermal constraints. We develop a novel hybrid swarm intelligence algorithm (DE-ERPSO) combining differential evolution (DE) and particle swarm optimization with an elite re-selection mechanism (ERPSO) to explore more energy-efficient VM placement schemes. Extensive experiments are conducted on an extended CloudSim to validate the performance of the proposed TEVP using real-world workload traces (PlanetLab and Azure). Results show that TEVP saves over 5.6% of the total energy consumption over the advanced baselines while maintaining low thermal violations.

Satin bowerbird algorithm with an adaptive constriction factor for enhanced photovoltaic integration in distribution feeders

—This paper introduces an enhanced Satin bowerbird optimizer (SBO), specifically tailored for the integration of photovoltaic distributed generation (DG) units into radial distribution systems. The upgraded SBO version involves two pivotal adjustments. Firstly, the positional updating mechanism of the newly generated bower is modified to enable exploration around the iteration's elite bower. Secondly, an adaptive constriction factor is introduced, progressively decreasing during iterations to concentrate the search in promising areas. These modifications significantly amplify the exploration capacity of each new bower in the SBO algorithm. The proposed upgraded SBO aims at minimizing costs related to CO2 emissions from the grid and those linked with photovoltaic units, in addition to energy losses. The variability of photovoltaic DG units is represented using the Beta Probability Density Function (PDF) to portray distinct solar irradiation conditions experienced daily. The enhanced SBO version undergoes testing on a practical Nigerian distribution system, the Ajinde 62-bus network, and a standard IEEE 69 nodes system. Simulation results underscore the effectiveness of the upgraded SBO version, revealing substantial reductions in energy losses and emissions. Specifically, for the Ajinde 62-bus network, the proposed SBO version achieves a noteworthy 31 % reduction in the combined yearly costs of energy losses and emissions compared to the initial case. Additionally, for the IEEE 69-bus system, it attains a considerable reduction of 35 %. Furthermore, the simulation results illustrate the competitive performance of the suggested SBO version when compared to Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms, as well as the standard SBO.

Optimizing pantograph fractional differential equations: A Haar wavelet operational matrix method

In this study, we developed an operational matrix method of integration using Haar wavelets to solve both linear and nonlinear pantograph fractional differential equations by taking Atangana's beta derivative. The proposed method utilizes an operational matrix and truncated Haar wavelet series to transform linear and nonlinear problems into objective functions. These objective functions are then minimized using differential evolution optimization. Illustrative examples demonstrate convergence and validation of the proposed method. The proposed method yields exceptional numerical outcomes in terms of competitiveness and accuracy when compared to exact solutions. In addition, performance metrics, including the mean absolute deviation, root mean squared error, P2norm, P∞ norm, Theil's inequality coefficient, variance account for, coefficient of determination, and Nash-Sutcliffe efficiency, were calculated for a varying number of collocation points. The results indicate that the Haar wavelet operational matrix method is a straightforward and efficient method for solving pantograph fractional differential equations.

Differential evolutionary optimization fuzzy entropy for gland segmentation based on breast mammography imaging

ObjectiveThe integration of fuzzy entropy into image segmentation techniques has proven effective in addressing issues related to ambiguous boundaries and uncertainties in complex image structures. This study aims to improve breast mammography image segmentation by optimizing minimum fuzzy entropy. The primary challenges identified are the presence of glandular burrs and irregular edges, as well as premature convergence and local optima in entropy optimization. MethodsWe propose an enhanced differential evolution algorithm combined with fuzzy entropy to address these challenges. This algorithm specifically targets glandular burrs, irregular edges, premature convergence, and local optimal entropy issues. The algorithm's performance was evaluated using breast mammography images representing four types of glands and benchmarked against five state-of-the-art algorithms. ResultsExperimental results demonstrate that the proposed algorithm significantly improves segmentation accuracy compared to the other advanced algorithms. It effectively resolves issues related to glandular burrs, irregular edges, premature convergence, and local optimal entropy, leading to superior segmentation outcomes. ConclusionThe proposed algorithm, which combines an improved differential evolution approach with fuzzy entropy, delivers the best segmentation results for breast gland segmentation. It successfully overcomes the challenges of glandular burrs, irregular edges, premature convergence, and local optimal entropy, thus enhancing breast mammography image segmentation.

Hybridization of Social Group Optimization and Differential Evolution Algorithm for Solving Speed Reducer Design Problem

Objectives: The objective of this study is to present a hybrid approach named SGO-DE, which combines the Social Group Optimization (SGO) algorithm and differential evolution (DE), aiming to balance exploration and exploitation capacities to improve the accuracy of the optimization algorithm in finding optimal solution for speed reducer design problem. This hybrid approach is simulated for a speed reducer mechanical engineering design problem and the results are compared to several other state-of-the-art optimization algorithms. Method: To improve the exploration and exploitation of SGO, in its acquiring phase Differential Evolution (DE) is introduced. The individual candidate solutions derived from the Improving phase of SGO tries to acquire better values using DE. This helps in striking a better balance between exploration and exploitation, there by achieving improved optimal values and not getting trapped in local optima. The performance of the SGO-DE method is then evaluated and compared to other optimization algorithms through experimentation on the speed reducer design challenge. Findings: The findings of this study indicate that the SGO-DE hybrid approach outperforms other state-of-the-art algorithms by a significant margin in terms of optimization results. The numbers of function evaluations (FEs) significantly go low as less as 6000 compared to other state-of-the algorithms. The comparison demonstrates the efficacy of the SGO-DE method in enhancing solution quality and speeding up execution. Novelty: The novelty of this study lies in the development a hybrid approach of SGO and DE which is efficient in achieving competitive performance in less numbers of function evaluation in speed reducer design problem. This hybridization can strike a better balance between exploration and exploitations. Keywords: SGO, DE, Hybridization, Nature-inspired, Optimization algorithm

An Improved Back Propagation Neural Network Based on Differential Evolution and Grey Wolf Optimizer and Its Application in the Height Prediction of Water-Conducting Fracture Zone

Given that the conventional back propagation neural network (BPNN) easily falls into the local optimal solutions, resulting in poor prediction accuracy, an improved BPNN based on the differential evolution and grey wolf optimizer (DEGWO) is proposed, the so-called DEGWO-BPNN. The prediction of the water-conducting fracture zone (WCFZ) height is significant for mine safety operations. A total of 104 sample data are trained and 25 sample data are tested to identify the optimal prediction model. Five evaluation indexes are selected to assess the prediction performance of the models quantitatively. Finally, the DEGWO-BPNN model is applied to a specific engineering case. The main conclusions are as follows: (1) Mining height, mining depth, coal seam dip, panel width, and ratio of hard rock as the main factors affecting the WCFZ height are selected. The topology structure of the model is defined as ‘5-12-1’; (2) the bias between the predicted value and the actual value of the training samples is smaller with an average error of 2.39. Test samples further validate the prediction precision through evaluation indexes. The values of MAE, RMSE, MAPE, and R2 are 2.3952, 3.4674, 5.3148%, and 0.99077, respectively. The prediction accuracy is 94.6852%; (3) ‘Mining Code’, MLR, BPNN, and GWO-BPNN models are treated as the comparison groups. The comparative analysis shows that the prediction performance of ‘Mining Code’ is the worst, while that of DEGWO-BPNN is the best, and it outperforms other algorithms and statistical approaches; (4) the prediction of WCFZ height in the 11601 panel is in line with the actual value. The prediction error of the DEGWO-BPNN model is lower than that of the comparison models. As such, the DEGWO-BPNN model can be well applied to the prediction of WCFZ height and is suitable for coal mines with different regional geological conditions. It can provide a valuable reference for mine safety operations.

Economically optimized heat exchanger design: a synergistic approach using differential evolution and equilibrium optimizer within an evolutionary algorithm framework

Economically optimized heat exchanger design: a synergistic approach using differential evolution and equilibrium optimizer within an evolutionary algorithm framework

A Novel Mayfly Algorithm with Response Surface for Static Damage Identification Based on Multiple Indicators

This paper proposes a novel structural damage identification approach coupling the Mayfly algorithm (MA) with static displacement-based response surface (RS). Firstly, a hybrid optimal objective function is established that simultaneously considers the sensitivity-based residual errors of static damage identification equation and the static displacement residual. In the objective function, the static damage identification equation is addressed by the Tikhonov regularization technique. The MA is subsequently employed to conduct an optimal search and pinpoint the location and intensity of damages at the structural element level. To handle the inconformity of the static loading points and the measurement points of displacements, the model reduction and displacement extension techniques are implemented to reconstruct the static damage identification equation. Meanwhile, the static displacement-based RS is constructed to calculate the displacement residual in the hybrid objective function, thereby circumventing the time-consuming finite element calculations and improving computational efficiency. The identification results of the numerical box girder bridge demonstrate that the proposed method outperforms the particle swarm optimization, differential evolution, Jaya and whale optimization algorithms about both convergence rate in optimal searching and identification accuracy. The proposed method enables more accurate damage identification compared to methods solely based on the indicator of the residual of static damage identification equations or displacement residual. The results of identifying damage in the 21 element-truss structure and the static experiments on identifying damage in an aluminum alloy cantilever beam confirm the high efficiency of the proposed approach.

Optimizing Power Generation Scheduling: A Comparative Analysis of Metaheuristic Algorithms

Purpose: This research compares six optimization methods, including the Mayfly Optimization Algorithm, Genetic Algorithm, Simulated Annealing, Firefly Algorithm, and Differential Evolution (DE). Design/Methodology/Approach: The evaluation of any algorithm is predicated on its ability to strike a balance between meeting demand, taking into account renewable energy sources, and lowering the total cost of producing power. Findings: The analysis shows that although PSO and GA converge to similar overall costs, the algorithms' performances differ. Then come SA, FA, and DE in close succession, with the Mayfly Optimization Algorithm showing higher total costs than the other techniques. Originality: By addressing difficult power generating scheduling problems, this work advances our understanding of the benefits and drawbacks of various optimization techniques.

Advanced forecasting of COVID-19 epidemic: Leveraging ensemble models, advanced optimization, and decomposition techniques

In the global effort to address the outbreak of the new coronavirus pneumonia (COVID-19) pandemic, accurate forecasting of epidemic patterns has become crucial for implementing successful interventions aimed at preventing and controlling the spread of the disease. The correct prediction of the course of COVID-19 outbreaks is a complex and challenging task, mainly because of the significant volatility in the data series related to COVID-19. Previous studies have been limited by the exclusive use of individual forecasting techniques in epidemic modeling, disregarding the integration of diverse prediction procedures. The lack of attention to detail in this situation can yield worse-than-ideal results. Consequently, this study introduces a novel ensemble framework that integrates three machine learning methods (kernel ridge regression (KRidge), Deep random vector functional link (dRVFL), and ridge regression) within a linear relationship (L-KRidge-dRVFL-Ridge). The optimization of this framework is accomplished through a distinctive approach, specifically adaptive differential evolution and particle swarm optimization (A-DEPSO). Moreover, an effective decomposition method, known as time-varying filter empirical mode decomposition (TVF-EMD), is employed to decompose the input variables. A feature selection technique, specifically using the light gradient boosting machine (LGBM), is also implemented to extract the most influential input variables. The daily datasets of COVID-19 collected from two countries, namely Italy and Poland, were used as the experimental examples. Additionally, all models are implemented to forecast COVID-19 at two-time horizons: 10- and 14-day ahead (t+10 and t+14). According to the results, the proposed model can yield higher correlation coefficient (R) for both case studies: Italy (t+10 = 0.965, t+14 = 0.961) and Poland (t+10 = 0.952, t+14 = 0.940) than the other models. The experimental results demonstrate that the model suggested in this paper has outstanding results in various kinds of complex epidemic prediction situations. The proposed ensemble model demonstrates exceptional accuracy and resilience, outperforming all similar models in terms of efficacy.

Optimization Strategies for Electric Vehicle Charging and Routing: A Comprehensive Review

Based on information from recent research, by 2045, Electric Vehicles (EV) will dominate the roads with presence of more than 80% of its kind. Hence, these vehicles' grid level penetration will increase proportionally, which challenges the existing grid infrastructure in terms of its reliability and energy management capabilities. New techniques to store and consume massive quantities of energy from the power grid, as well as infusing the captive energy within the EV in response to grid demands, are emerging with the advent of electric vehicles. Everything could be handled smoothly only if we schedule the EV operation (charging/discharging) more optimally and efficiently using scheduling algorithms. Despite the existence of many routings and charging schedule computations, nature-inspired optimization approaches might play a critical role in responding to such routing challenges. Researchers have created several optimum scheduling approaches, such as Dynamic Programming, Differential Evolutionary Optimization Techniques, Collaborative Optimization Scheduling, Two-stage optimal scheduling strategy, and so on. The optimum schedule review examines the operation of an EV fleet while considering uncertainty sources and varied EV operating circumstances by integrating heuristic and meta-heuristic techniques. This paper exhibits a deep review on the various EV optimal scheduling techniques and adopted algorithms which are the emerging best practices like predictive analytics, dynamic routing, user centric planning, multi-objective optimization, etc. that reflect the industry's focus on leveraging advanced technologies, data-driven decision-making, and collaborative approaches to enhance the efficiency and sustainability of electric vehicle routing and charging scheduling.

Observer-based differential evolution constrained control for safe reference tracking in robots

Big torque inputs in controls could increase energy consumption, and big estimated perturbations in observers could produce device damages. Therefore, it would be interesting to propose a constrained control for safe reference tracking and a constrained observer for safe perturbation estimation in robots. Furthermore, the best gains in controls produce a balance between safe reference tracking and save energy consumption. Therefore, it would be interesting to propose a method to find the best gains. In this paper, an observer-based differential evolution constrained control is proposed for safe reference tracking in robots. The contributions are described as follows: (1) a constrained observer is proposed for safe perturbation estimation in robots, (2) a constrained control is proposed for safe reference tracking in robots, (3) a differential evolution optimizer is used to find the best gains in an observer-based constrained control, (4) the robust stability in an observer-based constrained control is assured, (5) the pseudo-code of an observer-based differential evolution constrained control is detailed. The proposed observer-based differential evolution constrained control is applied for safe reference tracking in two robots.

Development of near-infrared spectroscopy calibration model and monitoring software: For monitoring hexamethylenetetramine concentration in hexamethylenetetramine–acetic acid solution

In recent years, near-infrared spectroscopy has been increasingly used in chemical engineering processes. However, accurately and in real-time monitoring concentrations remains highly challenging. This study presents a method for accurately monitoring the hexamethylenetetramine concentration in hexamethylenetetramine-acetic acid solution by integrating near-infrared spectroscopy with software techniques. Compared to the methods of zero mean standardization (Z-score), standard normal variate (SNV), first derivative (D1), second derivative (D2), and vector normalization (VN), the Savitzky-Golay first derivative (SGFD) method effectively addresses issues related to baseline drift, noise, and other interferences. This results in clearer identification of characteristic absorption peaks of different components and a significant improvement in the accuracy of the analysis. The study combined the uninformative variable elimination (UVE), differential evolution (DE), and moth flame optimization (MFO) algorithms to optimize a feature wavenumber selection method, which reduced the number of variables by 78.74 %, and the values of root mean square error of calibration set (RMSEC) and root mean square error of prediction (RMSEP) by 18.86 % and 30.38 %, respectively. Additionally, the analytical method was integrated with real-time monitoring software, enabling the monitoring of hexamethylenetetramine concentration. This integration supports the improvement of the quality and safety of the manufacturing process. The results demonstrate the potential application of near-infrared spectroscopy in real-time monitoring and automated control of chemical processes in the chemical industry.

Ultra-short term wind power prediction based on quadratic variational mode decomposition and multi-model fusion of deep learning

To address the challenges associated with the intricate selection of decomposition technical parameters and the adverse impact of high-frequency non-stationary components on prediction accuracy, a differential evolution (DE) and sparrow search algorithm (SSA) parameter optimization model is formulated. Through the optimization of variational mode decomposition (VMD) and bidirectional short and long-term memory (BiLSTM) neural networks, enhancements are made to the overall performance of the prediction method. Subsequently, DESSA–VMD is employed to quadratically decompose the high-frequency unstable component, mitigating the detrimental effects of randomness and volatility on the prediction accuracy of the primary component. Following this, the DESSA–BiLSTM neural network is applied to predict the high-frequency strong non-stationary component, whereas the autoregressive integrated moving average is utilized for predicting the low-frequency periodic component. Finally, a case analysis is conducted using actual data comprising 2000 sets of wind power in a province. When the test set consisted of 600 groups, the root mean square error index value of the proposed prediction model exhibited reductions of 1.95 MW, 2.86 MW, and 1.16 MW, respectively, compared with the BP, SVM, and LSTM methods. Additionally, the mean absolute percentage error index showed decreases of 2.26 %, 2.96 %, and 1.73 %, respectively.

A Multi-level Surrogate-assisted Algorithm for Expensive Optimization Problems

With the development of computer science, more and more complex problems rely on the help of computers for solving. When facing the parameter optimization problem of complex models, traditional intelligent optimization algorithms often require multiple iterations on the target problem. It can bring unacceptable costs and resource costs in dealing with these complex problems. In order to solve the parameter optimization of complex problems, in this paper we propose a multi-level surrogate-assisted optimization algorithm (MLSAO). By constructing surrogate models at different levels, the algorithm effectively explores the parameter space, avoiding local optima and enhancing optimization efficiency. The method combines two optimization algorithms, differential evolution (DE) and Downhill simplex method. DE is focused on global level surrogate model optimization. Downhill simplex is concentrated on local level surrogate model update. Random forest and inverse distance weighting (IDW) are constructed for global and local level surrogate model respectively. These methods leverage their respective advantages at different stages of the algorithm. The MLSAO algorithm is evaluated against other state-of-the-art approaches using benchmark functions of varying dimensions. Comprehensive results from the comparisons showcase the superior performance of the MLSAO algorithm in addressing expensive optimization problems. Moreover, we implement the MLSAO algorithm for tuning precipitation parameters in the Community Earth System Model (CESM). The outcomes reveal its effective enhancement of CESM's simulation accuracy for precipitation in the North Indian Ocean and the North Pacific region. These experiments demonstrate that MLSAO can better address parameter optimization problems under complex conditions.

Bilevel planning of electric vehicle charging station and battery swapping station considering real-time uncertainty

The placement of electric vehicle charging stations (EVCS) and battery swapping stations (BSS) is crucial to meet demand while minimizing their impact on the power system network. This article addresses the placement and scheduling of EVCS and BSS within a radial distribution network (RDN) overlaid with a road network. Electric Vehicle Routing Problem (EVRP) and Traffic Assignment Problem (TAP) is introduced to reduce EV energy consumption during trips to EVCS and BSS. A Bi-layer optimization approach is used, with the outer layer minimizing energy loss by allocating EVCS and BSS optimally, and the inner layer optimizing scheduling considering associated costs. Uncertainties related to EV is considered on a real-time trip basis and modelled using 2m-Point estimation method. The problem is solved using Differential Evolution (DE) and Prairie Dog Optimization (PDO) techniques. PDO results in a 9.6% reduction in total energy losses and a 22.5% decrease in total associated costs by optimally placing EVCS at 69, 25,114 and BSS at 19, 84,113 of the RDN compared to DE. Inclusion of 2-m PEM uncertainty increases total energy loss by 8.76% but decreases total associated costs by 6.97% compared to real-time uncertainty cases, enhancing the realism of the results.

Estimating Non-Linear Heat Flux in Continuous Billet Casting Process With Limited Sensors

In a continuous billet caster, the heat transfer from the pool of molten steel to the cooling water via the copper mold depends non-linearly upon several casting parameters. A reliable and accurate methodology based on the principle of inverse heat transfer technique has been proposed in this work to obtain the nonlinear heat flux of a continuous billet casting mold. Differential evolution optimization technique has been used, in conjunction with the 2-D and 3-D steady state conduction heat transfer equations to develop the complete algorithm. It has been observed that both the 2-D and 3-D models are able to accurately predict the heat flux for different numbers and locations of temperature sensors. While the 2-D model estimates the 1-D heat flux profile varying along casting direction within a very short time period, the 3-D model offers the advantage of estimating a more accurate 2-D heat flux profile varying along both the mold length and width. The 2-D model has also been used to estimate the heat flux for an industrial continuous casting mold using measured plant data. It is observed that the present methodology accurately estimates the boundary heat flux in the continuous billet caster mold.