Processes

The power output of a photovoltaic (PV) system is inherently dependent on climatic factors. To maximize the energy harvested from PV arrays, maximum power point tracking (MPPT) algorithms are employed. These algorithms dynamically adjust the operating point of the system to extract the maximum available power. However, under partial shading conditions (PSCs), conventional MPPT algorithms often fail to locate the global maximum power point, leading to suboptimal power extraction. In this study, a robust MPPT technique based on sliding mode control (SMC) is proposed to enhance tracking efficiency and optimize power extraction from PV arrays under PSC. Particle swarm optimization (PSO) is incorporated into the MPPT framework, enabling the dynamic tuning of SMC parameters for improved adaptability and performance. The proposed SMC structure is designed to regulate the duty cycle of a boost converter, ensuring effective power conversion. The system is simulated in Matlab/Simulink for various PSCs. The simulation results demonstrate that the PSO-tuned SMC methodology exhibits superior tracking performance, enabling the PV system to rapidly and accurately converge to the true MPP under varying weather and shading scenarios. The findings indicate that the proposed technique enhances the efficiency and reliability of PV energy harvesting in PSCs. Full article

Hydraulic fracturing involving proppant injection is currently the most effective technology to stimulate tight, unconventional reservoirs. The conductivity offered by the created propped and unpropped fracture segments is directly linked to the well deliverability. The accurate modeling of the fracture network conductivity is key to well performance prediction. Unlike most previous studies that have focused on the single-fracture conductivity, a comprehensive fracture network conductivity model was developed by incorporating more complex rock and proppant deformation mechanisms and integrating the conductivity of different propped and unpropped fracture segments through hydraulic–electric analogies. Specifically, for propped fracture segments, the proppant pack permeability was described by simultaneously considering the viscous shear from fracture walls, stress sensitivity, and multiple- or single-proppant-layer placement, while the dynamic width was controlled through proppant pack compaction and proppant embedment. In unpropped fracture segments, as self-supported fracture surface deformation changes the fracture compressibility, the stress-dependent compressibility was utilized to depict the dynamic width. The developed propped and unpropped fracture conductivity models were separately verified against experimental measurement data. Through the hydraulic–electric analogies, a new partially propped fracture network conductivity model was established. For propped fracture segments, an increase in the proppant pack compressibility significantly reduced the fracture conductivity, particularly under high-stress conditions. A larger initial propped fracture aperture offered higher fracture conductivity under identical stress conditions. For single-layer propped fractures, a decrease in the fracture surface elastic modulus from 15 GPa to 10 GPa slightly reduced the fracture conductivity due to greater proppant embedment. For unpropped fractures, a larger compressibility reduction rate (lower fracture compressibility) led to better fracture conductivity maintenance. The fracture network conductivity was dominated by the unpropped fracture segment conductivity when the unpropped length reached 45.5% of the total fracture network length. Full article

Transition metal oxide aerogels (AGLs) have attracted considerable attention in recent years due to their exceptional properties, including high surface area, significant porosity, and ultralow density. In this study, we report the first-time synthesis of zinc oxide nano-wafers and zinc aerogels for application as supercapacitor electrodes. The aerogels were synthesized via a novel one-pot hydrolysis method using NaBH₄ as a reducing agent and subsequently annealed at 200 °C (Zn_AGL(200)) and 450 °C (Zn_AGL(450)) to investigate the influence of temperature on their electrochemical properties. Structural and morphological characterizations were conducted using XRD, FTIR, BET, XPS, SEM, and TEM analyses. Among the fabricated electrodes, the aerogel annealed at 200 °C (Zn_AGL(200)) exhibited superior energy storage performance, attributed to its amorphous, continuous network structure, which enhanced its surface area and reduced its density compared to both the as-synthesized (Zn_AGL(RT)) and 450 °C-annealed (Zn_AGL(450)) counterparts. A two-electrode device demonstrated excellent cycling stability over 10,000 cycles, achieving an energy density of 7.97 Wh/kg and a power density of 15 kW/kg. These findings highlight the potential of zinc aerogels as materials for next-generation lightweight energy storage systems, with promising applications in industrial, mechanical, and aerospace technologies. Full article

In the context of intelligent manufacturing, equipment fault early-warning technology has become a critical support for ensuring the continuity and safety of industrial production. However, with the increasing complexity of modern industrial equipment structures and the growing coupling of operational states, traditional fault warning models face significant challenges in feature recognition accuracy and adaptability. To address these issues, this study proposes a hybrid fault early-warning framework that integrates an improved bees algorithm (IBA) with a categorical boosting (CatBoost) model and kernel density estimation (KDE). The proposed framework first develops the IBA by integrating Latin Hypercube Sampling, a multi-perturbation neighborhood search strategy, and a dynamic scout bee adjustment strategy, which effectively overcomes the conventional bees algorithm (BA)’s tendency to fall into local optima. The IBA is then employed to achieve global optimization of CatBoost’s key hyperparameters. The optimized CatBoost model is subsequently used to predict equipment operational data. Finally, the KDE method is applied to the prediction residuals to determine fault thresholds. An empirical study on a deflection fault in the valve position sensor connecting rod of the mineral oil system in a gas compressor station shows that the proposed method can issue early-warning signals two hours in advance and outperforms existing advanced algorithms in key indicators such as root mean square error (RMSE), coefficient of determination (R²) and mean absolute percentage error (MAPE). Furthermore, ablation experiments verify the effectiveness of the strategies in IBA and their contribution to CatBoost hyperparameter optimization. The proposed method significantly improves the accuracy and reliability of fault prediction in complex industrial environments. Full article

This study presents the fabrication of a samarium-doped Ti/Sb-SnO₂/PbO₂ electrode and investigates its applications in polluted water treatment and energy conversion. Physicochemical properties were characterized by scanning electron microscopy with energy-dispersive X-ray spectroscopy, X-ray powder diffraction analysis, and Raman spectroscopy. The Ti/Sb-SnO₂/Sm-PbO₂ electrode showed 2.5 times higher oxygen evolution potential activity than the Ti/Sb-SnO₂/PbO₂ electrode. Density Functional Theory was used to conduct first-principles calculations, and the obtained results indicated that Sm doping enhances the production of reactive oxygen species. The application of the Ti/Sb-SnO₂/Sm-PbO₂ electrode in carbendazim (CBZ) removal was investigated, since CBZ is a fungicide whose presence in the environment, including food, water, and soil, poses a threat. After 60 min of the treatment under optimized working parameters, the degradation rate of CBZ reached 94.2% in the presence of 7.2 g/L Na₂SO₄ with an applied current density of 10 mA/cm² in an acidic medium (pH 4). Of the four investigated parameters, the current density had the most significant influence on the degradation process. At the same time, the initial pH value of the solution was shown to have the least impact on degradation efficiency. These results imply a potential use of the proposed treatment for CBZ removal from wastewater. Full article

Due to the increasing volumes of plastic waste generated from electric and electronic devices, research has focused on the investigation of recycling methods for their safe handling. Pyrolysis converts plastics from waste electric and electronic equipment (WEEE) into valuable products (pyrolysis oil). Nevertheless, the frequent presence of flame retardants, mainly brominated flame retardants (BFR), hinders pyrolysis’s wide application, since hazardous compounds may be produced, limiting the use of pyrolysis oils. Taking the aforementioned into account, this work focuses on the recycling, via pyrolysis, of various plastic samples gathered from WEEE, to explore the valuable products that are formed. Specifically, 14 plastic samples were collected, including parts of computer peripheral equipment, remote controls, telephones and other household appliances. Considering the difficulties when BFRs are present, the study went one step further, applying XRF analysis to identify their possible presence, and then Soxhlet extraction as an environmentally friendly method for the debromination of the samples. Based on the XRF results, it was found that 23% of the samples contained bromine. After each Soxhlet extraction, bromine was reduced, achieving a complete removal in the case of a remote control sample and when butanol was the solvent. Thermal pyrolysis led to the formation of valuable products, including the monomer styrene and other secondary useful compounds, such as alpha-methylstyrene. The FTIR results, in combination with the pyrolysis products, enabled the identification of the polymers present in the samples. Most of them were ABS or HIPS, while only three samples were PC. Full article

The development of deep coalbed methane (CBM) wells faces challenges such as significant reservoir depth, low permeability, and severe liquid loading in the wellbore. Traditional drainage and gas recovery techniques struggle to meet the dynamic production demands. This study, using the deep CBM wells at the Jishen 15A platform as an example, proposes a “cyclic gas lift–wellhead compression-vent gas recovery” composite synergy technology. By selecting a critical liquid-carrying model, innovating equipment design, and dynamically regulating pressure, this approach enables efficient production from low-pressure, low-permeability gas wells. This research conducts a comparative analysis of different critical liquid-carrying velocity models and selects the Belfroid model, modified for well inclination angle effects, as the primary model to guide the matching of tubing production and annular gas injection parameters. A mobile vent gas rapid recovery unit was developed, utilizing a three-stage/two stage pressurization dual-process switching technology to achieve sealed vent gas recovery while optimizing pipeline frictional losses. By combining cyclic gas lift with wellhead compression, a dynamic wellbore pressure equilibrium system was established. Field tests show that after 140 days of implementation, the platform’s daily gas production increased to 11.32 × 10⁴ m³, representing a 35.8% rise. The average bottom-hole flow pressure decreased by 38%, liquid accumulation was reduced by 72%, and cumulative gas production increased by 370 × 10⁴ m³. This technology effectively addresses gas–liquid imbalance and liquid loading issues in the middle and late stages of deep CBM well production, providing a technical solution for the efficient development of low-permeability CBM reservoirs. Full article

In situ thermal desorption is one of the most promising remediation techniques for soils contaminated with non-aqueous phase liquids (NAPLs), but its remediation efficiency is limited by the thermal conductivity (k) of NAPL-contaminated soils. The fractal dimension is an important factor affecting k. To systematically study the influence of the fractal dimension on k, firstly, this research establishes a three-dimensional numerical model of NAPL-contaminated soils and calculates its k. Subsequently, the reliability of the numerical simulation results is verified through experiments. Combining the numerical simulation method with Hausdorff fractal theory, we explored the relationship between the fractal dimension and k. This research shows that k decreases with increasing porosity and increases with increasing saturation. The liquid phase can form a “liquid bridge” between solid phases, greatly shortening the path of heat flux and increasing k. k is more affected by porosity. With the increase in porosity, the pore fractal dimension and liquid phase fractal dimension of NAPL-contaminated soils increase, while the solid phase fractal dimension and pore curvature fractal dimension decrease. The fractal dimension of the liquid phase increases with the increase in NAPL content. k increases with the increase in the solid phase fractal dimension, liquid phase fractal dimension, and pore curvature fractal dimension and decreases with the increase in the pore fractal dimension. This study provides a basis for the investigation of the thermal conductivity of NAPL-contaminated soils and the development of in situ thermal desorption technology. Full article

In an integrated gasification combined cycle (IGCC), a gasification process produces a gas stream from a solid fuel, such as coal or biomass. This gas (syngas or synthesis gas) resulting from the gasification process contains carbon monoxide, molecular hydrogen, and carbon dioxide (other gaseous components may also be present depending on the gasified solid fuel and the gasifying agent). Separating hydrogen from this syngas stream has advantages. One of the methods to separate hydrogen from syngas is selective permeation through a palladium-based metal membrane. This separation process is complicated as it depends nonlinearly on various variables. Thus, it is desirable to develop a simplified reduced-order model (ROM) that can rapidly estimate the separation performance under various operational conditions, as a preliminary stage of computer-aided engineering (CAE) in chemical processes and sustainable industrial operations. To fill this gap, we present here a proposed reduced-order model (ROM) procedure for a one-dimensional steady plug-flow reactor (PFR) and use it to investigate the performance of a membrane reactor (MR), for hydrogen separation from syngas that may be produced in an integrated gasification combined cycle (IGCC). In the proposed model, syngas (a feed stream) enters the membrane reactor from one side into a retentate zone, while nitrogen (a sweep stream) enters the membrane reactor from the opposite side into a neighbor permeate zone. The two zones are separated by permeable palladium membrane surfaces that are selectively permeable to hydrogen. After analyzing the hydrogen permeation profile in a base case (300 °C uniform temperature, 40 atm absolute retentate pressure, and 20 atm absolute permeate pressure), the temperature of the module, the retentate-side pressure, and the permeate-side pressure are varied individually and their influence on the permeation performance is investigated. In all the simulation cases, fixed targets of 95% hydrogen recovery and 40% mole-fraction of hydrogen at the permeate exit are demanded. The module length is allowed to change in order to satisfy these targets. Other dependent permeation-performance variables that are investigated include the logarithmic mean pressure-square-root difference, the hydrogen apparent permeance, and the efficiency factor of the hydrogen permeation. The contributions of our study are linked to the fields of membrane applications, hydrogen production, gasification, analytical modeling, and numerical analysis. In addition to the proposed reduced-order model for hydrogen separation, we present various linear and nonlinear regression models derived from the obtained results. This work gives general insights into hydrogen permeation via palladium membranes in a hydrogen membrane reactor (MR). For example, the temperature is the most effective factor to improve the permeation performance. Increasing the absolute retentate pressure from the base value of 40 atm to 120 atm results in a proportional gain in the permeated hydrogen mass flux, with about 0.05 kg/m².h gained per 1 atm increase in the retentate pressure, while decreasing the absolute permeate pressure from the base value of 20 bar to 0.2 bar causes the hydrogen mass flux to increase exponentially from 1.15 kg/m².h. to 5.11 kg/m².h. This study is linked with the United Nations Sustainable Development Goal (SDG) numbers 7, 9, 11, and 13. Full article

CO₂ electrochemical reduction is a promising way to convert CO₂ to valuable fuels and chemicals. This study presents a porous Cu@Zn foam catalyst with a tailored hydrophobic surface for enhanced CO₂ reduction. The catalyst is synthesized via a modified dynamic hydrogen bubble template method, incorporating polytetrafluoroethylene (PTFE) during electrodeposition to control wettability. This strategy creates a hydrophobic microenvironment that significantly increases the three-phase (gas–liquid–solid) contact area, promoting CO₂ mass transfer and suppressing the competing hydrogen evolution reaction. The optimized Cu@Zn-8PTFE catalyst achieves a CO Faraday efficiency (FE_CO) of 87.53% at −35 mA cm⁻², a 40% improvement over the unmodified Cu@Zn. Furthermore, it also exhibits excellent stability, maintaining FE_CO > 90% for 64 h at −15 mA cm⁻². While hydrophobic modification is beneficial, excess PTFE loading reduces performance by covering active sites and diminishing the three-phase interface. This work highlights the importance of controlling catalyst wettability to optimize the three-phase interface for enhanced CO₂ electroreduction. Full article

Today, hydrogen fuel cells occupy a crucial position in sustainable energy systems. However, a precise model of their performance is needed to improve their efficiency and integrate them into hydrogen electric vehicles. This paper presents a hydrogen fuel cell model based on artificial neural networks (ANNs) to predict its performance characteristics. Using experimental data from a PEMFC NEXA 1200 hydrogen fuel cell in the ISA laboratory, an ANN model optimized by deep learning was developed, integrating advanced training techniques. The model’s performance was evaluated on independent test sets, revealing predictive precision with a low mean squared error (MSE) of 0.0429, a low Mean Absolute Percentage Error (MAPE) of 1.05%, a low Root-Mean-Square Error (RMSE) of 0.2071, and a high coefficient of determination (R²) of 0.9071. The model’s development and evaluation will be reviewed here in order to visualize the training progress and the results of the simulation. The main advantages of the proposed ANN model lie in both its flexible architecture, which can capture complex relationships without the need for explicit physical models, and its predictive and optimization capability. Full article

In this paper, a two-stage framework is proposed for the energy management of microgrids, which combines a hybrid Convolutional Neural Network-Gated Recurrent Unit (CNN-GRU) forecast model and the Improved Teaching–Learning-Based Optimization (ITLBO) algorithm. The CNN-GRU model captures spatiotemporal patterns in historical data for effective renewable energy and load demand uncertainty quantification, while the ITLBO algorithm improves generation scheduling performance through utilization of adaptive luminance coefficients, Latin Hypercube initialization, and hybrid genetic operations. The proposed framework is then compared with four different forecasting models: standalone CNN or MLANN, and three popular optimization algorithms (PSO, TLBO, CO) for four cases, including baseline (perfect foresight), CNN-GRU forecast, CNN forecast, and MLANN forecast. The results show that the hybrid framework outperforms dedicated, in-domain models for forecast and scheduling, with the state-of-the-art CNN-GRU sliding window model producing the best forecasting accuracy, which subsequently translates into near-optimal scheduling performance. Through many experiments, we show that the ITLBO algorithm is robust and outperforms the classical optimization methods on convergence speed and solution quality while significantly eliminating the forecast errors uncertainty. Demand response is also a feature of these models, which boosts operational efficiency by scaling down peak grid usage without sacrificing affordability through energy saving capabilities. According to the results, the hybrid framework exhibits significant cost-efficiency by reducing the RMSE of solar irradiance forecasting by 11.6% when compared to standalone CNN and achieving a 69.7% reduction in operational costs under ITLBO optimization. The comparative analysis emphasizes the robustness and versatility of the framework, reinforcing its feasibility across a range of forecasting and optimization scenarios for real-world microgrid deployment. Full article

High-performance copper alloys are crucial for integrated circuit lead frames due to their high density, multifunctionality, and low cost. High-performance copper alloys typically address the competing issues of high strength and high electrical conductivity through alloying and processing control methods. However, the traditional methods for developing these alloys are time-consuming, expensive, and complex processes. This study utilizes Explainable AI by employing machine learning (ML) and deep learning (DL) techniques to predict the hardness (HRC) and electrical conductivity (mS/m) based on the alloy composition, including Cr, Zr, Ce, and La, and the processing parameters, namely the aging time, of Cu-Cr-Zr alloys. A comprehensive dataset of 47 experimental Cu-Cr-Zr alloy samples, derived from prior experimental studies, was analyzed using feature engineering, correlation analysis, and explainability methods such as SHapley Additive exPlanations (SHAP). Various ML models, including ensemble methods like XGBoost, CatBoost, and AdaBoost, were evaluated for their predictive performance. The feature importance analysis revealed that the aging time and Zr content significantly influence the hardness, followed by Ce content, while Cr and La contents reveal a weak contribution to hardness values. Electrical conductivity is predominantly controlled by aging time, with a weak negative influence of the alloying elements. These findings align well with metallurgical principles, where microstructural refinement and precipitation behavior dictate the hardness and conductivity of Cu-Cr-Zr alloys. Hyperparameter tuning and model stacking further enhanced the predictive accuracy, with the final stacked models achieving R² scores of 0.8762 for hardness within a training time of 1.739 s and 0.8132 for electrical conductivity within a training time of 1.091 s. These findings demonstrate the effectiveness of ML-driven approaches in material property predictions, providing valuable insights for material design and property processing parameter optimization. Full article

This study investigated a factory fire that resulted in an unusual situation that caused the deaths of two firefighters. The official fire investigation report was analyzed, records were obtained, and on-site investigations and interviews were conducted. Using these additional data and a calorimetric analysis to determine the combustibility of goods stored in the building at the time, a functional 3D model was produced, and a fire dynamics simulator (FDS) was run. The model was augmented using the results of calorimetric experiments for three types of primary goods being stored in the warehouse area: paper lunch boxes, tissue paper, and corrugated boxes. The reaction heat data obtained for each of the three sample types was 848.24, 468.29, and 301.21 J g⁻¹, respectively. The maximum mass loss data were 98.522, 84.439, and 90.811 mass% for each of the three types, respectively. A full-scale fire scene reconstruction confirmed the fire propagation routes and changes in fire hazard factors, such as indoor temperature, visibility, and carbon monoxide concentration. The FDS results were compared to the NIST recommended values for firefighter heat exposure time. The cause of death for both firefighters was also investigated in terms of the heat resistance of the facepiece lenses of their self-contained breathing apparatus. Based on the findings of this study, recommendations can be made to forestall the recurrence of similar events. Full article

To duly and correctly deliver parcels, both the capacity and the delivery route of a delivery vehicle need to be considered. Thus, the delivery process of a delivery vehicle can be characterized as a capacitated vehicle routing problem with three-dimensional loading constraints (3L-CVRP), which is an NP-hard problem. To solve the problem, a mathematical model is established in this paper to minimize the total delivery distance and maximize the loading rate, simultaneously. Additionally, a hybrid algorithm that combines a three-dimensional (3D) packing algorithm based on the residual space optimized (RSO) strategy and an improved genetic algorithm (IGA) is proposed. Initially, the proposed hybrid algorithm employs a modified Clarke–Wright savings algorithm to generate a feasible set of route solutions. Furthermore, building upon the traditional genetic algorithm, an elite retention strategy is introduced, and an enhanced order crossover method is utilized to improve the stability of the hybrid algorithm and its global search capability for optimal solutions. Finally, during each iteration of the algorithm, the RSO algorithm is integrated to verify the feasibility of 3D packing scheme. Two comparative experiments are conducted on 22 modified benchmark instances and actual logistics data of a university against two other algorithms, demonstrating that the proposed RSO-IGA algorithm achieves superior solutions in delivery efficiency. Full article

To address the challenge of transverse thickness consistency in wide-width electrode calendering, this study developed a flexible roll profile regulation technology based on electromagnetic induction heating. An axisymmetric electromagnetic–thermal–structural coupling finite element model is established and validated on a self-built experimental platform. Systematic simulations were conducted to investigate the influence of equivalent current density J_s, current frequency f, and coil turn n on the roll temperature and roll profile. The maximum temperature of the roll’s inner bore and the roll crown exhibit a positive correlation with J_s, f, and n. A cyclic heating strategy was developed to control and stabilize the roll profile. The stable crown C_W shows linear correlation with heating durations t₁ and a nonlinear trend with J_s. Under fixed J_s and t₁, further optimization of duty cycle and cooling conditions enables long-term stabilization of the roll profile. Full article

To address the challenges of accuracy and stability in current detection methods, this paper proposes an enhanced online leak detection and localization approach based on an improved pipeline flow model and the Extended Kalman Filter within the state-space method. By establishing a comprehensive pipeline flow model, the proposed method relies solely on flow and pressure data at both ends of the pipeline, while also accounting for noise interference from instrumentation. This allows for precise leak location identification and calculation of key parameters such as leak volume, pressure, and leakage coefficient. The study primarily focuses on the linearization of noise variation and the refinement of the leakage detection model. The proposed method incorporates noise dynamics throughout the entire nonlinear calculation process and utilizes the Jacobian matrix to achieve noise linearization. To improve the leakage model, the leakage position is replaced with pipeline length, and the fourth-order Runge–Kutta method is used to solve the resulting equations. Data simulations and experimental validation confirm the effectiveness and accuracy of the proposed method. The experimental results indicate that the relative error in leak localization is less than 2%, with an accuracy improvement of 1.4% and 1.5% compared to conventional methods. Full article

To address the nonlinear and non-stationary characteristics of dissolved gas concentration data in transformer oil, this paper proposes a hybrid prediction model (VMD-SSA-LSTM-SE) that integrates Variational Mode Decomposition (VMD), the Whale Optimization Algorithm (WOA), the Sparrow Search Algorithm (SSA), Long Short-Term Memory (LSTM), and the Squeeze-and-Excitation (SE) attention mechanism. First, WOA dynamically optimizes VMD parameters (mode number k and penalty factor α to effectively separate noise and valid signals, avoiding modal aliasing). Then, SSA globally searches for optimal LSTM hyperparameters (hidden layer nodes, learning rate, etc.) to enhance feature mining for non-continuous data. The SE attention mechanism recalibrates channel-wise feature weights to capture critical time-series patterns. Experimental validation using real transformer oil data demonstrates that the model outperforms existing methods in prediction accuracy and computational efficiency. For instance, the CH₄ test set achieves a Mean Absolute Error (MAE) of 0.17996 μL/L, a Mean Absolute Percentage Error (MAPE) of 1.4423%, and an average runtime of 82.7 s, making it significantly faster than CEEMDAN-based models. These results provide robust technical support for transformer fault prediction and condition-based maintenance, highlighting the model’s effectiveness in handling non-stationary time-series data. Full article

Robot path planning plays a critical role in enhancing the efficiency and accuracy of inspections and ultimately contributes to the safety of chemical production. In particular, the performance of robot inspection is influenced by amount of gas leakage and path length. In this study, a chemical safety inspection path multi-objective optimization model is constructed that considers minimizing path length and maximizing gas leakage detection sensitivity. To address this model, an improved multi-objective discrete growth optimization algorithm is proposed, which adopts discrete operators to meet the solution requirements of the discrete model and an adaptive leader selection strategy to further improve the algorithm solution performance. Finally, numerical computations and simulation experiments are conducted to validate the feasibility of the proposed method for inspection path planning. The results demonstrate that the method outperforms multi-objective discrete particle swarm optimization, non-dominated sorting genetic algorithm-II, and multi-objective gray wolf optimization in terms of solution convergence and distribution uniformity. Moreover, it can provide better non-dominated solutions in simulation experiments and provide multiple references for practical applications. Full article