Multi-objective Optimization Research Articles

Between green hills and green bills: Unveiling the green shades of sustainability and burden shifting through multi-objective optimization in Swiss energy system planning

The Paris Agreement is the first-ever universally accepted and legally binding agreement on global climate change. It is a bridge between today’s and climate-neutrality policies and strategies before the end of the century. Critical to this endeavor is energy system modeling, which, while adept at devising cost-effective carbon-neutral strategies, often overlooks the broader environmental and social implications. This study introduces an innovative methodology that integrates life-cycle impact assessment indicators into energy system modeling, enabling a comprehensive assessment of both economic and environmental outcomes. Focusing on Switzerland’s energy system as a case study, the model reveals that optimizing key environomic indicators can lead to significant economic advantages, with system costs potentially decreasing by 15% to 47% by minimizing potential impacts from the current system still operating with fossil technologies to an alternative only relying on renewable and where the impact are mainly related to the construction of the infrastructure. However, a system optimized solely for economic efficiency, despite achieving 63% reduction in carbon footprint compared to 2020, shows a potential risk of burden shift to other environmental issues. The adoption of multi-objective optimization in this approach nuances the exploration of the complex interplay between environomic objectives and technological choices. The results illuminate pathways towards more holistically optimized energy systems, effectively addressing trade-offs across environmental problems and enhancing societal acceptance of the solutions to this century’s defining challenge.

Optimizing building energy efficiency with a combined cooling, heating, and power (CCHP) system driven by boiler waste heat recovery

In light of increasing challenges related to fossil fuel consumption, global warming, and rising energy costs, optimizing energy systems has become essential. This study introduces a multi-purpose system designed to capture and utilize waste heat from boiler flue gases at the Tous power plant for simultaneous power generation, cooling, and heating. The system integrates an Organic Rankine Cycle (ORC) for power generation and an Absorption Refrigeration Cycle (ARC) for cooling, with the added function of recovering waste heat to preheat natural gas for the boiler and power plant. The system's performance was rigorously analyzed through energy, exergy, and exergoeconomic assessments. To determine the optimal operating conditions, a multi-objective optimization was conducted using the TOPSIS technique, focusing on critical parameters such as flue gas exit temperature, natural gas inlet temperature, and turbine inlet pressures. The results identified optimal conditions with a flue gas exit temperature of 532.5 K, a natural gas inlet temperature of 285 K, and turbine inlet pressures of 2.54 MPa and 14.62 MPa for the first and second turbines, respectively. Under these conditions, the system achieved an exergy efficiency of 41.1 %, cooling capacity of 133.1 kW, power generation of 210.4 kW, heat transfer to natural gas of 979.6 kW, and operational costs of 8.53 $/h. This study highlights the potential of the proposed system to significantly enhance energy efficiency and reduce operational costs in practical applications, offering a sustainable solution for energy management.

Multi-objective topological design considering functionally graded materials and coated fiber reinforcement

This study presents a multi-objective topology optimization method tailored to structures fabricated from functionally graded materials (FGMs), coated FGMs, and coated fiber-reinforced composite materials (FRCMs) with fixed fiber thickness. The design objective is the simultaneous minimization of elastic and thermal compliance. The material properties of these composite materials were derived to generate datasets using the representative volume element method under periodic boundary conditions. Subsequently, machine learning modules were developed based on the datasets to combine with the design process. The multi-objective optimization problem was addressed using the weighted sum method ensuring the generation of the Pareto front. The adaptive weighting strategy is employed to avoid biased results toward a single objective function. To define the coated boundaries within the design domain, image post-processing techniques such as convolution filters, interpolation schemes, and erosion methods were employed on the material layout information of the optimized FGM structures. Through numerical examples, optimized material layouts for coated assemblies incorporating FGMs and FRCMs are presented, with the performance verified through objective function values.

A multi-objective optimization and evaluation framework for LID facilities considering urban surface runoff and shallow groundwater regulation

Currently, the goals of sponge city construction mostly focus on urban surface water, with few considerations of groundwater indicators, and there is a lack of simulation methods that consider the interaction between surface water and groundwater under low impact development (LID) scenarios. Taking a sponge campus in Xi'an as the research object, this paper proposes a method to realize the interaction between surface water and groundwater at different spatial and temporal scales, so as to construct a SWMM-MODFLOW coupled numerical model to carry out the analysis of hydrological effect of sponge city comprehensively taking into account both surface water and groundwater. Simultaneously, the SWMM is coupled with the NSGA-III algorithm for multi-objective optimization of LID facility configurations, aiming to identify a globally optimal solution set for LID facility configurations under both long and short-duration rainfall scenarios. A novel framework for a comprehensive evaluation system of surface water-groundwater benefits is also developed to comprehensively assess LID facility optimization schemes that meet the goals of stormwater runoff infiltration and reduction, pollution interception and purification, and groundwater recharge conservation. The simulation results show that after optimization, the LID scheme has good surface runoff regulation effects and pollution reduction capabilities, reducing the runoff peak from 2.297 m3/s to 2.128 m3/s, significantly lowering the risk of inundation and effectively reducing the total suspended solids (SS) load by 42.38 kg at the outfall. Meanwhile, the groundwater recharge effect is particularly significant in September. Compared to the baseline scenario, the average groundwater levels from June to September were raised by 3.966 cm, 5.120 cm, 6.743 cm, and 7.639 cm, respectively. The maximum daily groundwater level rise reached 7.82 cm, while the average groundwater level for the whole year of 2023 increased by 2.61 cm. The maximum transport area of pollutants decreased from 2359.44 m2 to 1796.54 m2, and the maximum transport distance reduced from 79.985 m to 69.977 m. Additionally, the central concentration of pollutants also decreased. This optimization evaluation framework will aid decision-makers in selecting LID facility management strategies that balance the dual benefits of surface water runoff and groundwater regulation.

Multi‐criteria hydraulic turbine optimization using a genetic algorithm and trust‐region postprocessing

AbstractA two‐stage, multi‐objective optimization approach is proposed to improve the overall efficiency of the time‐consuming and computationally expensive optimization process for hydraulic turbines. The purpose is to optimize the shape of the turbine blades, designed using 30 parameters, in order to maximize its efficiency and minimize both the cavitation volume and the deviation between the desired and the calculated design head. In the first step of the routine, the genetic algorithm “Non‐Dominated Sorting Genetic Algorithm II (NSGA‐II)” is used to generate an initial approximation of the Pareto front that covers a wide variety of possible solutions, that is, optimal trade‐offs between the conflicting objectives. Subsequently, to ensure convergence, the trust region optimizer “Constrained Multiobjective Problem Optimizer with Model Information to Save Evaluations (CoMPrOMISE)” is used, which is initialized with individuals selected from the Pareto set generated by the genetic algorithm.

Enhancement of heat transfer characteristics in wavy microchannel heat sinks with streamlined micropins within convergent-divergent flow passages

In the current study, the heat transfer characteristics of a novel design microchannel with a wavy sinusoidal convergent-divergent wall structure featuring streamlined pins have been numerically investigated under laminar flow conditions. Various amplitudes, wavelengths, pin heights, and Reynolds numbers are considered as parameters. The thermal and hydraulic characteristics are analyzed in terms of Nusselt number, Fanning friction factor, and Performance Evaluation Criteria number (PEC), which evaluates the heat transfer enhancement against the associated pressure drop. It is revealed that increasing the amplitude and decreasing wavelength, along with moderate pin heights, significantly augment heat transfer. The streamlined pins effectively direct the flow, and the resulting secondary flow and chaotic advection considerably enhance heat transfer in the designed configuration. The study demonstrates that the heat transfer can be improved by a factor of 4.79 compared to a straight microchannel. Under these geometric and flow conditions, the pressure drop increases by a factor of 9.87, and the PEC is found to be around 2.23. A multi-objective optimization study using the Non-dominated Sorting Genetic Algorithm (NSGA-II) is conducted with Genetic Aggregation Response Surface Methodology to evaluate the impact of various parameters on thermal-flow performance and to identify the optimal design with material quantity variation. According to the optimal results, a 5 % increase in material can augment thermal-flow performance by approximately 206.6 % compared to traditional microchannels. Finally, practical correlations for the Nusselt number and friction factor, accounting for various parameters, have been developed to facilitate in designing of microchannel cooling systems.

Fixed Switching Frequency Model Predictive Control and Passivity Based Control for DC-DC Converter

The DC-DC converter represents a crucial component in the renewable energy sources. The stability and dynamic capability enhancement of the DC/DC converter have emerged as a significant research topic in the current era. Model predictive control (MPC) is particularly prevalent due to its high dynamic response speed, simplicity of the controller design, and capacity for multi-objective optimization. However, the traditional finite control set model predictive control (FCS-MPC) method is suffer to variable switching frequency and vast computing. To improve the dynamic performance of the converter, a novel nonlinear control strategy named fixed switching frequency MPC and passivity-based control (PBC), named FSFPBMPC, is proposed, which could achieve fixed switching frequency and enhance the system's dynamic response speed. Firstly, the Euler-Lagrange (EL) model of the boost converter is established. Secondly, the relationship between duty cycle and MPC is established. Ultimately, the output voltage of PBC is incorporated into the cost function of the FCS-MPC. The characteristics of PBC power shaping and damping injection can enhance the system's immunity to interference, improve the system's dynamic response speed, and thus reinforce the system's stability. Then, depending on MATLAB, the simulation results proved that the proposed strategy has the same effect as we expected.

Failure mechanism and crashworthiness optimization of variable stiffness nested origami crash box

In recent years, the study of the crashworthiness of lightweight and efficient thin-walled energy-absorbing structures has received increasing attention. In this work, 3D printing technology was adopted to create a nested origami crash box with stiffness variation, which was made of short carbon fiber reinforced nylon material. The structure effectively inhibits the development of failure behavior of short carbon fiber-reinforced nylon origami crash box due to material brittleness. The quasi-static compression experiment results indicate that compared to origami crash box, nested origami crash box improves by 40% in specific energy absorption and 50% in crash force efficiency, while the initial peak crushing force remains unchanged. The effects of three key geometrical parameters, namely dihedral angle, distance between tubes, and height difference on the damage mechanism of the nested origami crash box are discussed in detail using the finite element method, and the response surface model combined with the non-dominated sorting genetic algorithm II is used for multi-objective optimization. In this work, the concepts of origami theory and nested systems are integrated for the first time, aiming to achieve a stable and efficient energy-absorbing deformation mode by precisely modulating the stress transfer path of the structure and its stiffness. This work provides new ideas for the design and fabrication of novel lightweight energy-absorption boxes.

Multi-objective optimization for connected and automated truck platoon control with improved CACC model

Connected and Automated Truck Platoon (CATP) refers to a group of trucks traveling closely together with minimal spacing to improve fuel economy and safety. However, challenges arise from instability due to internal platoon factors and external traffic disturbances. This research presents an improved Cooperative Adaptive Cruise Control (CACC) model tailored for CATP to address these challenges. The model is designed to enhance safety, fuel efficiency, and traffic efficacy. The improvements of the proposed model are in two aspects: the optimizing of the time headway strategy and the dynamic parameter adjustments of controller based on multi-objectives. The Dynamic Safety Requirement Time Headway (DSRTH) strategy facilitates the timely detection of the accelerations of the leading vehicles within the platoon, enabling quick driving responses. Additionally, Model Predictive Control (MPC) enables dynamic calibration of Proportional-Derivative (PD) control parameters and issuance of velocity commands. Meanwhile, the integration of a second-order time-delay response model has been implemented to adapt to dynamic changes in commands. A transfer function has been established, and stability has been proven. To evaluate the model performance, simulation analysis was performed using real vehicle trajectories as the CATP following vehicles. The results indicate that the DSRTH strategy outperforms both the Constant Time Headway (CTH) and Variable Time Headway (VTH) strategies, allowing rear vehicles to reach the speed trough earlier, with response speeds improved by 3.1 % and 1.5 %, respectively. Compared to the Intelligent Driver Model (IDM) and CACC models, the improved CACC model achieves a steady state of constant acceleration sooner, with recovery times reduced by 17.7 % and 3.2 %. Additionally, compared to the IDM model, the improved CACC model can save 3.23 % in fuel consumption. Furthermore, sensitivity analysis indicates that as the CATP proportion and platoon size increase, there is a positive impact on traffic flow. However, when the platoon size exceeds 5 vehicles, it shows a negative impact on the stability of other vehicles in the traffic flow besides those in the CATP.

Energy, exergy and exergoeconomic analyses and ANN-based three-objective optimization of a supercritical CO2 recompression Brayton cycle driven by a high-temperature geothermal reservoir

The use of CO2-based power cycles to harness high-temperature geothermal resources is an interesting application that has been little explored. Therefore, to obtain a more holistic understanding of these systems, in this work, a supercritical CO2 recompression Brayton cycle is assessed. For comparison, the performances of a recuperative cycle and a recompression cycle with intercooling were also computed. Detailed mathematical models were developed and then, artificial neural network-based surrogate models were adopted to conduct multi-objective optimization. Results of the baseline simulations show that, the high temperature recuperator and the turbine are the most important components from both exergy and exergoeconomic approaches. The optimizations reveal that the intercooled cycle is superior to the other layouts in all the cases while the recuperative cycle is not feasible with reinjection temperatures greater or equal to 150 °C. When the reinjection temperature is constrained to 150 °C, the intercooled cycle attains 4472.70 kW, 62.10 % and 14.42 $/GJ for net power, exergy efficiency and product unit cost, respectively, whereas without this constraint, it achieves 5394.09 kW, 61.83 %, 11.79 $/GJ. In conclusion, the adoption of advanced layouts of the CO2 cycle is beneficial for this application from both technical and economic points of view.

A multi-objective dual dynamic genetic algorithm-based approach for thermoelectric optimization of integrated urban energy systems

In order to reduce the loss of energy in the process of conversion and utilization, and to improve the energy utilization effect and economic benefits of urban integrated energy system, a thermoelectricity optimization method of urban integrated energy system based on multi-objective double dynamic genetic algorithm is proposed. The method analyzes the operation characteristics of the urban integrated energy system through its operation model, constructs a multi-objective optimization model for the thermoelectricity of the urban integrated energy system, determines the optimization multi-objective function that minimizes the operation cost, minimizes the carbon emission, minimizes the technical dissatisfaction and the related constraints, and then solves the optimization model by using the dual dynamic genetic algorithm to output the results of the optimization of the thermoelectricity of the urban integrated energy system.The test results show that the algorithm has a crowding distance of 0.75 or above when solving, and the overall unit energy consumption cost reduction ratio is about 22.97 %. The state of charge results of the four energy storage power stations are all below 10 %, and the lowest convergence speed is only 7 seconds, effectively improving energy utilization efficiency.

Multi-objective human-robot collaborative disassembly line balancing considering components remanufacture demand and hazard characteristics

Disassembly enterprises face significant challenges in managing increasingly intensive workloads with a workforce alone. To address this, current study focuses on balancing a human-robot collaborative disassembly line. For the task operator allocation problem, a mapping constraint mechanism between the disassembly tasks and the task operators is established based on the remanufacture demand and hazard characteristics of components. A mixed-integer programming model is formulated, encompassing four optimization objectives: the number of workstations, the task operator idle balancing index, the demand index, and the hazard index. A novel modified teaching and learning optimization approach is proposed for the addressed human-robot collaborative disassembly line balancing problem. A two-layer encoding strategy is designed based on the solving characteristics of the problem and an embedded perturbation strategy based on randomly transforming the task operator is introduced to enhance the optimization performance of the proposed method. The validity of the mixed-integer programming model and the efficacy of the proposed algorithm are demonstrated through two small-scale human-robot collaborative disassembly case studies. The proposed algorithm is then applied to two real-life cases of human-robot collaborative disassembly lines with different scales. The results of the proposed optimization method are compared with other advanced algorithms, demonstrating its superior performance in both single-objective and multi-objective optimization based on multiple evaluation indicators.

Investigation on the Multi-Objective Optimization of Machining Parameters and Prediction for EN Series Materials

Investigation on the Multi-Objective Optimization of Machining Parameters and Prediction for EN Series Materials

Research on Multi-Objective Optimization Methods of Urban Rail Train Automatic Driving Based on NSGA-II

In order to improve the control performance of automatic train operation (ATO) in urban rail trains, five typical operating sequences of urban rail trains were studied. Under the condition of meeting the safety and comfort principles of train operation, a train dynamics model was established to achieve the goals of low energy consumption, short running time, and high stopping accuracy in urban rail transit trains. In the process of finding a multi-objective solution to this problem, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) was used with an elite retention strategy, and the optimal Pareto multi-objective solution set was sought. In the process of optimal solution weight assignment, the hierarchical analysis Mahalanobis distance method, which combines subjective and objective analysis, was used. Finally, taking the Beijing Yizhuang subway line as the background design example, the simulation verified the effectiveness and feasibility of the algorithm and obtained high-quality automatic train driving curves under various working conditions. This research has important reference significance for the actual operation of automatic driving in urban rail trains.

MMD-TSC: An Adaptive Multi-Objective Traffic Signal Control for Energy Saving with Traffic Efficiency

Reducing traffic energy consumption is crucial for smart cities, and vehicle carbon emissions are a key energy indicator. Traffic signal control (TSC) is a useful method because it can affect the energy consumption of vehicles on the road by controlling the stop-and-go of vehicles at traffic intersections. However, setting traffic signals to reduce energy consumption will affect traffic efficiency and this is not in line with traffic management objectives. Current studies adopt multi-objective optimization methods with high traffic efficiency and low carbon emissions to solve this problem. However, most methods use static weights, which cannot adapt to complex and dynamic traffic states, resulting in non-optimal performance. Current energy indicators for urban transportation often fail to consider passenger fairness. This fairness is significant because the purpose of urban transportation is to serve people’s mobility needs not vehicles. Therefore, this paper proposes Multi-objective Adaptive Meta-DQN TSC (MMD-TSC), which introduces a dynamic weight adaptation mechanism to simultaneously optimize traffic efficiency and energy saving, and incorporates the per capita carbon emissions as the energy indicator. Firstly, this paper integrates traffic state data such as vehicle positions, velocities, vehicle types, and the number of passengers and incorporates fairness into the energy indicators, using per capita carbon emissions as the target for reducing energy consumption. Then, it proposes MMD-TSC with dynamic weights between energy consumption and traffic efficiency as reward functions. The MMD-TSC model includes two agents, the TSC agent and the weight agent, which are responsible for traffic signal adjustment and weight calculation, respectively. The weights are calculated by a function of traffic states. Finally, the paper describes the design of the MMD-TSC model learning algorithm and uses a SUMO (Simulation of Urban Mobility) v.1.20.0 for traffic simulation. The results show that in non-highly congested traffic states, the MMD-TSC model has higher traffic efficiency and lower energy consumption compared to static multi-objective TSC models and single-objective TSC models, and can adaptively achieve traffic management objectives. Compared with using vehicle average carbon emissions as the energy consumption indicator, using per capita carbon emissions achieves Pareto improvements in traffic efficiency and energy consumption indicators. The energy utilization efficiency of the MMD-TSC model is improved by 35% compared to the fixed-time TSC.

Accelerating depression intervention: identifying critical psychological factors using MCDM-MOORA technique for early therapy initiation

BackgroundA thorough psychosocial assessment is time-consuming, often requiring multiple sessions to uncover the psychological factors contributing to mental illness, such as depression. The duration varies depending on the severity of the patient’s condition and how effectively the psychotherapist can establish rapport. However, prolonged assessment periods pose a significant risk of patient deterioration.MethodsThe comprehensive psychosocial intervention, led by the Multi-Criteria Decision-Making (MCDM) approach utilizing the Multi-Objective Optimization by Ratio Analysis (MOORA) method, played a pivotal role in identifying the key psychological factors contributing to the depression of the client among the 21 factors specified by BDI-II analysis.ResultsThe integration of the MOORA strategy compared to traditional psychotherapy on 254 samples demonstrates a Jaccard similarity coefficient of 0.8, with a minimum error margin of 7% (vulnerability index = 0.57), indicating a significant agreement between the two approaches, both converging towards a similar solution. For patients with extreme depression, the number of sessions reduced from 18 ± 2 to 11 ± 2, showing a 33–35% reduction (χ2 = 6.94, p = 0.008). Severe depression patients experienced a reduction from 14 ± 2 to 8 ± 1 sessions i.e., 34–39% reduction (χ2 = 8.32, p = 0.004). Moderate depression patients saw sessions drop from 9 ± 1 to 5 ± 1, i.e., 37–43% reduction (χ2 = 0.29, p = 0.001). The accuracy for detecting dominant psychological factors improved to 82.88% for extreme, 86.74% for severe, and 90.34% for moderate depression, respectively. ConclusionThe implementation of MOORA facilitated the identification and prioritization of key psychosocial intervention strategies, making the process significantly faster compared to traditional methods. This acceleration greatly enhanced the precision and efficacy of the work. Additionally, critical vulnerable factors were identified through ordered statistics and correlation analysis [Pearson (r) = 0.8929 and Spearman’s rank (ρ) = 0.7551] on the Beck Depression Inventory-II model. These findings were supported by other MCDM schemes such as EDAS and TOPSIS, demonstrating high stability and robustness in dynamic decision-making environments, maintaining consistency across scenarios adapted by different psychotherapists. Overall, the combined application of MCDM (MOORA) and targeted psychological interventions yielded substantial positive outcomes in enhancing the well-being of individuals with psychological illnesses, such as depression, cognitive, affective, and somatic syndromes.

Study on Cavity Filling Defects and Tensile Properties of L-Shaped Profiled Rings

Severe cavity filling defects and poor mechanical properties increase the difficulty in the integrated forming of L-shaped profiled rings due to its asymmetrical section geometry. A novel rolling method of a C-shaped ring was proposed in this study, and two symmetric L-shaped rings were prepared simultaneously. A numerical model of C-shaped ring rolling was established, and the cavity filling defects in different directions and the overall forming defect were defined for a qualitative analysis of the geometry’s accuracy. The effect of the rolling parameters on the forming defects and ring quality was investigated. The forming defects increased with an increase in the groove depth ratio as well as decreases in the groove angle and rolling ratio. The feeding strategy with a constant ring growth velocity led to the best geometric accuracy and strain uniformity of the C-shaped rings. Optimized rolling parameters can be acquired by the Box–Behnken optimization method with multi-objective optimization of the rolling stability and ring quality. An experiment of C-shaped ring rolling was successfully prepared, based on the optimized parameters. The hardness distribution on the cross-section was symmetric and uniform. The C-shaped ring showed obvious anisotropy of the tensile properties of the cast ring’s blank, and heat treatment had little effect on the improvement of the isotropy.

Multi-objective grounding system optimisation using NSGA-II

This study investigates the optimisation of grounding infrastructure in substations by implementing the philosophy of the multi-objective algorithm NSGA-II Elite. A complete description of the operating scheme and the characteristic mechanisms that support the behaviour and development of optimal Pareto solutions is provided. A detailed comparison was made with the optimisation method used in the GMAT program of Aplicaciones Tecnológicas, based on a semi-optimization process derived from the correlation of semi-precision optimisation solutions. The results show that multi-objective optimisation using NSGA-II results in a significant cost reduction compared to the semi-optimization method, although the computational time required to reach the final solution increases significantly. This approach allows a more adequate understanding of optimising the terrestrial substation grid. It highlights its ability to generate more cost-effective and performance-efficient solutions by carefully considering the computing time required.

Structural Performance Analysis and Optimization of Small Diesel Engine Exhaust Muffler

In recent years, the optimization of diesel engine exhaust mufflers has predominantly targeted acoustic performance, while the impact on engine power performance has often been overlooked. Therefore, this paper proposes a parallel perforated tube expansion muffler and conducts a numerical analysis of its acoustic and aerodynamic performance using the finite element method. Then, a Kriging model is established based on the Design of Experiments to reveal the impact of different parameter couplings on muffler performance. With transmission loss (TL) and pressure loss (PL) as the optimization objectives, a multi-objective optimization study is carried out using the competitive multi-objective particle swarm optimization (CMOPSO). The optimization results indicate that this method can simplify the optimization model and improve optimization efficiency. After CMOPSO calculation, the average TL of the muffler increased from 27.3 dB to 31.6 dB, and the PL decreased from 1087 Pa to 953 Pa, which reduced the exhaust noise and improved the fuel economy of the engine, thus enhancing the overall performance of the muffler. This work provides a reference and guidance for the optimal design of mufflers for small agricultural diesel engines.

Multi-Objective Optimization of the Forming Process Parameters of Disc Forgings Based on Grey Correlation Analysis and the Response Surface Method

This paper introduces a multi-objective optimization problem (MPO) for the forming process parameters of disc forgings using grey relational analysis (GRA) and the response surface methodology (RSM). Firstly, an experimental design based on the Box–Behnken design (BBD) principle was established, and simulations were performed in Deform to obtain response data. Secondly, GRA was used to transform the MPO into a grey relational degree (GRD) problem, and the entropic weight method was integrated to ascertain the influence weights of each variable on GRD. Then, a quadratic polynomial prediction model based on the RSM was constructed, and its accuracy was ensured through model validation. Finally, the optimal process parameter combination was determined through the particle swarm optimization algorithm, which included a friction coefficient of 0.3, an initial temperature of 1250 °C, and a downward pressing speed of 7.5 mm/s. The results of the experimental investigation indicate that optimized process parameters significantly reduce the forming load, equivalent stress, and damage value, effectively enhancing the overall quality of forged parts.