Differential Evolution Optimization Research Articles

Handling imbalanced class in melanoma: Kemeny–Young rule based optimal rank aggregation and Self-Adaptive Differential Evolution Optimization

Melanoma, despite its relatively low incidence compared to other types of skin cancer, accounts for a significant proportion of skin cancer-related deaths. Early detection of melanoma is crucial for improving patient survival rates. Deep learning algorithms, which heavily rely on data, are widely used in melanoma detection. However, the performance of these algorithms is greatly influenced by the distribution of the dataset, particularly class imbalance. In this manuscript, the authors present a novel method based on the Kemeny–Young rule for optimal rank aggregation to address the class imbalance problem in melanoma detection. The proposed approach aims to reduce class bias and enhance overall classification accuracy. Furthermore, a cost-sensitive learning approach is introduced to improve the classifier’s ability to handle class imbalance effectively. This novel cost-sensitive learning method utilizes Self-Adaptive Differential Evolution Optimization to determine optimal weights for each class. Our approach differs from traditional methods that assign weights based on predefined criteria. To evaluate the effectiveness of the proposed methods, extensive experiments and ablation studies are conducted on the highly imbalanced ISIC 2020 dataset, which is widely used in melanoma detection research. The Kemeny–Young rule-based majority voting achieves an overall error rate of 2.44%, while the cost-sensitive learning based on the Self-Adaptive Differential Evolution approach achieves an even lower error rate of 1.99%. Moreover, the proposed method achieves a sensitivity of 87.93% and a specificity of 98.19%. These experimental results demonstrate the competitiveness and effectiveness of the proposed methods in addressing the challenges posed by class imbalance and improving the accuracy of melanoma detection. By effectively mitigating class imbalance, these methods improve the accuracy and reliability of melanoma detection, thus offering valuable insights for developing advanced computer-aided diagnosis systems in dermatology. The relevant codes for our proposed approach are publicly available at: https://github.com/ctrl-gaurav/Handling-Imbalanced-Class-in-Melanoma.

Internal force analysis of beams on elastic foundation using differential evolutionary optimization algorithm based on hybrid mutation technique

The paper presents the Finite element method (FEM) that calculates the internal force and the displacement of beams on elastic foundation in the case of the uncertainty input parameters described in terms of the number intervals. Using the interval function optimization algorithm combined with the FEM to determine the internal force values of the span reinforced concrete beam structure. This study applies the hybrid differential evolutionary optimization algorithm combined with FEM interval functions to determine the required internal force results of reinforced concrete beams placed on an elastic foundation. The calculation process is programmed using Maple.17 software to determine the displacement output and the resulting internal force in the beam. To check the correctness of the program calculated on Maple.17, the input declared dataset corresponds to the central values of the interval numbers and is recalculated by SAP2000v21 software, then evaluates the results error of internal force on the beam under consideration.

THD Minimization in a Seven-Level Multilevel Inverter Using the TLBO Algorithm

This paper presents the minimization of total harmonic distortion in a seven-level cascaded H-bridge multilevel inverter with resistive load using the teaching–learning-based optimization algorithm. The minimization of Total Harmonic Distortion (THD)is a challenging optimization problem due to the fact that nonlinear equations are involved. Recently, bio-inspired algorithms have become very popular approaches to solving various optimization problems in different areas of engineering. For this reason, the results obtained with the Teaching–Learning-Based Optimization (TLBO)algorithm were compared with three other popular bio-inspired algorithms, the genetic algorithm, differential evolution, and particle swarm optimization. The comparative analysis, conducted by sweeping the modulation index, made it possible to obtain graphs and data on the behavior of the four analyzed algorithms. Finally, it was concluded that the TLBO algorithm is very effective and is able to solve the THD-minimization problem. Its main advantage over the other algorithms is the fact that it does not require control parameters for its correct operation in the solution of the problem.

Near-optimal 3D trajectory design in presence of obstacles: A convolutional neural network approach

This paper proposes an approach based on neural networks for designing near-optimal 3D trajectories connecting two points separated by obstacles. A reference path is first built with a novel Theta* algorithm implementation, upgraded to reduce the number of waypoints and the angular variations. Starting from the path, a trajectory based on piecewise Bézier curves is designed with an algorithm relying on two design parameters. The optimal value of these parameters is estimated with a Convolutional Neural Network (CNN) architecture receiving as inputs an image of the path and its properties. The CNN training is performed on a synthetic dataset of optimal parameters built with Differential Evolution optimization for a variety of randomly generated paths. The parameters from CNN are refined with an algorithm capable of providing with high success rate near-optimal trajectories within minimum computation time.

A synergy of the adaptive whale optimization algorithm and differential evolution for abrupt motion tracking

Aiming at the problem that conventional trackers are difficult to adapt to abrupt motion, a tracking algorithm based on a synergy of the adaptive whale optimization algorithm and differential evolution (AWOA-DE) is proposed in this paper. Firstly, the non-linear dynamic feedback strategy based on the one-fifth principle is employed to replace the linear mechanism, which is the variation of exploring step in the basic whale optimization algorithm (WOA), and an adaptive WOA (AWOA) is generated to improve the global optimization ability of the WOA. Secondly, AWOA adopts a random sampling strategy to generate new samples, which could ensure the diversity of solutions, but may lead to instability. By mixing AWOA and DE algorithms, the population is divided into two groups, which are updated by AWOA and DE algorithms respectively, to ensure the diversity of the populations and improve the optimization accuracy of the algorithm. Finally, a visual tracker based on AWOA-DE is proposed, which can deal with the problem of abrupt motion in tracking. In addition, the effectiveness of the hybrid optimization algorithm is evaluated using 23 benchmark functions. In the experiment of visual tracking, extensive experimental results show that the AWOA-DE tracker (AWOADET) has much stronger competitiveness compared to the WOA tracker (WOAT) and the other 10 state-of-the-art trackers, especially for abrupt motion tracking.

Application of a novel metaheuristic algorithm based two-fold hysteresis current controller for a grid connected PV system using real time OPAL-RT based simulator

Grid connected photovoltaic (GCPV) rooftop systems have been considered as fast development and promising renewable energy sources due to low maintenance cost, secure investment, noise-free and do not require additional space for installation. Various factors considered for the installation of GCPV are mathematical models of PV module, sizing methods based on techno-economic objectives, PV panels and configurations, selection of the final optimum configuration and environmental criteria. Selection of appropriate controller and its optimal design for power electronic based converters also plays a crucial role in the performance of GCPV. Therefore in this article, a two-fold hysteresis current controller (TFHCC) based on an Improved Arithmetic Optimization Algorithm (IAOA) is introduced and investigated for the first time, for a GCPV system to minimize the switching loss and total harmonic distortion (THD). A novel multi-objective function considering switching frequency and current error is proposed by assigning appropriate weights to obtain the optimal values of duty cycle and hysteresis bands using IAOA, AOA, Forensic Based Investigation (FBI), Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms. TFHCC utilizes zero level of the inverter by properly switching it on for a half cycle only and either on or off for the other cycle. Comparative performance analysis of the optimal TFHCC obtained with different algorithms is presented and it is proved that IAOA based TFHCC exhibits substantial reductions in variation and magnitude of the average switching frequency by 2.82 kHz and THD by 0.65%. Initially, the study is carried out with MATLAB Simulink environment and then experimentally validated with real time simulator based on OPAL-RT 4510.

Electromagnetic Imaging for Buried Conductors Using Deep Convolutional Neural Networks

In the past, many conventional algorithms, such as self-adaptive dynamic differential evolution and asynchronous particle swarm optimization, were used to reconstruct buried objects in the frequency domain; these were unfortunately time-consuming during the iterative, repeated computing process of the scattered field. Consequently, we propose an innovative deep convolutional neural network approach to solve the electromagnetic inverse scattering problem for buried conductors in this paper. Different shapes of conductors are buried in one half-space and the electromagnetic wave from the other half-space is incident. The shape of the conductor can be reconstructed promptly by inputting the received scattered fields measured from the upper half-space into the deep convolutional neural network module, which avoids the computational complexity of Green’s function for training. Numerical results show that the root mean square error for differently shaped—circular, elliptical, arrow, peanut, four-petal, and three-petal—reconstructed images are, respectively, 2.95%, 3.11%, 17.81%, 15.10%, 14.14%, and 15.24%. Briefly speaking, not only can circular and elliptical buried conductors be reconstructed; some irregular shapes can be reconstructed well. On the contrary, the reconstruction result by U-Net for buried objects is worse since it is not able to obtain a good preliminary image by processing only the upper scattered field—that is, rather than the full space. In other words, our proposed deep convolutional neural network can efficiently solve the electromagnetic inverse scattering problem of buried conductors and provide a novel method for the microwave imaging of the buried conductors. This is the first successful attempt at using deep convolutional neural networks for buried conductors in the frequency domain, which may be useful for practical applications in various fields such as the medical, military, or industrial fields, including magnetic resonance imaging, mine detection and clearance, non-destructive testing, gas or wire pipeline detection, etc.

Frequency Regulation of Interlinked Microgrid System Using Mayfly Algorithm-Based PID Controller

The primary goal of this article is to design and implement a secondary controller with which to control the system frequency in a networked microgrid system. The proposed power system comprises of Renewable energy sources (RESs), energy-storing units (ESUs), and synchronous generator. RESs include photovoltaic (PV) and wind turbine generator (WTG) units. The ESU is composed of a flywheel and a battery. Because renewable energy sources are not constant in nature, their values fluctuate from time to time, causing an effect on system frequency and power flow variation in the tie line. The nonlinear output from the RESs is balanced with the support of ESUs. In order to address this situation, a proportional integral derivative (PID) controller based on the Mayfly algorithm (MA) is proposed and built. Comparing the responses of controllers based on the genetic algorithm (GA), differential evolution (DE), and particle swarm optimization (PSO) technique-optimized to demonstrate the superiority of the MA-tuned controller.. The results of the validation comparisons reveal that the implemented MA-PID controller delivers and is capable of regulating system frequency under various load demand changes and renewable energy sources. A robustness analysis test was also performed in order to determine the effectiveness of the suggested optimization technique (1%, 2%, 5%, and 10%) step load perturbation (SLP) with ±25% and ±50% variation from the nominal governor and reheater time constant).

Equilibrium Optimizer Based FOPID Control of BLDC Motor

The main challenges of proportional integral derivative (PID) control are sudden set-point changes and parameter changes, which leads to poor response. It can be taken into account that this control unit can be replaced by another similar control unit, but it differs from it in the degree of integration and differentiation, and this is what is known as fractional-order PID (FOPID), which improves the performance of the system in the transient state. To choose the FOPID constants, various methodologies, including optimization algorithms, are used to obtain the best possible performance. In this paper, the speed of brushless DC motor (BLDC) was regulated using (FOPID), where the equilibrium optimizer (EO) algorithm was used to find the values of the controller constants, and the performance of this algorithm was compared with several other optimization algorithms such as particle swarm optimization (PSO), differential evolution (DE), and golden jackal optimization (GJO). Simulation results in Matlab-Simulink 2016a showed the effectiveness of the proposed algorithm (EO) in achieving response time, overshot, and lower steady state error compared with the rest of the algorithms.

Enhanced Diffusion and Confusion Based Encryption Algorithm Using Differential Evolution and Chaotic Mapping

Encryption is critical to protecting sensitive data, especially images, against potential illegal access and breaches. The use of chaotic maps for image encryption is widespread among researchers. However, it is necessary to set up initial parameters for chaotic maps to generate random sequences. These parameters need to be selected with care. To determine the optimal initial parameters for image encryption, evolutionary optimization techniques have been used. In this paper, we propose a secure image-based communication system based on an optimized image encryption algorithm. This approach uses differential evolution optimization, which is an ideal solution for reducing convergence time when optimizing chaotic map parameters. Furthermore, the security parameters of these techniques are evaluated, including entropy, Number of Pixel Change Rate (NPCR), Unified Average Changed Intensity (UACI), and correlation coefficients. The simulation results of the proposed encryption approach by combining Arnold’s cat map, chaotic logistic map and optimization method show that the encrypted image is safe against attacks.

Optimization of convolutional neural network hyperparameters using improved competitive gray wolf optimizer for recognition of static signs of Indian Sign Language

In the last decade, the success achieved by convolutional neural networks (CNN) has changed the trend of research in the computer vision field from manual features to learned features for various applications. However, designing the architecture of CNN and selecting optimum values of its hyperparameters poses a critical challenge because of their massive and complex search space. Automatically picking up the optimal values of hyperparameters may facilitate the designers of CNN-based deep learning models. Swarm intelligence (SI)-based improved competitive gray wolf optimizer (ICGWO) in continuous search space is proposed for optimizing hyperparameters of custom-designed CNN architecture. To evaluate the performance of the ICGWO, we employ 16 benchmark functions. We also assess the effectiveness of the ICGWO by evaluating it with six state-of-art meta-heuristic algorithms. The experiment results show that the ICGWO can obtain the best accuracy on eleven benchmark functions and second best on two benchmark functions. The optimized CNN recognizes static signs of English alphabets in Indian Sign Language (ISL). We also evaluated the optimized CNN on the publicly available ISL dataset for the English alphabet, where it attains 99.93% validation accuracy. In order to evaluate the efficacy of the proposed variant of CGWO, we optimized the hyperparameters of CNN using the existing SI-based search optimization algorithms namely particle swarm optimization, whale optimization algorithm (WOA), differential evolution, and gray wolf optimizer as well.

Integral Field Spectroscopy of the cometary starburst galaxy NGC 4861

ABSTRACT Using the PMAS Integral Field Unit on the Calar Alto 3.5 m telescope, we observed the southern component (Markarian 59) of the ‘cometary’ starburst galaxy NGC 4861. Mrk 59 is centred on a giant nebula and concentration of stars 1 kpc in diameter. Strong $\rm H\,\alpha$ emission points to a star-formation rate (SFR) at least 0.47 $\rm M_{\odot }\, yr^{-1}$. Mrk 59 has a very high [O iii] $\rm \lambda 5007/H\,\beta$ ratio, reaching 7.35 in the central nebula, with a second peak at a star-forming hotspot further north. Fast outflows are not detected but nebular motion and galaxy rotation produce relative velocities up to 40 km $\rm s^{-1}$. Spectral analysis of different regions with ‘Fitting Analysis using Differential evolution Optimization’ (FADO) finds that the stars in the central and ‘spur’ nebulae are very young, $\rm \le 125~Myr$ with a large $\rm \lt 10~Myr$ contribution. Older stars ($\rm \sim 1~Gyr$) make up the northern disk component, while the other regions show mixtures of 1 Gyr age with very young stars. This and the high specific SFR $\rm \sim 3.5~Gyr^{-1}$ imply a bimodal star formation history, with Mrk 59 formed in ongoing starbursts fuelled by a huge gas inflow, turning the galaxy into an asymmetric ‘green pea’ or blue compact dwarf. We map the He ii λ4686 emission, and identify a broad component from the central nebula, consistent with the emission of ∼300 Wolf–Rayet stars. About a third of the He ii λ4686 flux is a narrow line emitted from a more extended area covering the central and spur nebulae, and may have a different origin.

Runge–Kutta optimization‐based selective harmonic elimination in an H‐bridge multilevel inverter

AbstractThe application of iterative techniques for solving the Selective Harmonic Elimination Pulse Width Modulation (SHE‐PWM) problem, such as the Newton–Raphson (NR) method, can tend to get stuck at local optima in the solution space. Additionally, these methods may be sensitive to the initial value estimation of the solution. In contrast, metaheuristic approaches demonstrate resilience in seeking out the optimal solution. As such, this study utilizes the Runge–Kutta (RUN) metaheuristic optimization algorithm to demonstrate the SHE‐PWM technique in multilevel inverters (MLIs), including 5‐ and 7‐level modified H‐bridge (MHB) topology and a 9‐level asymmetric cascaded H‐bridge (CHB) inverter topology. The switching angles are obtained by varying the modulation index from 0.01 to 1.0 in steps of 0.01 for 5‐, 7‐, and 9‐level MLIs. The performance of the RUN algorithm in minimizing the total harmonic distortion (THD) value is verified through simulations in MATLAB/Simulink software. The superiority of RUN is established by comparing the results with state‐of‐the‐art metaheuristic algorithms, such as the Differential Evolution (DE), Genetic Algorithm (GA), and Grey Wolf Optimizer (GWO). Additionally, the switching angles obtained through RUN are validated by hardware experiments. According to the simulation and experimental results, the proposed RUN method exhibits better performance in terms of objective function values, algorithm robustness, fundamental harmonic magnitude, and THD values. The findings confirm the elimination of fifth harmonic, fifth, and seventh harmonics, and fifth, seventh, and ninth harmonics in 5‐, 7‐, and 9‐level MLIs, respectively.

Gene regulatory networks with binary weights

An evolutionary computation framework to learn binary threshold networks is presented. Inspired by the recent trend of binary neural networks, where weights and activation thresholds are represented using 1 and -1 such that they can be stored in 1-bit instead of full precision, we explore this approach for gene regulatory network modeling. We test our method by inferring binary threshold networks of two regulatory network models: Quorum sensing systems in bacterium Paraburkholderia phytofirmans PsJN and the fission yeast cell-cycle. We considered differential evolution and particle swarm optimization for the simulations. Results for weights having only 1 and -1 values, and different activation thresholds are presented. Full binary threshold networks were found with minimum error (2 bits), whereas when the binary restriction is relaxed for the activation thresholds, networks with 0 bit error were found.

Turbine Endwall Contouring Through Advanced Optimization Techniques

AbstractNon-axisymmetric endwall profiling offers features to simultaneously mitigate aerodynamic losses and hot gas ingestion in axial turbines. This paper presents an optimization methodology to generate a contoured surface integrated with real geometrical effects such as blade fillets and a rim seal channel with the aim of achieving higher efficiencies while reducing hot gas ingestion. The contoured rotor platform is constructed using a B-spline surface clamped in the axial direction. In the azimuthal direction, the surface is unclamped to allow geometrical continuity across the periodic boundaries. The endwall parameterization is used to optimize a rotor hub platform of a high-pressure turbine stage. A differential evolution optimizer is used to rank individuals in terms of efficiency. The single-objective optimization is set to maximize the aerodynamic efficiency and it is defined such that it accounts for the flow non-uniformity through a mixed-out averaging procedure. Engine representative conditions typical of a two-stage high-pressure turbine are used as boundary conditions. Geometrical and aerodynamic constraints are set to guarantee a fair comparison among individuals and to meet engine requirements. Two surface parameterizations, which use a different number of design variables but share the same construction strategy, are presented to show the trade-off between the number of degrees-of-freedom and the aerodynamic improvement. Different purge flow conditions are considered to assess the robustness of the optimization results at off-design conditions for relevant geometries. The aim of this paper is to show the advanced shape flexibility of the implemented parameterization for contoured platforms featuring technological effects such as blade fillet and rim seal channel. The work provides design guidelines to setup engine-realistic constraints for endwall contour optimization of turbine stages.

Differential Evolution Optimization of Microwave Focused Hyperthermia Phased Array Excitation for Targeted Breast Cancer Heating.

Microwave hyperthermia using the phased array applicator is a non-invasive treatment modality for breast cancer. Hyperthermia treatment planning (HTP) is critical to accurately treating breast cancer and avoiding damage to the patient's healthy tissue. A global optimization algorithm, differential evolution (DE) algorithm, has been applied to optimize HTP for breast cancer and its ability to improve the treatment effect was proved by electromagnetic (EM) and thermal simulation results. DE algorithm is compared to time reversal (TR) technology, particle swarm optimization (PSO) algorithm, and genetic algorithm (GA) in HTP for breast cancer in terms of convergence rate and treatment results, such as treatment indicators and temperature parameters. The current approaches in breast cancer microwave hyperthermia still have the problem of hotspots in healthy tissue. DE enhances focused microwave energy absorption into the tumor and reduces the relative energy of healthy tissue during hyperthermia treatment. By comparing the treatment results of each objective function used in DE, the DE algorithm with hotspot to target quotient (HTQ) as the objective function has outstanding performance in HTP for breast cancer, which can increase the focused microwave energy of the tumor and decrease the damage to healthy tissue.

Feature Selection Menggunakan Algoritma Meta-Heuristik

Machine learning requires data to make predictions. Data can have a large number of features. The large number of features can cause machine learning models to overfit, increase model complexity, and high computational costs. Feature selection is one method for optimizing machine learning models. Feature selection reduces the number of features used in the learning process. This research proposes a feature selection method using meta-heuristic algorithms. The machine learning model serves as the objective function for the meta-heuristic algorithm. The objective function is evaluated at each iteration to obtain the most influential features in the model. The machine learning models used are Random Forest, k-Nearest Neighbors, and Support Vector Machine. The meta-heuristic algorithms used are Differential Evolution, Flower Pollination, Grey Wolf, and Whale Optimization. The research shows that using meta-heuristic algorithms can improve the accuracy of machine learning models with fewer features. The Support Vector Machine – Differential Evolution scheme has the highest accuracy and uses the fewest features.

Determination of the Optimum Values of the Natural Frequency of the Nanocomposite Multilayer Organic Solar Cell by using Basic Differential Evolution Optimization Algorithms

By the analytical approach, the equation of natural frequency of nanocomposite multilayer organic solar cell (NMOSC) is analyzed in this work. The NMOSC is composed of 6 layers: Al, LiF, P3HT: PCBM, PEDOT: PSS, ITO and Glass. By using the classical plate theory, the Hooke’s Law, the geometrical compatibility equation and the nonlinear equilibrium equations are proposed. These equations combined with the Galerkin method in order to investigate the effect of elastic foundations, geometrical parameters and initial imperfection on the natural frequency. Besides, in order to determine the maximum natural frequency of NMOSC, basic differential evolution optimization algorithm (DE) was used with five variables: elastic foundations include Winkeler foudation and Pasternak foudation, temperature, width and length. In the numerical results, the influence of length to width ratio, imperfection, elastic foundations and temperature increment were evaluated in detail. The optimal results from DE algorithm are shown and compared.

Aerodynamic System Machine Learning Modeling with Gray Wolf Optimization Support Vector Regression and Instability Identification Strategy of Wavelet Singular Spectrum

The prediction of a stall precursor in an axial compressor is the basic guarantee to the stable operation of an aeroengine. How to predict and intelligently identify the instability of the system in advance is of great significance to the safety performance and active control of the aeroengine. In this paper, an aerodynamic system modeling method combination with the wavelet transform and gray wolf algorithm optimized support vector regression (WT-GWO-SVR) is proposed, which breaks through the fusion technology based on the feature correlation of chaotic data. Because of the chaotic characteristic represented by the sequence, the correlation-correlation (C-C) algorithm is adopted to reconstruct the phase space of the spatial modal. On the premise of finding out the local law of the dynamic system variety, the machine learning method is applied to model the reconstructed low-frequency components and high-frequency components, respectively. As the key part, the parameters of the SVR model are optimized by the gray wolf optimization algorithm (GWO) from the biological view inspired by the predatory behavior of gray wolves. In the definition of the hunting behaviors of gray wolves by mathematical equations, it is superior to algorithms such as differential evolution and particle swarm optimization. In order to further improve the prediction accuracy of the model, the multi-resolution and equivalent frequency distribution of the wavelet transform (WT) are used to train support vector regression. It is shown that the proposed WT-GWO-SVR hybrid model has a better prediction accuracy and reliability with the wavelet reconstruction coefficients as the inputs. In order to effectively identify the sign of the instability in the modeling system, a wavelet singular information entropy algorithm is proposed to detect the stall inception. By using the three sigma criteria as the identification strategy, the instability early warning can be given about 102r in advance, which is helpful for the active control.

A new uncertain remanufacturing scheduling model with rework risk using hybrid optimization algorithm.

As a resource-conserving and environmentally friendly manufacturing paradigm, remanufacturing with the potential to realize sustainability in production has been extensively investigated. Scheduling plays a significant role in achieving the remanufacturing benefits. However, the remanufacturing process involves intricate uncertainties because it takes end-of-life products with different qualities as workblanks, which increases the risk of rework and complicates remanufacturing scheduling. Though the traditional stochastic optimization methods or fuzzy theory have been employed to address uncertainties in the remanufacturing scheduling problem, they are constrained with the limited historical data which renders it difficult to describe uncertainties accurately and intuitively. Therefore, a new uncertain remanufacturing scheduling model with rework risk is proposed, in which the interval grey numbers are applied to describe the uncertainty clearly and consider the rework risk in remanufacturing process. To solve this model, a hybrid optimization algorithm that combines differential evolution and particle swarm optimization algorithms through an efficient representation scheme is proposed. Besides, this algorithm integrates multiple improvements to maintain the diversity of the population and enhance its performance. Simulation experiments are conducted on 18 sets of instances with different scales, and the results demonstrated that the proposed algorithm obtains a better optimal solution than other baseline algorithms on 17 sets of instances. The main finding of this study is providing a new method for solving uncertain remanufacturing scheduling problem with rework risk practically and effectively.