Multi-objective Genetic Algorithm Method Research Articles

Multi-objective optimization of tribological properties of camshaft bearing pairs using DNN coupled with NSGA-II algorithm and TOPSIS

PurposeThis study aims to propose an optimization framework using deep neural networks (DNN) coupled with nondominated sorting genetic algorithm II and technique for order preference by similarity to an ideal solution method to improve the tribological properties of camshaft bearing pairs of internal combustion engine.Design/methodology/approachA lubrication model based on the theory of elastohydrodynamic lubrication and flexible multibody dynamics was developed for a V6 diesel engine. Setting DNN model as fitness function, the multi-objective optimization genetic algorithm and decision-making method were used to optimize the bearing pair structure with the goal of minimizing the total friction loss and the difference of the average values of minimum oil film thickness.FindingsThe results show that the lubrication state corresponding to the optimized bearing pair structure is elastohydrodynamic lubrication. Compared with the original structure, the optimized structure significantly reduces the total friction loss.Originality/valueThe optimized performance and corresponding structural parameters are obtained, and the optimization results were verified through multibody dynamics simulation.Peer reviewThe peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-12-2023-0417/

Thermal analysis and structure optimization of wavy microchannel with combining ribs of porous layer and solid wall in multi objective genetic algorithm

The combining rib of porous layer and solid wall is set in wavy microchannel heat sink to enlarge heat transfer area and convection with smaller increase in flow resistance, in which the consumption of pump power relates to the ratios of wave amplitude to length or to width and the thickness of porous layer due to vortices generation while coolant passing through channel. The local thermal equilibrium occurs in porous layer, and the Forchheimer-Brinkman-Darcy relations were used to describe the flow inside porous ribs. The effects of channel-to-pitch width ratio, width ratio of porous layer to pitch and microchannel height on its cooling performance are investigated, and the parameter of figure of merit (FOM) is defined to evaluate thermo-hydraulic performance in wavy microchannel. Besides, the multi objective genetic algorithm method is employed to optimize structure parameters in wavy microchannel to obtain better performances, in which the increase in thermal resistance from 0.062 K/W to 0.166 K/W together with consumption of pump power decreasing from 0.00416 W to 0.00185 W can be obtained in the Pareto front set, and it relates to the heat dissipation in convection between coolant and bottom surface or vertical side ribs. Compared to wavy microchannel with solid rib, the 37.61% and 16.67% decreases respectively in thermal resistance and consumption of pump power occur in the case with optimal combining rib of porous layer and solid wall.

Enhancing Steel Wheel Ventilation Efficiency Through Multi-Objective Optimization

This study focuses on the optimization of ventilation hole design in steel wheels used for heavy commercial vehicles. The primary objective is to reduce the weight of the wheel while ensuring compliance with radial fatigue and cornering fatigue test requirements. Four distinct ventilation types were parametrized using ANSYS Mechanical, with the von Mises stress on the disk, number of ventilations, and wheel weight serving as design parameters. Stress analysis and weight comparisons were performed between wheels featuring different ventilation types and an ellipse ventilation wheel. Incorporating the design of experiment (DoE) and response surface optimization (RSO) module in ANSYS Workbench 2022 R1 was employed to compare and evaluate the obtained values. Subsequently, the multi-objective genetic algorithm (MOGA-II) method was employed for optimization, aiming to identify the optimal design. The optimization process, utilizing a maximum of 20 iterations, a convergence stability percentage of 2%, and a maximum allowable Pareto percentage of 70%, yielded 1, 3, 3, and 3 candidate design points for round, slot, trapezoid, and halfmoon-type ventilation holes, respectively. Among the various ventilation types considered, the halfmoon-type ventilation hole exhibited the most promising results. Compared to the current design, the optimized wheel achieved a weight reduction of 0.9 kg (2.05%). This outcome demonstrates the effectiveness of the proposed methodology. Although lighter designs were not attainable while maintaining the same stress values for the other three ventilation types, the halfmoon-type ventilation hole was ultimately selected as the preferred design.

Optimization of PMSM for EV based on Vibration and Noise Suppression

The key to the suppression of vibration and noise for PMSM is the optimization of electromagnetic excitation force. The method of motor body optimization can effectively reduce the radial excitation force of the motor, so as to suppress the vibration and noise of the motor. Firstly, the stator structure of the motor is optimized with V-shape skew slot based on the analytical modeling of the radial electromagnetic excitation force of the motor. Then, the structural parameters of the motor that affect the electromagnetic excitation force of the motor are determined, and the average torque, torque ripple and radial electromagnetic excitation force generated by tangential electromagnetic excitation force are taken as the optimization objectives. The sensitivity analysis and classification of the structural parameters of the motor are carried out. The multi-objective genetic algorithm and response surface method are combined to optimize the structural parameters of the motor. Finally, the finite element analysis, modal analysis, multi-speed vibration and noise analysis of the optimized motor are done. The performance comparisons before and after optimization have proved that the peak of equivalent sound power level have decreased by 8.65% after the optimization of V-shaped skewed slot structure. After the optimization of structural parameters, the power level of permanent magnet synchronous motor has been reduced by 9.22%. For the vibration noise caused by resonance and the main frequency of vibration noise harmonics, the suppression effects are also better than those of V-shape skewed slots optimization, and the ERPL values are reduced by 9.22% and 10.12%, respectively, in two cases. The results show that the vibration and noise of permanent magnet synchronous motor are effectively suppressed.

Multi objective optimization for house roof using artificial neural network model

Roof models with low heat loss and low heating costs for buildings are crucial for reducing energy consumption and greenhouse gas emissions in cold regions. This study aimed to calculate the heat loss for various roof models with low heat loss, which are widely used in houses in Europe and other cold regions. We created 324 models for three types of roofs (light, medium, and heavy) with different materials and thicknesses using the HAP program. We then trained a neural network (ANN) to generate a mathematical function that can be used to calculate the optimal surface using a multi-objective genetic algorithm method. The resulting optimal roof design was simulated using the Ansys program on a January day. We compared the heat loss results for the optimal roof for HAP, ANN, and transient thermal analysis by Ansys, respectively, showing a close agreement among the methods.

Multi-objective optimization and simulation for multiple models of walls to estimate heat gain using Artificial Neural Network model

In homes all around the world and other hot climates, different types of walls are frequently used to provide small heat gains from the outside. Climate-related factors have been the subject of several studies, but there has been relatively little quantitative study on the best wall types and thicknesses. In this study, an effort was made to determine how much heat would be gained by a different form of wall. The HAP program allows us to change the parameters flexibly and easily calculate the heat gain. We used this advantage to collect data for our analysis, 432 models have been produced for three distinct wall types—light, medium, and heavy—made of various materials and thicknesses using the HAP software, where the direction of the walls and the color of their outer surface were considered. Using a function from a neural network that was built later, the optimal wall model was determined by the multi-objective Genetic algorithm method. The results showed that for the optimal wall, which were 9.548, 9.598, and 9.62 W/m2, heat gain for ANN, HAP, and transient thermal analysis by Ansys, respectively, showed a close agreement among the methods.

Enhancing the performance of radial distribution systems via optimal integration of electric vehicles

<span lang="EN-US">Electric vehicles (EVs) and their associated charging stations (CSs) are a promising avenue for greenhouse gas reduction and energy security. However, improper location and size of the EV charging station (CSs/EVs) negatively affect the power system. It results in some technical challenges such as increased real power-loss, decreased voltage stability and increased voltage deviation. This paper suggests optimum planning of CSs/EVs locations to conserve voltage, improve power-loss and reduce the effect of CSs/</span><span lang="EN-US">EVs in electrical distribution systems. The multi objective genetic algorithm method (MOGA) is utilized to solve the optimization problem and reduce the impact of the random location of CSs/EVs. <span>The simulations are</span> performed on IEEE 33-bus and IEEE 69-bus radial distribution systems (RDS). In addition, the optimal EV allocation is carried out with two fixed levels of loading from 100% to 150% of the candidate EV load. A comparison between the proposed MOGA technique and other optimization techniques is carried out. The results demonstrated the capability of the proposed technique for optimal placement of CSs/EVs in RDS. </span><span lang="EN-US">Moreover, it is providing an objective value to solve a complex multi-objective nonlinear optimization problem to reduce the total power-loss, improve the voltage profile and extend the voltage stability.</span>

Selection of Optimal Well Trajectory Using Multi-Objective Genetic Algorithm and TOPSIS Method

This study presents a novel approach for optimizing well paths in extended reach drilling (ERD) wells. Different trajectories can be used for ERD wells, each with its pros and cons. Previous research overlooked certain objective functions in single-objective optimization and lacked an autonomous method for selecting the best solution from Pareto optimal solutions in multi-objective optimizations. Furthermore, they lacked comparing different profiles in well design. Risk assessment and operational factors, which greatly influence optimization and drilling success, were insufficiently considered. This study utilized the multi-objective genetic algorithm (MOGA) and the technique for order preference by similarity to an ideal solution (TOPSIS) method to select the optimal well path based on torque, wellbore length, risk (e.g., keyseat), and required tools. First, all possible trajectories were determined, and MOGA identified the optimal path with minimal torque and length. The fuzzy decision-making method automatically selected the best solution from the Pareto optimal solution set. The associated risks and required tools are evaluated for each trajectory. Finally, the TOPSIS method selected the optimal trajectory based on torque, length, risks, and required tools. The case study demonstrated that the undersection path was the most advantageous trajectory for ERD wells, with a 60% closeness to the ideal state. The multiple build trajectory achieved 57% closeness, while the build and hold and double build paths had lower closeness values (43 and 28%, respectively). Consequently, it can be inferred that in the context of ERD wells, it is preferable to carry out the deviation process at deeper depths.

Simulation and Optimization Study on the Performance of Fin-and-Tube Heat Exchanger

Heat exchangers (HX) are often utilized in industry, and the optimization of the performance of HX is a key area of research. In this study, EVAP-COND software 4.0 and genetic algorithm (GA) based optimization methods were proposed to optimize the circuitry and fin pitch of a finned tube heat exchanger for an air conditioner. A simulation model for a multi-circuit finned-tube evaporator used in an air conditioning unit was developed using the EVAP-COND software, and further validated based on the experimental data. Considering the refrigerant flow maldistribution of the original HX, four different circuit arrangements, i.e., types A, B, C, and D, were designed and optimized circuitry obtained. Based on both simulation and experimental results, D-type HX with 1.8 mm fin pitch was selected as 10% tubes could be saved with no significant loss of heat transfer capacity. Then the fin pitch was further optimized using the multi-objective GA method, with both Colburn factor j and friction factor f being considered. Optimization results showed that, in Pareto front, points 1 to 4 showed the increase in the Colburn factor j was negative, while the decrease in the friction factor f was positive. The friction factor decreased by 3.5% as one moved from Point 1 to Point 4, but the Colburn factor rose by 1.02%. Points 5 to 10 demonstrated that, while the decrease in the friction factor was negative, the increase in the Colburn factor was positive. The friction factor decreased by 5.31%, but the Colburn factor increased by 1.51% when going from Point 5 to Point 10. The results of optimization demonstrated that the objective function performed at its optimum when the fin pitch was around 1.77 mm.

Optimization on high-pressure side of pump-turbine runner based on high efficiency and stability criterion via multi-objective genetic algorithm method

Pumped storage power plants are doomed to play a more important role in peak-valley shifting hence the demand for operation stability is gradually regarded as an equal important criterion as high efficiency. In our paper, new concepts, namely “swept,” “bowed (lean),” and “twisted” are introduced to systematic innovative design the geometry of high-pressure side (HPS) of a pump-turbine runner. Thereafter, a multi-objective optimization process, which consists of design of experiment (DoE), meta model generation, multi-objective genetic algorithm (MOGA), self-organization map (SOM) and takes both high efficiency and stability discipline into account is produced. The final optimization plan is selected and testified numerically. Compared to the original runner, the efficiency is improved from 91.7% to 91.9% at pump mode and improved from 92.3% to 92.8% at turbine mode. Moreover, the S margin is increased from 89.34° to 90.23° at small GVO and increased from 79.56° to 80.29° at large GVO. Besides, hump unsteady region is completely eliminated. Moreover, the flow characteristic comparation is conducted based on local hydraulic loss rate (LHLR) method. For design points, the optimized runner obviously decreases the hydraulic loss in hub and middle part of runner domain for turbine mode and slightly decrease the hydraulic loss in stay vane region for pump mode. For unsteady characteristics, HPS can better adjust the hydraulic loss distribution in corresponding discharge operating points, largely decreasing S unsteady characteristic in turbine mode and eliminating hump unsteady characteristic in pump mode. We believe that the methods proposed in our paper can bring the design of hydraulic machinery to a new level.

Analysis and Optimization of an Expansion Energy-Absorbing Anti-Crawler for Rail Vehicles

This paper describes the crashworthiness optimization of an intumescent energy-absorbing anti-crawler, which was applied to anti-crawling devices for rail vehicles. The energy absorption characteristics of the expansion-type energy-absorbing anti-crawler were studied experimentally, a finite element model (FEM) was established, and the finite element simulation results were verified with the experimental results. In this paper, the response of the expansion structure was predicted using a validated finite element model. Then, the effects of the variables (expansion tube thickness (T), friction coefficient (μ), and slope angle of conical mandrel (α)) on the response were sampled using the design-of-experiments (DOE) method, including a full factorial design and a central composite. Based on these samples, an alternative model was developed using the moving least-squares method (MLSM). Using the results from the full factorial design for main effects analysis, T was found to have the most significant effect on the average force (Favg), while α had the greatest effect on the specific energy absorption (SEA). The Favg, fracture strain, thickness, taper, and friction coefficient of the structure were used as constraints, and the multiobjective genetic algorithm (MOGA) method was used for parameter optimization to obtain a higher SEA. Finally, the best parameters (T = 5.76 mm, μ = 0.178, α = 25°) with an SEA value of 36.52 kJ/kg were obtained. The SEA value was increased by 31.70% compared to the initial results.

Optimization of a Container Ship Dimensions Using Multi-Objective Genetic Algorithm Method

Optimization of a Container Ship Dimensions Using Multi-Objective Genetic Algorithm Method

Overview of Numerical Analysis and Optimization Methods for Eddy Current Retarders

Aiming at the analysis and optimization of eddy current retarder, this paper reviews the development of numerical analysis based on finite element method. The characteristics of finite element method and the application of numerical method in the analysis of eddy current retarder are briefly introduced. In terms of algorithm, the different applications of multi-objective genetic algorithm, robustness principle, Taguchi algorithm and Rogowski method in the analysis of important parameters of eddy current retarder are introduced and summarized; In terms of software, the application of commercial software in magnetic field and temperature field is briefly introduced; In industrial practice, the development of numerical simulation methods in the research of braking torque is introduced. On the basis of reviewing the numerical analysis and optimization methods of eddy current retarder, the future of its digital design is prospected.

Topology Optimization and Multiobjective Optimization for Drive Axle Housing of a Rear Axle Drive Truck.

As one of the important load-bearing components of a truck, the drive axle housing must meet the requirements of stiffness and strength. The traditional design method uses redundancy design to meet the performance requirements. The joint design between the three-dimensional mathematical model and finite element model is adopted, and the optimal design of the drive axle housing is realized based on topology optimization and multiobjective optimization. Firstly, the static analysis of the drive axle housing of a rear axle drive truck was carried out with four typical working conditions. It was concluded that the four working conditions all operate under the yield limit of the material, and it was found that the maximum equivalent stress of the four working conditions occurs at the step of the half-shaft casing. Among the four working conditions, the most critical one is the maximum vertical force working condition. Then, based on the maximum vertical force working condition, the fatigue life analysis is conducted, and the minimum fatigue life appears at the transition position of the half-shaft sleeve and the arc transition position of the main reducer chamber. The remaining parts can meet the design requirements. The overall safety factor of the drive axle housing is mainly between 1 and 5 when operating under this working condition. Then, through modal analysis, the first to sixth natural frequency and vibration modes of the drive axle housing are extracted. Based on the modal analysis, the dynamic characteristics of the drive axle housing are further studied by harmonic response analysis and random vibration analysis. Finally, two kinds of lightweight optimization schemes for the drive axle housing are given. Topology optimization reduces the mass of the drive axle housing by 17.4%, but the overall performance slightly decreases. Then, the five dimensional parameters of the drive axle housing are selected as design variables. The mass, maximum deformation, equivalent stress, service life, and the first-, second- and third-order natural frequencies are defined as objective functions. Through the optimal space-filling design method, the experimental designs are performed and the sample points are obtained. Based on the results of experiment design, the multiobjective genetic algorithm and response surface method are combined to optimize the objective functions. The analysis results show that the mass is reduced by 4.35%, the equivalent stress is reduced by 21.05%, the minimum life is increased by 72.28%, and the first-, second-, and third-order natural frequency are also increased to varying degrees. Two different optimization strategies are provided for the design of the drive axle housing.

Thermo-economic optimization of a hydrogen storage structure using liquid natural gas regasification and molten carbonate fuel cell

Liquid natural gas (LNG) regasification and fuel cells can be employed to supply the required precooling and electrical power for hydrogen liquefaction, respectively. Such an approach helps reduce the process complexity and the number of equipment, total costs, and carbon footprints, and enhance the controllability of the process. This paper proposes an integrated structure for hydrogen liquefaction and storage by employing the LNG regasification process for precooling and four multi-component refrigerant cycles for liquefaction. Molten carbonate fuel cells, gas turbines power cycles, the two-stage organic Rankine cycle, and the carbon dioxide power cycle are used for supplying the electrical power. A liquid hydrogen production capacity of 1766 kmol/h and 1576.7 MW electrical power generation are attained in this integrated process. The coefficient of performance, specific energy consumption, and specific power consumption of the integrated structure are calculated to be 0.175, 4.772 kWh/kgLH2, and 3.872 kWh/kgLH2, respectively. The exergy efficiency of 83.03% and the exergy destruction of 47.87 MW are obtained based on the exergy analysis. The maximum shares of exergy destruction are attributed to the heat exchangers, gas turbines, and fuel cells with the magnitudes of 45.43%, 24.75%, and 10.93%, respectively. The prime cost of product and rate of return are calculated to be 0.0840 US$/kWh and 24.02%, respectively. According to the sensitivity analysis, it is found that increasing the molar fraction of helium in the multi-component refrigerant cycle from 81.31% to 93.61% leads to a reduction in the net power production (151.2 MW) and total exergy efficiency (81.39%) of the proposed process. Using the multi-objective genetic algorithm method, the total exergy efficiency and the rate of return are optimized to be 86.32% and 29.66%, respectively.

Numerical and experimental investigation of a radially reduced diffuser design concept for a centrifugal compressor performance at design point

Large scale, high pressure ratio (PR) centrifugal compressors are commonly made up of a radial impeller with a vaned diffuser. In research to date, the majority of research and design has focused on extending the operating range or improving the compressor efficiency. However, a cost and weight saving can be achieved by reducing the compressor dimensions. This is a study of a vaned diffuser design concept aiming to reduce the overall radial dimensions of the compressor without any sacrifice of compressor performance at design point (DP).The study parameterized a diverging endwall diffuser concept and optimized it to achieve a similar performance within a reduced radial outlet dimension. A metamodel assisted Multi Objective Genetic Algorithm (MOGA) method has been used. A numerical approach has been used to investigate how the flow physics within the diffuser passage changed with the new geometry and detailed experimental measurements have been used to validate the numerical approach. The result of this study is a summary of the impact of vane geometry defining parameters within a diverging endwall concept which offers design guidance for application of the concept. The measured performance showed that the same efficiency performance was achieved within a 15% radially reduced diffuser passage using the diverging endwall concept.

Potential for optimization of energy consumption and costs in saffron production in central Iran through data envelopment analysis and multi‐objective genetic algorithm

AbstractTechnical management of agricultural units plays an important role in increasing the yield, energy efficiency, and decreasing the production costs. Based on that, the present study aimed to evaluate and optimize the technical and economic efficiency in Saffron farms in the 2019–20 cropping season in Iran. Required data were collected from 70 Saffron farms through interviews and questionnaires and were analyzed and compared using two optimization methods including data envelopment analysis (DEA), and multi‐objective genetic algorithm (MOGA). Based on the results related to the energy section, the total energy input was obtained as 43,578 MJ ha−1 before any optimization, while it was determined as 36,033 and 36,910 MJ ha−1 after optimization using DEA, and MOGA, respectively. Also DEA and MOGA methods improved the energy ratio index (ER) (0.002) by 50, and 159%, respectively. Results related to the economic section showed that the total production costs were mitigated from 1260 $ ha−1 to 863.5 and 1069 $ ha−1 after optimization by DEA, and MOGA, respectively. After optimization of revenue (using MOGA method), and total costs (using MOGA, and DEA), the benefit cost ratio index was improved from 1.43 to 2.09 (using DEA), and 3.3 (using MOGA). Consequently, MOGA optimization method showed better results compared to DEA in both energy and economic sections.

Design and Optimization of a New Alternating Electromagnetic-Field-Generation System for an Inverted Microscope.

This paper presents the design and optimization of a new alternating electromagnetic-field-generation system, which is dedicated to actuating untethered magnetic microrobots under an inverted microscope. Its uniqueness is that the system parameters are optimally designed by considering both electric and geometry constraints for the target-driving application. The dominant parameters of the system are first determined by establishing analytical models. According to the requirements of targeted application, the optimization problem with certain constraints is formulated, which is solved via the multiobjective genetic algorithm method. A prototype system with the optimal parameters is developed for experimental testing. Experimental studies are carried out to characterize actual performance of the developed actuation system. For demonstration, a magnetic microball has been actuated for navigation by surface rolling in a petri dish filled with pure water. Results indicate that the reported electromagnetic-field-generation system meets the actuation requirements for potential applications.

Optimal Current Allocation Strategy for Hybrid Hierarchical HVDC System with Parallel Operation of High-Voltage and Low-Voltage DC Lines

For long-distance and bulk-power delivery of new energy, high-voltage direct current (HVDC) is a more effective way than high-voltage alternative current (HVAC). In view of the current capacity disparity between line commutated converter (LCC) and voltage source converter (VSC), a hybrid hierarchical HVDC topology with parallel operation of 800 kV and 400 kV DC lines is investigated. The optimal current allocation method for hybrid hierarchical HVDC is proposed distinct from the same rated current command configuration method of high-voltage and low-voltage converters in traditional topology. Considering the transmission loss reduction of the HVDC system, a multi-order fitting function of transmission loss including LCC converter stations, VSC converter stations and DC lines is established. To minimize the transmission loss and the voltage deviation of key DC nodes comprehensively, a multi-objective genetic algorithm and maximum satisfaction method are utilized to obtain the optimal allocation value of rated current command for high-voltage and low-voltage converters. Through the optimization model, an improved constant current controller based on the current allocation strategy is designed. The hybrid hierarchical HVDC system model is built in PSCAD software, and simulation results verify the effectiveness of the proposed topology and optimal current allocation strategy.

Crop-growth-based spatially-distributed optimization model for irrigation water resource management under uncertainties and future climate change

The spatially distributed AquaCrop-multiobjective robust possibilistic programming (distributed AquaCrop-MORPP) model that considers spatially-distributed land, soil and management features has been proposed for irrigation scheduling optimization under uncertain conditions. Compared with traditional simulation-optimization models, it improved the robustness of decision making by optimizing irrigation amounts and dates considering physical crop growth process and the spatial heterogeneity of soil, crop and irrigation. Additionally, it enhanced the AquaCrop-optimization model by handling uncertainties presented as fuzzy and stochastic variables. Moreover, it enhanced the applicability of multi-objective programming (MOP) by balancing contradictory relationships between the objectives of the net economic benefit and field water use efficiency, which were simulated and calculated by the spatially-distributed AquaCrop model. Fifty groups of optimal Pareto solutions were obtained by solving the spatially-distributed AquaCrop-MORPP model using a fast and elitist multi-objective genetic algorithm (NSGA-II) method. Subjective decision-making methods (e.g., Technique for order preference by similarity to an ideal solution (TOPSIS) and prospect theory) were used to select specific alternatives from the Pareto solutions to provide recommendations for managers from different viewpoints. The alternatives that maximized field water use efficiency or net economic benefit separately were selected to cope with emergencies. To obtain optimal irrigation scheduling under future climate change, the RCP4.5 future climate scenario was integrated with the spatially-distributed AquaCrop-MORPP model. The model was verified by applying it to the Yingke Irrigation District (YID), Heihe River Basin (HRB), China. The results showed that the maximum field water use efficiency and net economic benefit in 2021 improved by 24% and 1.3% than those in 2012 for the alternative selected by TOPSIS method. The irrigation scheduling with varied irrigation dates improved by 3.7% and 5% than the irrigation scheduling with fixed irrigation dates for field water use efficiency and net economic benefit, separately. The study provides a framework about how to build spatially-distributed crop simulation-optimization model with consideration of tradeoffs amid multiple objectives to optimize irrigation schedules, and how to select alternatives based on managers’ risk attitudes, and offer a series of Pareto solutions for managers.