Multi-objective Optimization Methodology Research Articles

Daylighting and energy performance optimization of anidolic ceiling systems for tropical office buildings

A simple window is often unable to ensure standard illumination to the deep parts of large office spaces, and advanced daylighting systems are necessary to ensure the level of interior illuminance. Anidolic ceiling systems are one of the less popular daylighting strategies designed to redirect and redistribute daylight deeper, which can reduce the demand for artificial lighting and energy use for lighting purposes. This study shows how a parametric approach can be applied to optimize the daylighting and energy performance of an anidolic ceiling system in a tropical climate. Multi-objective optimization (MOO) techniques were applied to combine different design variables to establish multiple design alternatives and find the optimal design by comparing their performances. A simulation study of an anidolic ceiling system was conducted with test models primarily developed by Rhinoceros and ClimateStudio, and optimization of performance metrics was conducted using Grasshopper and Octopus. Data exportation was done using the TT toolbox, while data analysis was done through mathematical and statistical analyses and cross-checked by Design Explorer. By incorporating an optimum anidolic ceiling system into the case office space, spatial daylight autonomy (sDA) increased 20.51 %∼68.18 %, annual sunlight exposure (ASE) decreased 15.83 %∼8.52 %, mean illuminance increased 221 lux–3027 lux and energy use intensity (EUI) reduced 189.3 kWh/(m2y)∼174 kWh/(m2y) for different configurations of test models. The results demonstrated a MOO methodology that successfully finds the optimum solutions for the anidolic ceiling systems in a deep plan office space to enhance daylighting and energy performance.

System simulation and multi-objective optimization methodology for sustainable municipal solid waste classification management: A case study in China

Cities worldwide are actively implementing waste classification policies to develop efficient waste management systems that address the growing challenges of waste disposal and promote sustainable development. However, selecting tailored waste classification solutions is challenging due to the intricate interrelationships within the system and the complex trade-offs between different management objectives. This study presents a comprehensive methodology that simulates the entire waste classification management system by integrating the stages of waste generation, source classification, and final disposal, all linked by waste quantities and properties. A multi-objective optimization model is employed to identify optimal technical pathways that balance economic, environmental, and energy objectives. This methodology was applied in Zhangjiagang, a medium-sized city in China, revealing that economically optimal solutions focusing on landfill and composting as disposal pathways could exacerbate environmental impacts, with indicators deteriorating by 23.1 %–419.1 % except for freshwater eutrophication potential. In contrast, a multi-objective optimization solution prioritizing incineration and anaerobic digestion achieves environmental and energy benefits valued at 18.7 USD/t, with a modest increase in economic costs of 5.7 USD/t compared to the base year. The unconstrained optimal scenarios achieve net negative environmental costs and recover 2.0 × 106 MJ of energy. The study recommends moderate and dynamically adjusted kitchen waste separation rates depending on the stage of implementation. Additionally, the findings reveal that the “lock-in” effects of mismatched disposal facilities can significantly escalate costs. In conclusion, this study underscores the importance of systematic design and multi-objective optimization, offering a comprehensive methodology for cities aiming to enhance their waste classification strategies.

Microscale structure optimization of catalyst layer for comprehensive performance enhancement in proton exchange membrane fuel cell

The catalyst layer plays a significant role in promoting the redox reaction of proton exchange membrane fuel cells (PEMFC). Especially at high current densities, as the oxygen reduction rate increases and more water is produced, the pores of the catalyst layer are easily clogged, thus preventing the oxygen from reaching the reactive sites. In this work, a cathode catalyst layer with micro-grooved structure is proposed to optimize the water-gas transport and output performance of PEMFC. Three-dimensional two-phase numerical simulation results show that the catalyst layer with grooves significantly improves the water-gas transport performance of PEMFC, with a maximum increase of 4.76 % in output performance. Combining the response surface methodology and non-dominated sorting genetic algorithm-II for multi-objective optimization (MOO), the optimal solution corresponding to anode/cathode relative humidity and ionomer volume fraction is confirmed to be 86.73 %, 80.10 %, and 0.2592, respectively. The optimization objectives (oxygen concentration, liquid saturation, and net power density) are improved by 3.88 %, 1.95 %, and 1.79 %, respectively. The differences between the three optimization objectives obtained by numerical simulation verification are only 0.61 %, 0.32 %, and 0.55 %, indicating that the MOO results are reliable and accurate.

Design and Performance Assessment of Base Isolated Structures Supplemented with Vibration Control Systems

This paper investigates the implementation of supplemental vibration control systems (VCS) in base isolated (BI) structures, to improve their dynamic performance. More specifically, the aim of the VCS is to reduce the base displacement demand of BI structures, and at the same time mitigate the superstructure seismic responses. The purpose of the examined VCS is dual, and for this reason a multi-objective optimization methodology is formulated for the design of the VCS. The examined vibration absorbers include modifications of the KDamper concept. The KDamper is an extension of the traditional Tuned Mass Damper (TMD), and introduces a negative stiffness (NS) element to the additional oscillating mass of the TMD. The generated NS force is exactly in phase with the inertia force of the added mass, thus, artificially amplifying it. This way, lighter configurations are possible with an enhanced damping behavior. These VCS are designed based on engineering criteria and manufacturing constraints, while the excitation input used in the multi-objective optimization procedure is selected from a dataset of artificial accelerograms, designed to be spectrum-compatible with the EC8 design acceleration response spectrum. The effectiveness of the examined VCS is also assess with real near-fault earthquake records, and a comparison is performed with TMD-based VCS having 50 times larger additional masses. The numerical results demonstrate the superiority of the KDamper-based VCS in improving the dynamic behavior of BI structures over other mass-related systems (TMD).

Brownian motion based multi-objective particle swarm optimization methodology and application in binary classification

The particle swam optimization (PSO) method has been widely applied in evolutionary computation and related industrial areas. However, the optimization performance of traditional PSO is usually influenced by particle updating displacement and velocity, which is randomly distributed and makes the solution solving process inefficient. To deal with this challenge, a Brownian particle motion and Euler-Maruyama (EM) methodology-based model is proposed to improve the performance of the multi-objective PSO. The EM based PSO principles and algorithm framework are introduced by theoretical analysis and mathematical modeling, and then the optimization performance of four comparing PSO models is tested, while the feasibility of the new PSO4 is verified by typical benchmark problems. Afterwards, the characterizations of the EM based PSO method are investigated from the perspective of particle motion mechanism analysis, binary classification application and various optimization performance comparison. The result manifests that the new PSO4 features higher accuracy and less running time among 24 related optimization methods for 4 typical standard datasets of Ionosphere, Breast, Diabetes and Wine. Finally, the multi-objective optimization and classification application potential of the Brownian motion and EM based PSO4 is demonstrated, and the future work regarding the new PSO model is discussed.

Multi-objective prediction and optimization of performance of three-layer latent heat storage unit based on intermittent charging and discharging strategies

An intermittent heat charging and discharging strategy is proposed for on-demand thermal utilization in a three-layer latent heat storage unit filled with nanoparticle-enhanced phase change materials. To optimize the utilization ratio of phase change materials, and the stored and released thermal exergy amounts, a multi-objective prediction and optimization methodology combining orthogonal experimental design, range and variance analyses, multi-nonlinear regression models, and non-dominated sorting genetic algorithm-II is introduced while considering the variables of nanoparticle concentration, heat transfer fluid velocity, and intermittent time interval. Results show that the time interval presents the most significant influence. Multi-nonlinear regression models for the above three variables are established with determination factors of 0.9871, 0.9625, and 0.9253, respectively. The ultimate optimal results are 0.8, 57094.03 J, and 43066.73 J, achieved at the three variables of 44.37 min, 0.38 m s−1 and 8.99%, respectively. The maximum verification error of 5.11% indicates the reliability of this methodology. The methodology aims to enhance the overall performance of the three-layer latent heat storage system by mitigating the constraints associated with single-performance optimization.

A Multi-Objective Topology Optimization Methodology Using Deep Learning and Its Application to Electromagnetic Devices

A Multi-Objective Topology Optimization Methodology Using Deep Learning and Its Application to Electromagnetic Devices

Investigation on carbon fiber-reinforced polymer combined with graphene nanoparticles subjected to drilling operation using response surface methodology and non-dominated sorting genetic algorithm-II

In this article, drilling of carbon fiber-reinforced plastics combined with graphene nanoparticles is investigated. These nanocomposites have the potential to be used widely in different industrial applications such as electrical, biomedical and aerospace engineering due to their superior mechanical and thermal specifications. Nonetheless, to be assembled on different sets, drilling nanocomposites is required especially for rivets and joints. In drilling carbon fiber-reinforced polymers (CFRPs), delamination is one of the main challenges that should be minimized in order to enhance the produced hole quality. Besides, machining force is a chief factor to control the drilling-induced damages, especially delamination. This article evaluates the effects of machining parameters on machining force and delamination using response surface methodology experimental design and non-dominated sorting genetic algorithm-II (NSGA-II) multiobjective optimization methodology. Examining delamination is conducted in two parts including peel-up and push-down delamination which are the principal drawbacks in drilling of fiber-reinforced composites. Analysis of variance is also carried out in order to examine the effects of the machining parameters. In addition, predictive quadratic correlations are established by regression analysis. Eventually, multiobjective optimization was implemented by NSGA-II and the optimal values were obtained from pareto-optimal solution set aimed at enhancing the drilling process.

Machine learning and multi-objective optimization methodology for planning construction phases of airport expansion projects

This study presents the development of an innovative methodology to optimize phasing plans of airport expansion projects to minimize construction-related disruptions in airport operations and project construction cost. This methodology integrates a machine learning model to predict the impact of generated phasing plans on flights ground movement time during construction, and a multi-objective genetic algorithms optimization model to identify optimal construction phasing plans for airport expansion projects. An airport expansion case study is analyzed to demonstrate the capabilities of the developed models. The results of this analysis confirm the original contributions of the novel methodology in predicting the impact of alternative construction phasing plans on flights ground movement time without the need for repetitive and time-consuming simulations, quantifying and optimizing the impact of alternative construction phasing plans on airport operations disruption cost and project construction cost, and generating detailed optimum phasing plans for airport expansion projects. These novel capabilities are expected to enable planners improving cost-effectiveness of airports during expansion projects while minimizing construction cost.

Design methodology based on multi-objective optimization with evolutionary algorithms for humidification-dehumidification desalination systems using updated approaches

This paper develops a methodology for multi-objective optimization using Non-Dominated Sorting Genetic Algorithm II (NSGA-II). The methodology aims to address the problem of the close relation between variables based on a mathematical model that simulates design variants of humidification-dehumidification (HDH) desalination systems, where the variation of one parameter can affect another. The approach consists of an exhaustive study of the state of the art to incorporate as many results as possible, including variable and parameter constraints established by previous research. Energy efficiency and potable water production are optimized with respect to the total area of the system's active components and the ratio of seawater converted to potable water. The calculations generate 20 Pareto optimal solutions, with an average pure water production of 14.01 l/h, and an average of the total and solar heating areas of 22.43 m2 and 8.52 m2, respectively, including many other parameters with similar values compared to other publications. The methodology is flexible, updatable, and generates high efficiency values, confirmed by the comparison of equivalent parameters and the pinch analysis, also with respect to previous results. The sensitivity analysis performed, presents different trends in the relation between variables in this scenario contributing to feedback on the behavior of hyperparameters of the algorithm, indicating a very wide potential of solutions. For the water temperature entering the dehumidifier, the range between 30 and 37 °C is determined as the optimum range, however, this is not the only result from the trend analysis of these 20 solutions, compared with other references. This methodology is a contribution to the overall objective of improving the HDH technology design process; optimal solutions are obtained for systems of the configuration chosen to apply it, but it can be adapted to others.

The multi-objective optimization framework: A step towards minimizing life-cycle costs and energy consumption of carbon fibre automotive structures

Design of a sustainable and economical composite structure is challenging due to the often contradicting design drivers such as energy consumption and cost. Therefore, predicting the environmental and economic impact in the early stages of product design results in the significant reduction of energy consumption and cost. Consequently, the impact of contrasting objectives on an optimized carbon fibre reinforced polymer (CFRP) demonstrator is evaluated in this study. This evaluation is performed by integrating a predictive life-cycle assessment and costing framework in a multi-objective optimization methodology. The varying design configurations include designs with and without stiffeners. Furthermore, the impact of end-of-life allocation on the optimized design is also evaluated in this study. The results show a marked difference between the energy consumption of the various optimized designs with energy optimization producing the most efficient solution. However, the mass of the demonstrator increases by 7–9 kg across the different design configurations when the closed loop allocation model is implemented. Consequently, the results show the importance of selecting an appropriate EOL allocation methodology in evaluating the energy consumption of a product. The results also show that the parameters driving the energy consumption (mass and material configuration) and cost (complexity and manufacturability) are varied and often contrasting. The differences in mass, cost, and energy optimized designs further reinforces the importance of coupling cost and energy evaluation in design of sustainable products. Finally, the study demonstrates the need for a holistic life-cycle based assessment in early stage sustainable product design.

Optimizing Real and Reactive Power Dispatch Using a Multi-Objective Approach Combining the ϵ-Constraint Method and Fuzzy Satisfaction

Optimal power dispatch is essential to improve the power system’s safety, stability, and optimal operation. The present research proposes a multi-objective optimization methodology to solve the real and reactive power dispatch problem by minimizing the active power losses and generation costs based on mixed-integer nonlinear programming (MINLP) using the epsilon constraint method and fuzzy satisficing approach. The proposed methodology was tested on the IEEE 30-bus system, in which each objective function was modeled and simulated independently to verify the results with what is obtained via Digsilent Power Factory and then combined, which no longer allows for the simulation of Digsilent Power Factory. One of the main contributions was demonstrating that the proposed methodology is superior to the one available in Digsilent Power Factory, since this program only allows for the analysis of single-objective problems.

Study of optimization for material processing parameters by means of probabilistic methodology for multi-objective optimization

Optimization for material processing parameters is a typical problem of multi-objective optimization, therefore selection and use of proper multi-objective optimization approach is indispensible. The inherent characteristic of newly proposed probabilistic methodology for multi-objective optimization is that it is with the feature of optimization of multiple objectives at the same time in viewpoint of system theory and in spirit of probability theory. In the present paper, the probabilistic methodology is employed to perform the designs of materials processing for improving quality and cost saving at the same time. The laser welding process of ANSI 304 austenitic stainless steel by using a pulsed Nd: YAG laser welding system and thin-wall machining of milling aluminum alloy 2024-T351 are taken as two examples. The quantitative optimum design of materials processing is performed equitably by conducting the assessment of preferable probability of each alternative. The studies indicate that: (1). the optimized parametric combination for the laser welding process of 2 mm thickness ANSI 304 austenitic stainless steel by using a pulsed Nd: YAG laser welding system is at laser parameters of 2.7 kW peak power, welding speed of 2 cm/min and pulse duration of 4 ms; (2). the optimized combination parameter for the thin-wall machining of milling aluminum alloy 2024-T351 is at tool diameter of 8 mm, feed per tooth of 0.06 mm/z, axial cut depth of 24 mm and radial cut depth of 0.625 mm. The optimal configurations guarantee the comprehensive quality of product and reducing energy consumption.

Using response surface methodology for multi-objective optimization of an efficient/clean combined heating/power system based on sugarcane bagasse gasification for environmental sustainability

Developing CHP (combined heat and power) systems-based biomass gasification is crucial for achieving environmental sustainability. These systems offer numerous profits, counting abridged greenhouse gas emissions, efficient energy utilization, and sustainable waste management. By investing in and promoting the adoption of biomass gasification-based CHP systems, it can be moved towards a more sustainable and greener energy future. In this regard, a clean CHP system is integrated by comprising a sugarcane bagasse gasifier, a proton conducting solid oxide fuel cell, a supercritical carbon dioxide Brayton cycle, and a heating recovery unit. The system performance is evaluated with respect to input variables from energy and environmental viewpoints. The integrated system performs more efficiently at lower equivalence ratios, higher temperatures, lower utilization factors, and higher pressure ratios. The efficiency initially improves with an increase in current density from 1400 A/m2 to 3000 A/m2, but starts to decline when the current density is pushed beyond this threshold to 5400 A/m2. According to the results, it has been concluded that the most favorable conditions for attaining the optimum goals are an equivalence ratio of 0.4, current density of 5400 A/m2, temperature of 1200 K, utilization factor of 0.7, and pressure ratio of 3.7. The best performance yields a power generation of 344.6 kW, heating generation of 3422.9 g/s, efficiency of 28.60%, and emissions of 1281 g/kWh.

Mathematical modeling and optimization of machining parameters in CNC turning process of Inconel 718 using the Taguchi method

To remain competitive, machining processes must be optimized to provide increased productivity and higher quality products. The aim of most efforts in these machining processes is to establish the optimal parameters to obtain the maximum material removal rate with minimum surface roughness which represents two of the main quality responses. This paper focuses on the optimization of process parameters in dry turning of Inconel 718, a nickel-based superalloy with PVD-coated carbide inserts based on single-objective optimization Taguchi technique, desirability function approach combined with response surface methodology (RSM), which is known as the multi-objective Desirability Optimization Methodology (DOM). Taguchi’s orthogonal-array design L9 (33) and ANOVA analysis of variance are used to study the relationship between cutting parameters (cutting speed, feed rate and depth of cut) and the dependent output variables i.e., the arithmetic mean deviation of the profile's surface roughness (Ra) and material removal rate (MRR). A regression analysis was used to develop a mathematical model based on the first-order model to predict the Ra and MRR model. Using multiple regression analysis, first order linear prediction model was obtained to find the correlation between surface roughness and MRR with independent variables. In the range of parameters investigated, the obtained mathematical models accurately represent the response index, and the results of the experiments demonstrate that the feed rate and the depth of cut are the most important factors influencing Ra and MRR, respectively. Finally, confirmatory tests proved that Taguchi's method, desirability function approach combined with linear regression models was successful in optimizing turning parameters for minimum surface roughness and maximum MRR.

Investigation of the mechanical properties, surface quality, and energy efficiency of a fused filament fabrication for PA6

Abstract Practitioners in the industry are developing predictive methods for assessing key parameters and responses of engineering materials. The aim of this research is to optimize the average surface roughness (R a), flexural strength (FS), tensile strength (TS), print time (T), and print energy consumption (E) of 3D printed Nylon 6 (PA6). Quantitative parameters for infill density (ID), layer thickness (LT), and print speed (PS) were selected. Employing the central component design (CCD)-response surface methodology (RSM) for investigational design, statistical analysis, and multi-objective optimization, a total of 20 samples were produced and analyzed to develop prediction models. The implication of the selected parameters was confirmed through variance analysis (ANOVA), and the models were validated using confirmatory trial tests. It was found that LT was essential in achieving appropriate R a and T values, while ID was a crucial factor in obtaining the necessary mechanical properties. RSM optimization led to an FS of 70.8 MPa, TS of 40.8 MPa, lowest T of 53 min, lowest possible R a of 8.30 µm, and 0.203 kW·h “E” at ID = 84%, LT = 0.21 mm, and PS = 75 mm·s−1. The study also revealed weak bond strength between layers and layers debonding after bending tests, as shown in SEM micrographs. The PA6 material exhibited flexibility during tensile testing, going into plasticity before breaking. The created numerically optimized model is anticipated to benefit manufacturers and practitioners in predicting the required surface quality for various factors before conducting experiments, ultimately improving 3D printing (3DP) processes and outcomes. Despite limitations such as limited parameter selection, small sample size, and material-specific focus, this research presents valuable insights for the 3DP industry.

Exploring a multi-objective optimization operation model of water projects for boosting synergies and water quality improvement in big river systems

Due to excessive nutrient enrichment and rapidly increasing water demand, the occurrence of riverine environment deterioration events such as algal blooms in rivers of China has become more frequent and severe since the 1990s, which has imposed harmful consequences on riverine ecosystems. However, tackling river algal blooms as an important issue of restoring riverine environment is very challenging because the complex interaction mechanisms between the causes are impacted by multiple factors. The contributions of our study consist of: (1) optimizing joint operation of water projects for boosting synergies of water quality and quantity, and hydroelectricity; and (2) preventing algal bloom from perspectives of hydrological and water-quality conditions by regulating water releases of water projects. This study proposed a multi-objective optimization methodology grounded on the Non-dominated Sorting Genetic Algorithm to simultaneously minimize the excess values of algal bloom indicators (water quality, O1), minimize the used reservoir capacity for water supply (water quantity, O2), and maximize the hydropower generation (hydroelectricity, O3). The proposed methodology was applied to several catastrophic algal bloom events that took place between 2017 and 2021 and thirteen water projects in the Hanjiang River of China. The results indicated that the proposed methodology largely stimulated the synergistic benefits of the three objectives by reaching a 36.7% reduction in total nitrogen and phosphorus concentrations, a 33.1% improvement in the remaining reservoir capacity, and a 41.0% improvement in hydropower output, as compared with those of the standard operation policy (SOP). In addition, the optimal water release schemes of water projects would increase the minimum streamflow velocity of downstream algal bloom control stations by 8.6%–9.4%. This study provides a new perspective on water project operation in the environmental improvement in big river systems while boosting multi-objectives synergies to support environmentalists and decision-makers with scientific guidance on sustainable water resources management.

Development of a green process based on a novel tri-reforming reactor to produce syngas for methanol synthesis: Process Design, Modeling and Multi objective optimization

In this study, a clean and energy-efficient reforming process is introduced that can act as a promising alternative to the conventional reforming process for syngas production used in methanol synthesis process. In this proposed configuration, a pre-reformer is combined with a novel tri-reformer consisting of a combustion chamber and a catalytic bed. The combustion chamber was simulated using the CHEMKIN package incorporating GRI3.0 as a comprehensive mechanism and the catalytic bed was modeled by a heterogeneous plug flow model. A multi-objective optimization model was used to explore operational conditions of the proposed process to optimize CH4 conversion, H2 yield, and CO2 net production. Hence, the other aspect of novelty in this study deals with the use of a new methodology for multi-objective optimization of this process. This methodology is the first to integrate the CHEMKIN package and MATLAB software that leads to a higher degree of accuracy and comprehensiveness. The mathematical model of the conventional process was also developed and the favorable comparison between the performances of both processes was studied. The results indicate that eliminating a steam reformer in the novel configuration, not only reduces toxic emissions and the need for a large quantity of energy, but it also significantly decreases the required value of H2O/CH4 ratio. Therefore, the steam content of the process gas is reduced and energy efficiency is improved. Analyzing the characteristics of the synthesis gas produced by the studied cases results, that the proposed case produces a synthesis gas with higher quality (SN = 2 and a higher CO/CO2 ratio) while substantially reducing energy consumption as well as toxic emissions production.

INFORM: Inverse Design Methodology for Constrained Multiobjective Optimization

Many system design methods use population-based optimization or a surrogate model for solving constrained multi-objective optimization. When designing a system with multiple objectives and constraints, the designer may first be interested in understanding the trade-offs among different objectives from a small number of simulations. In the next step, the designer may focus on specific regions of interest in the design space near a set of non-dominated solutions to further improve performance on the targeted objectives. This may help make the search process sample-efficient. We propose INFORM: a two-step approach for sample-efficient constrained multi-objective optimization of real-world nonlinear systems. In the first step, we modify a genetic algorithm (GA) to make the design process sample-efficient. We inject candidate solutions into the GA population using inverse design methods instead of determining the candidate solutions for the next generation using only crossover and mutation, as is done in standard GA. We present three types of inverse design techniques based on a (i) neural network verifier, (ii) neural network, and (iii) Gaussian mixture model. The candidate solutions for the next generation are thus a mix of those generated using crossover/mutation and solutions generated using inverse design. At the end of the first step, we obtain a set of non-dominated solutions. In the second step, we choose the regions of interest around the non-dominated solutions to further improve the objective function values using inverse design methods. We demonstrate the efficacy of INFORM through synthesis of nonlinear systems and analog circuits. The experimental results show that INFORM reduces synthesis time by up to 29× and improves the value of the objective function by up to 33% compared to a state-of-the-art baseline design methodology.

Multiobjective and multicondition optimization for a gas–liquid mixed-flow pump based on a three-dimensional inverse design

The mixed-flow pump performs well in transporting gas–liquid mixtures with large flow rates and high inlet gas volume fractions. However, its extensive development is still limited by the operating range and poor overall performance. In this study, a multiobjective and multicondition optimization methodology for improving the gas–liquid flow performance of a mixed-flow pump based on the inverse design is proposed. The impeller blade load is taken as the optimization variable. Moreover, the Euclidean distances of the pressure increment, efficiency, and gas volume fraction in the diffuser are adopted as optimization objectives. Results show that the numerical methodology is verified by the pressure increment and gas distribution obtained in the tests of the original pump. Optimized results demonstrate that the slope of the straight line, the stacking angle at the hub, and the intersection point of the rear parabola and the straight line significantly affect the objectives. The increased load of the first half of the impeller and the reduced load of the second half may improve the comprehensive performance of mixed-flow pumps. The blade length and wrap angle are reduced after optimization, which changes the inlet and outlet angles and deflection of the blade, thereby helping to enhance the cognition of mixed-flow pump performance optimization.