Pareto Solutions Research Articles

Extension of the Directed Search Domain algorithm for multi-objective optimization to higher dimensions

This paper addresses the problem of generating an evenly distributed set of Pareto solutions. It appears in real-life applications related to multi-objective optimization when it is important to represent the entire Pareto front with a minimal cost. There exist only a few algorithms which are able to tackle this problem in a general formulation. The Directed Search Domain (DSD) algorithm has proved to be efficient and quite universal. It has successfully been applied to different challengeable test cases. In this paper for the first time the DSD approach is systematically extended and applied to problems with higher dimensions. The modified algorithm does not have any formal limitation on the number of objective functions that is important for practical applications. The efficacy of the algorithm is demonstrated on a number of test cases.

Enhancing compressive strength and sustainability: a machine learning approach to recycled brick and tile concrete mix design

Optimizing concrete mix designs, especially for recycled brick and tile (RBT) concrete, is critical in construction materials. The optimization of RBT concrete mix designs was investigated using machine learning (ML) methods and metaheuristic algorithms. Hyperparameter tuning of the XGBoost (XGB) model was conducted using SFO, HGS, and HBA algorithms. Critical hyperparameters, including population size and iterations, were identified to ensure model convergence and performance. The model's predictive accuracy for compressive strength (CS) was evaluated using the coefficient of determination (R2) metric, revealing its superiority in mitigating overfitting. SHAP analysis highlighted testing age, cement content, and total coarse aggregate as influential input variables. A practical approach to RBT concrete mix design optimization was introduced, enabling the achievement of specific CS targets while maximizing RBT usage. Pareto solutions provided actionable insights for engineers to create tailored high-performance concrete mixes. This research contributes significantly to sustainable concrete mix design by offering practical ML tools.

Balanced task allocation and motion planning of a multi-robot system under fuzzy time windows

PurposeA fleet of mobile robots has been effectively used in various application domains such as industrial plant inspection. This paper proposes a solution to the combined problem of task allocation and motion planning problem for a fleet of mobile robots which are requested to operate in an intelligent industry. More specifically, the robots are requested to serve a set of inspection points within given service time windows. In comparison with the conventional time windows, our problem considers fuzzy time windows to express the decision maker’s satisfaction for visiting an inspection point.Design/methodology/approachThe paper develops a unified approach to the combined problem of task allocation and motion planning for a fleet of mobile robots with three objectives: (a) minimizing the total travel cost considering all robots and tasks, (b) balancing fairly the workloads among robots and (c) maximizing the satisfaction grade of the decision maker for receiving the services. The optimization problem is solved by using a novel combination of a Genetic Algorithm with pareto solutions and fuzzy set theory.FindingsThe computational results illustrate the efficiency and effectiveness of the proposed approach. The experimental analysis leverages the potential for using fuzzy time windows to reflect real situations and respond to demanding situations.Originality/valueThis paper provides trade-off solutions to a realistic combinatorial multi-objective optimization problem considering concurrently the motion and path planning problem for a fleet of mobile robots with fuzzy time windows.

Optimization of H-type Anti-slide Pile Support Structure Based on RSM-NSGA-II

The parameters of an h-type anti-slide pile are optimized and analyzed with respect to its structural characteristics. Based on laboratory model tests, further analysis of its stress characteristics is carried out through numerical simulation methods. Then, the response surface methodology (RSM) combined with the NSGAII algorithm was employed to perform multiobjective optimization of the reinforcement performance and engineering cost for h-type anti-slide piles regarding landslide consideration. Finally, the entropy weight TOPSIS method was used for comprehensive evaluation to obtain the optimal structural parameters. The results show that the bending moment distribution of the front and rear rows of h-type piles first increases and then decreases with increasing depth, and the front soil pressure of the pile gradually increases. Using RSM-NSGA-II instead of finite element modeling can shorten the optimization time, and the accuracy of the surrogate model reaches 94.8%. NSGA-II is much stronger than that of the particle swarm optimization algorithm. The entropy weight method combined with the TOPSIS method can obtain the unique optimal solution from the Pareto solution set without prior knowledge. The h-type anti-slide pile with the best structural parameters reduces the cost by 75.19%, while the slope safety factor increases by 47.39%. This method provides a new idea for structural optimization.

An optimization framework for multi-timescale operations of pumped storage systems: Balancing stability and economy

Pumped storage hydropower system (PSHS) has multi-timescale operating characteristics which are divided into hour scale short-term scheduling and second scale power regulation with the objectives of minimizing water consumption and optimizing power regulation characteristics, respectively. However, the operating characteristics of these two scales are often analyzed independently, preventing decision makers from obtaining a strategy with optimal multi-timescale operating characteristics. This paper proposes a novel optimization framework by coupling the second scale model with the hour scale model which balances the stability (power regulation characteristics) with the economy (water consumption). Firstly, the power regulation characteristics of the unit under different operating conditions are summarized in terms of the integrated time and absolute error (ITAE) and maximum deviation of the rotational speed (ntdmax) based on a refined PSHS model. And a novel short-term scheduling model is developed which couples the power regulation characteristics. Secondly, with the novel model, the Pareto solution sets are obtained based on the non-dominated sorting genetic algorithm-III (NSGA-III) with the objective of minimizing the water consumption and ITAE/ntdmax. Finally, by the technique for order preference by similarity to an ideal solution (TOPSIS), the Pareto solution sets are further evaluated to obtain an operating strategy with optimal power regulation characteristics and water consumption. Compared to the traditional solution aiming for the minimum water consumption, this strategy results in a significant improvement in the stability (65.03 % reduction in ITAE and 68.43 % reduction in ntdmax) at the expense of a smaller economic behavior (0.0295 % increase in water consumption). The strategy outstands existing operating rules and innovatively introduces power regulation characteristics to obtain a short-term scheduling strategy that balances stability with economy. It provides a theoretical basis for the multi-timescale operation of PSHS.

Multi-objective optimization of forest ecosystem services under uncertainty

Forest ecosystems deliver multiple services crucial for human wellbeing and welfare, with complex relationships among forest ecosystem services (FESs). Implementing sustainable forest management (SFM) policy requires insights into trade-offs, conflicts and synergies among key FESs, necessitating decision-support tools for multiple objectives. However, uncertainty in key parameters adds complexity. We formulated a tri-objective optimization problem concentrating on three vital ecosystem services in Nordic boreal forests: timber supply, climate change mitigation, and biodiversity conservation. Furthermore, future timber price uncertainty was integrated into the optimization model. Utilizing the TreeSim individual-tree growth and yield simulator, we simulated forest growth and yields, carbon stocks, and biodiversity values. Pareto-optimal solutions were found for four distinct management strategies using the epsilon-constrain method to solve the optimization problem. These management strategies differed in spatial restrictions on harvest location and timing, including considerations like harvest adjacency, green-up and maximum harvest opening area (MOA). The analysis revealed trade-offs among all three objectives, with variations influenced by management intensity. Furthermore, within the Pareto solutions for each strategy, a compromise solution was identified based on the knee-point method. The study demonstrated nuanced impacts of green-up constraints related to harvest practices, showing minor effects on harvesting, carbon sequestration, and biodiversity conservation when MOA was restricted to 35 hectares or less. However, more substantial impacts were observed with a MOA limited to 60 hectares or in a strategy without spatial restrictions. Our results underscore the importance of considering multiple objectives in forest management and policy under uncertain wood prices, preventing undesired effects from a singular or deterministic approach. This work provides insights into trade-offs and synergies, contributing to strategic planning and policy design.

Data-driven urban configuration optimization: An XGBoost-based approach for mitigating flood susceptibility and enhancing economic contribution

The indiscriminate evolution of urban configurations aggravates flood vulnerabilities, threatening sustainable urban expansion. Present methodologies fall short in supplying urban planners with flood mitigative strategies centered on urban configuration facets. Leveraging the power of the XGBoost algorithm, this study posits an advanced optimization schema, adroitly balancing the dual objectives of mitigating urban flooding and enhancing economic growth, with minimal disruption to established urban layouts. Shenzhen serves as the investigative ground, where the model displays exceptional accuracy, resilience, and interpretability in predicting Pluvial Flooding Susceptibility (PFS) and Economic Contribution (EC). Model interpretation divulges the profound influence of three-dimensional urban configuration elements, primarily the Building Congestion Degree, on PFS and EC. Pareto solution exploration for multi-objective optimization unveils the ideal urban configuration interval. To minimize PFS while maximizing EC, the research suggests pertinent measures: augmenting vegetation density, regulating the impervious coverage ratio within 50–70%, limiting two- and three-dimensional building density thresholds, and moderately escalating urban drainage network density. Additionally, it encourages a comprehensive appreciation of function-oriented land usage and intrinsic site topographical characteristics to reconcile varied urban development goals during planning. By fusing data-derived insights with multi-objective optimization, this research anticipates influencing urban planning models, thus enhancing decision-making related to urban configuration and fostering flood-resilient, sustainable, and economically prosperous urban habitats.

Low-velocity impact analysis and multi-objective optimization of hybrid carbon/basalt fibre reinforced composite laminate

Three-dimensional in-plane progressive damage model was developed for carbon/basalt fibre interlayer hybrid composites in this study, and cohesive element model was employed to simulate interlaminar damage. Numerical simulation of low-velocity progressive impact damage of hybrid composite laminate was carried out, and its accuracy was verified by physical impact test, with the maximum error of the maximum contact force, maximum displacement and energy absorption not exceeding 6.1% and the maximum error in damage area size within 4.8%. The effects of lay-up structure and angle on the impact properties of hybrid laminate were investigated through simulation. Finally, real number coding strategy was proposed for the parametric representation of the lay-up material and angle of each layer. Multi-objective optimization of hybrid laminate based on Kriging surrogate model and hybrid algorithm composed of elitist non-dominated sorting genetic (NSGA2) algorithm and multi-objective particle swarm (MPSO) algorithm was conducted. The optimal trade-off solution was selected from the Pareto solutions using technique for ordering preferences by similarity to ideal solution (TOPSIS) coupled with principal component analysis (PCA) methods. The coefficient of variance between peak force and maximum displacement of the optimized laminate was 49.3%, 44.9% and 31.4% lower than those of the pure CFRP laminate, pure BFRP laminate, and hybrid laminate before optimization, respectively, indicating that the balance degree of impact displacement and force has been substantially improved. The progressive impact damage simulation and parametric optimization design methodology proposed in this study provide useful guidance for the design of hybrid composite laminate.

Non-dominated sorting artificial rabbit multi-objective sizing optimization for a conceptual powertrain of a 6 × 4 battery electric tractor truck

In order to tackle the increasingly severe energy crisis, improving the efficiency of the powertrain system in battery electric vehicles has become an effective approach. Based on a 6 × 4 battery electric tractor truck (BETT), the paper focuses on enhancing the dynamic and economic performance of vehicles through advancements in configuration, control strategies, and parameter design. Firstly, a novel multi-motor torque coupling powertrain system based on the parallel-axle transmission is proposed and modeled. Then, an instantaneous minimum energy consumption control strategy for the economic performance simulation and an instantaneous maximum acceleration control strategy for the dynamic performance simulation are designed. Furthermore, a conventional heuristic single-objective optimization algorithm, artificial rabbit optimization (ARO), is improved into a multi-objectives version, non-dominated sorting artificial rabbit multi-objective optimization (NSARMO), by combining the fast non-dominated sorting (FNS) and modifying the calculation method of the energy factor. Finally, an optimization framework consisting of a control layer, model layer, and optimization layer is established and applied to the parameter optimization of the proposed powertrain system. Simulation results demonstrate that the optimization results of the proposed method are superior to those optimized by commonly used non-dominated sorting genetic algorithm-II (NSGA-II) and NSARMO without the modified energy factor, achieving a better balance between dynamic performance and economic performance. Moreover, the proposed method exhibits demonstrates 40.67% and 24.67% improvement in its ability to search for optimal Pareto solutions compared to NSARMO (-)(- means the calculation method of energy factor is not modified) and NSGA-II. At last, a hardware-in-the-loop (HIL) experiment bench is established, and the experiment results indicate that a scheme optimized by the proposed NSARMO exhibits only an approximate performance in energy consumption in the HIL environment compared to the simulation environment, which signifies the effectiveness of control strategy equipped with the optimization results optimized by the proposed method.

Improving PID Controller Performance in Nonlinear Oscillatory Automatic Generation Control Systems Using a Multi-objective Marine Predator Algorithm with Enhanced Diversity

Power systems are pivotal in providing sustainable energy across various sectors. However, optimizing their performance to meet modern demands remains a significant challenge. This paper introduces an innovative strategy to improve the optimization of PID controllers within nonlinear oscillatory Automatic Generation Control (AGC) systems, essential for the stability of power systems. Our approach aims to reduce the integrated time squared error, the integrated time absolute error, and the rate of change in deviation, facilitating faster convergence, diminished overshoot, and decreased oscillations. By incorporating the spiral model from the Whale Optimization Algorithm (WOA) into the Multi-Objective Marine Predator Algorithm (MOMPA), our method effectively broadens the diversity of solution sets and finely tunes the balance between exploration and exploitation strategies. Furthermore, the QQSMOMPA framework integrates quasi-oppositional learning and Q-learning to overcome local optima, thereby generating optimal Pareto solutions. When applied to nonlinear AGC systems featuring governor dead zones, the PID controllers optimized by QQSMOMPA not only achieve 14%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document} reduction in the frequency settling time but also exhibit robustness against uncertainties in load disturbance inputs.

Customised product design optimisation considering module synergy effects and expert preferences

ABSTRACT Fierce marketing competition and varied customer requirements on products make a lot of companies transfer to the customisation strategy. However, customers may be overwhelmed by the vast assortment of products and options. This paper proposes a methodology aimed at optimising the range of customised product varieties considering synergy effects of modules and preferences of experts. The methodology outlines key steps required for a successful customised product configuration. Firstly, a questionnaire based on the Kano model is designed to identify customer preferences for product module customisation. The potential customers can be segmented based on the distance among their multidimensional preferences. Secondly, within each segmented market, the customer satisfaction function that considers module synergies is established using the quantified Kano model and coefficient matrix. Thirdly, the cost function that considers experts' preferences is established based on the prospect theory. Finally, a bi-objective optimisation model is formulated to maximise customer satisfaction and minimise cost under technical constraints. Pareto solutions are obtained by solving the model with the non-dominated sorting genetic algorithm II (NSGA-II). Modules and attributes available to customers can be determined by the solutions. An illustrative example of modular laptop computers confirms the methodology's effectiveness in optimising product configuration.

Multi-objective location-routing model and algorithm study of material reserve bases for large-scale railway engineering construction projects

Material supply is an important support for engineering construction and an important factor affecting the progress and quality of engineering construction. A multi-objective mixed-integer nonlinear programming model is proposed for the location routing problem of the material reserve base of large-scale railway engineering construction projects, considering realistic factors like the construction period, the cycle of the material reserve, the variety of materials, the heterogeneous fleet, and demand splitting. An improved Non-dominated Sorting Genetic Algorithm-II (NSGA- II) is developed for solving this model. This paper optimises obtaining the initial population based on the linear feature of railway engineering, improves the fitness function, and designs a two-stage crossover operator. In addition, the algorithm is compared with the augmented ϵ-constraint method with the help of a practical example. Three metrics are used to assess the performance of the algorithm's outputs, and two metrics are used to assess the similarity of the Pareto fronts obtained by the two algorithms. The results show that the proposed algorithm performs better in terms of ‘quantity’ and ‘spacing’, that the Pareto solutions obtained are accurate, and that the speed of solution is almost 10 times that of the augmented ϵ-constraint (AUGMECON) method.

Industrial Park low-carbon energy system planning framework: Heat pump based energy conjugation between industry and buildings

The accelerating urbanization, rapid industrial development, and excessive consumption of fossil fuels pose survival challenges such as energy depletion and environmental degradation for humanity. In the context of industrial park development, constructing a low-carbon energy system, increasing the proportion of renewable energy, enhancing energy-level matching, and utilizing heat pumps for deep waste heat recovery are effective approaches to reduce fossil energy consumption and alleviate environmental pressures. Addressing issues such as diverse thermal flows in industrial sites, complex electricity-heat-cooling energy demands, and unclear industrial-building energy coupling mechanisms, this paper proposes a two-stage planning framework, comprising the following five steps: (1) constructing a waste heat utilization system centered around heat pumps, (2) establishing a mechanism for matching heat sources, equipment, and thermal sinks, (3) establishing an energy conversion model and energy quality quantification system, (4) optimizing waste heat utilization path allocation, and (5) conducting a system energy flow analysis. Case studies demonstrate that the proposed system achieves optimized matching of multiple heat sources and sinks in industrial and building scenarios through thermal integration, meeting diverse energy demands in the park, including electricity, cooling, and multi-grade heat. After coupling with traditional steam pipeline networks, the annual total cost and annual steam power consumption decrease by 33% and 39% respectively, with a waste heat contribution rate of up to 26% and a renewable energy penetration rate of up to 25%, and a waste heat recovery system payback period of 6 years. By establishing an energy quality quantification system and conducting multi-objective optimization considering losses and economic costs, this paper provides Pareto frontier solutions, offering references for engineering proposals. The proposed networked waste heat recovery system is characterized by low energy consumption and high economic efficiency, effectively integrating the energy characteristics of industrial parks and demonstrating engineering applicability.

Enhancing mix proportion design of low carbon concrete for shield segment using a combination of Bayesian optimization-NGBoost and NSGA-III algorithm

The demand for segment concrete increases rapidly with the expansion of urban rail transit and underground space, which may lead to carbon emissions (CE). In the production of segment concrete, using supplement cementitious materials (SCM) can be used to reduce CE instead of cement. However, SCM contents are usually determined by many orthogonal experiments, which are often time-consuming and only consider the limited experimental variables. Therefore, a novel hybrid intelligent algorithm combining Bayesian optimization (BO), natural gradient boosting (NGBoost) and non-dominated sorting genetic algorithm (NSGA)-III is proposed, which overcomes these disadvantages. Firstly, NGBoost model after hyperparameter optimization using BO is used to establish a nonlinear mapping relationship between segment concrete mix proportion and performance, which was used as the fitness function of the non-dominated sorting genetic algorithm (NSGA-III). Secondly, the optimal Pareto solutions were obtained through NSGA-III, and the reasonable range of segment concrete mixing proportion was obtained. Finally, a segment concrete production case was used to verify the effectiveness of the proposed algorithm. The results showed that the proposed hybrid algorithm combining proposed scheme decision strategy can obtain an optimal design scheme for concrete mix proportion. In addition, the comprehensive optimization rate of the obtained optimal scheme compared to the experimental optimal group was 11.5%. Moreover, the amount of phosphorous slag (PS) and granulated blast furnace slag (GBFS) in the optimal scheme was 26%, with a mass ratio of 1:2. Compared to the experimental optimal group, the optimal scheme can reduce the cost and CE per cubic meter by 31.64 yuan and 31.04 kg, respectively. Furthermore, the hybrid algorithm proposed can accurately obtains an optimal amount of SCM, which could be used as a supporting tool to reduce the production cost and CE of segment concrete. Overall, this research contributes to combining machine learning algorithms with actual production processes, which overcomes the data limitations of traditional experiments. It also provides a new intelligent approach and reference cases for the low-carbon design and sustainable development of building materials such as concrete.

Finding a Small, Diverse Subset of the Pareto Solution Set in Bi-Objective Search (Extended Abstract)

Finding a Small, Diverse Subset of the Pareto Solution Set in Bi-Objective Search (Extended Abstract)

Designing a resilient-sustainable integrated broiler supply chain network using multiple sourcing and backup facility strategies dealing with uncertainties in a disruptive network: A real case of a chicken meat network

Increasing supply and demand uncertainty, coupled with unforeseen disruptions, pose challenges to the resilience of today's critical sectors in the global food industry, including the broiler supply chain. This study introduces a resilient model to enhance the sustainability and resilience of the broiler supply chain in the face of uncertainties and disruptions. The model integrates backup facilities and employs multiple sourcing strategies to reinforce resilience. Using mixed integer linear programming with bi-objective, multi-period, and multi-product features, the model aims to minimize carbon dioxide (CO2) emissions from transportation while maximizing overall supply chain profit. The goal programming, and the ε-constraint methods optimize decision-making and yield Pareto solutions, achieving a balanced approach to conflicting objectives. Also, robust optimization and stochastic programming provide practical solutions for handling uncertainties. Validation and sensitivity analysis confirm that the proposed model optimizes the broiler supply chain, enhancing resilience, sustainability, and profitability.

Design method for suspension parameters of high-speed railway vehicles considering uncertainties

A design method for suspension parameters is proposed to ensure the desired performance of a railway vehicle despite uncertainties. The method used in this study consists of two loops: a sub-loop, which uses parameter uncertainties to determine the minimum value of target performance, and a main loop, which optimises suspension parameters such that the minimal performance achieves Pareto optimality. Thus, by selecting a suitable Pareto solution that ensures the minimum performance is equal to or higher than the required performance, the robustness of the designed vehicle against the parameter uncertainties can be achieved. The lowest low-frequency damping ratio in the service speed range was selected as one of the design targets. The other target was the critical speed. Two wheel-rail contact characteristics were applied, considering the worst conditions for each design target. The distribution of the parameter uncertainties that minimised the vehicle performance showed distinct characteristics between the longitudinal and lateral suspension parameters, which provides useful information for the maintenance of railway vehicles. The performance analysis for 100,000 random samples shows that the vehicle performed better than the targets with a high probability despite the parameter uncertainties. Further, the simulation results using multi-body dynamics simulation software validated the viability of the proposed method.

Bi-Objective Battery Electric Truck Dispatching Problem with Backhauls and Time Windows

The battery electric truck (BET) has emerged as a promising solution to reduce greenhouse gas emissions in urban logistics, given the current strict environmental regulations. This research explores the formulation and solution of the bi-objective BET dispatching problem with backhauls and time windows, aiming to simultaneously reduce environmental impacts and enhance the efficiency of urban logistics. From the sustainability perspective, one of the objectives is to minimize total energy costs, which include energy consumption and battery replacement expenses. On the other hand, from an economic perspective, the other objective is the minimization of labor costs. To solve this bi-objective BET dispatching problem, we propose an innovative approach, integrating an adaptive large neighborhood search-based metaheuristics algorithm with a multi-objective optimization strategy. This integration enables the exploration of the trade-off between fleet energy expenses and labor costs, optimizing the dispatching decisions for BETs. To validate the proposed dispatching strategy, extensive experiments were conducted using real-world fleet operations data from a logistics fleet in Southern California. The results demonstrated that the proposed approach yields a set of Pareto solutions, showcasing its effectiveness in finding a balance between energy efficiency and labor costs in urban logistics systems. The findings of this research contribute to advancing sustainable urban logistics practices and provide valuable insights for fleet operators in effectively managing BET fleets to reduce environmental impacts while maintaining economic efficiency.

Optimization of hydrogen refueling strategy: Based on energy consumption and refueling demand

The energy and economic viability of hydrogen refueling stations (HRSs) hold significant importance during their promotion. The cascade hydrogen storage system is advantageous in reducing energy consumption and finds widespread application in HRS. Within the cascade hydrogen storage system, varying pressure switch difference values (PSDVs) correspond to different energy consumptions. Simultaneously, HRS must meet the demand for hydrogen refueling. Therefore, the primary objective of this study is to establish an optimization method for PSDV, aiming to optimize energy consumption while satisfying hydrogen refueling demand. In this study, an HRS simulation model was established using the MATLAB/SIMULINK platform to evaluate the effects of PSDV on energy consumption and refueling time. Accordingly, a BPNN proxy model was built to predict these outcomes. On the basis of the proxy model, the Pareto solution set of PSDV was obtained through NSGA-Ⅱ. Finally, the ideal point estimation method was integrated to assist the decision-makers in determining the refueling strategy. The proposed optimization strategy is capable of reducing energy consumption while still meeting the hydrogen refueling demands of HRS, resulting in a maximum energy reduction of 10.76%.

Performance enhancements of power density and exergy efficiency for high-temperature proton exchange membrane fuel cell based on RSM-NSGA III

In this study, a three-dimensional simulation model was developed and a multi-objective optimization of a single-channel high-temperature proton exchange membrane fuel cell (PEMFC) was carried out by the response surface methodology (RSM) and the non-dominated genetic algorithm III (NSGA III). Firstly, five main influencing factors including operating temperature (T), operating pressure (p), gas diffusion layer porosity (εGDL), proton exchange membrane (PEM) thickness (Mmem) and anode stoichiometry ratio (λa) were identified. The optimization objectives include three cell performance evaluation indexes: power density (wpow), system efficiency (ηsystem), and exergy efficiency (ηexergy). Secondly, the prediction accuracies of the RSM and artificial neural network (ANN) for the three performance evaluation indexes of high-temperature PEMFC were compared. Finally, the optimal solution from the Pareto solutions derived through RSM-NSGA III. The results show that the maximum wpow, maximum ηsystem and maximum ηexergy are 0.793 W cm−2, 22.31 % and 54.69 %, respectively. The optimal result obtained by combining EWM and VIKOR is wpow = 0.6726 W cm−2, ηsystem = 19.44 % and ηexergy = 54.01 %, respectively. The corresponding condition is T = 447.18 K, p = 1.15 atm, εGDL = 0.617, Mmem = 0.0412 mm, and λa = 1.26, respectively. Moreover, the suggestions are provided for the design of more efficient high-temperature PEMFC.