Multi-objective Optimization Research Articles (Page 1)

In this study, distributed generators (DGs) based on renewable energy sources (RESs), besides capacitor banks are optimally allocated in power distribution networks with a proposed multi-objective optimization approach. The proposed approach is used to maximize the hosting capacity (HC) of RES DGs besides decreasing energy loss and voltage deviation in power networks. Uncertainties of load demand and RESs are considered. To facilitate the optimization processes, reduction criterion is utilized for reducing the numerous numbers of uncertain data. The proposed approach is applied to practical and standard power networks for many cases under the uncertain scenarios. Comparative study with other algorithms is performed and robustness of proposed approach is verified in long-term dynamic environment. Also, impacts of changing parameters values on performance are investigated. Additionally, Wilcoxon statistical tests are applied with the proposed approach. Also, comparative study is carried out between weighted sum and Pareto front techniques. Results reveal efficacy of the proposed approach with distribution power networks.

ABSTRACT Used electromechanical products containing hazardous components pose a significant threat to both the environment and human health. Therefore, society must emphasize and explore strategies for constructing a recycling network to enhance the recycling efficiency of used electromechanical products. In this paper, we propose a multi-institutional recycling network that includes recycling centers, reprocessing centers, and disposal centers, with recyclers responsible for the recycling operations. To enhance the effectiveness of this recycling network, we establish three optimization objectives: economic, environmental, and social. We develop a multi-objective mathematical optimization model specifically designed for the recycling network of used electromechanical products. This model aims to assist government entities and recyclers in addressing environmental challenges while simultaneously balancing economic and social impacts. By applying the multi-objective Gray Wolf optimization algorithm, we analyzed the results pertaining to the utilized electromechanical products. A sensitivity analysis was conducted on key parameters, which illuminated the relationships among economic costs, carbon emissions, and employment opportunities, thereby confirming the model’s validity and practicality. Implications: This study on recycling networks for used electromechanical products holds significant implications. It promotes a circular economy by reducing primary resource use and environmental pollution. The network fosters a new industrial chain for recycling, dismantling, and remanufacturing, which can stimulate large-scale industry growth and create employment. Furthermore, the research aligns with national strategies like China’s “14th Five-Year” Plan, providing insights to help refine recycling policies and accelerate the development of a comprehensive waste materials recycling system.

Abstract Aerodynamic heaters are widely used in industrial applications, such as gas preheating, mine ventilation, and circulation drying, serving as critical gas heating equipment. Improving their efficiency is of great significance for energy conservation and emission reduction. However, despite their industrial importance, studies on the impact of blade geometry on the thermal and flow performance of aerodynamic heaters have not yet been reported. To address this gap, this study proposes a novel multi-objective optimization framework to enhance the heating performance and energy efficiency of aerodynamic heater blades. Parametric modeling of the heater was conducted using inlet angle, outlet angle, and blade height as design variables, with temperature and velocity as optimization objectives. A surrogate model was constructed using fuzzy C-means clustering, combined with the Non-Dominated Sorting Genetic Algorithm II (NSGA-II) for multi-objective optimization. The optimization results demonstrate that the redesigned blades significantly improve temperature and velocity distributions, enhance heat diffusion and fluid mixing, improve outlet flow stability, and reduce energy losses. Compared to the original model, the thermal efficiency of the optimized aerodynamic heater increased by 3%, while the heat flux density improved by 4%. This study provides a robust theoretical foundation for the optimal design of aerodynamic heater blades, offering valuable support for energy efficiency improvements in industrial applications.

ABSTRACT The economic viability of extracting tight gas reservoirs has been enabled by the combination of horizontal drilling and multi-stage hydraulic fracturing. The traditional optimization design of fracture parameters relies solely on engineers’ empirical judgment, resulting in poor accuracy. To enhance the accuracy of optimization, it is imperative to determine the optimal values of these parameters and evaluate their impacts on well performance as well as economic feasibility. Therefore, this study establishes a horizontal well fracturing model and introduces a multi-objective optimization strategy to explore the influence of fracture number, fracture half-length, fracture spacing and fracture conductivity on gas reservoir productivity. Four optimization algorithms are employed to determine the optimal fracture parameters, addressing the limited consideration of economic factors in previous optimization studies. The results show that the length of the horizontal section is 1000.9 meters, the half-length of the fracture is 124.2 meters, the number of fractures is 10, the fracture conductivity is 8.2 μm2 · cm and the fracture spacing is 82.4 meters. The necessity of parameter design using multiple optimization algorithms is elaborated, offering a theoretical basis and technical reference for the efficient development of unconventional gas reservoirs.

Under the "dual carbon" goal, the mismatch between the intermittent nature of wind-solar power generation and the stable energy demand of oil wells hinders efficient green energy utilization in oilfields, leading to low green electricity consumption, high curtailment rates, and poor economic benefits. To address this challenge, an optimization approach for oil well operation scheduling is proposed, which couples photovoltaic power fluctuations with the characteristics of intermittent pumping technology. Firstly, a multiobjective optimization model was developed to minimize grid electricity consumption per unit of liquid production and maximize the share of green electricity. The on-off schedule was mapped into a constrained binary sequence using a run-length encoding to reducing the solution space. Non-dominated Sorting Genetic Algorithm II (NSGA-II) was improved to increase both accuracy and convergence speed by introducing: (1) dual-mode initialization strategy guided by historical operating schedules and photovoltaic fluctuations. (2) a key-gene-preserving crossover operator to retain high-matching time segments; and (3) a peak-valley-guided mutation strategy to enable dynamic pruning of the solution space and goal-directed optimization. Case studies showed that the proposed method doubled green electricity consumption under stable production conditions, reduced grid electricity consumption per unit liquid by 41.67%, improved computational efficiency by two to three orders of magnitude, and enhanced the solution accuracy by 26.69%, indicating strong practical applicability.

The allocation of personnel and lift (elevator) maintenance route planning rely heavily on manual scheduling, leading to unbalanced workloads. Therefore, a route planning method for lift maintenance is proposed. Task precedence and multiple maintenance stations are considered from the perspective of workload balance. First, a multi-objective optimization model considering task precedence and multiple maintenance stations is established, with the objective of minimizing the total maintenance distance, total number of tasks assigned to maintenance personnel and standard deviation of the working time of each person. Then, an improved parallel two-population multi-objective genetic algorithm (IP-NSGA-II) is developed to solve the constructed model. Finally, the decomposition method is compared with the global method. The results show that the decomposition method is better than the global method under the same iteration number, and that IP-NSGA-II is better than the non-dominated sorting genetic algorithm-II (NSGA-II). The proposed method provides a valuable reference for planning lift maintenance routes.

In the field of multi-objective evolutionary optimization, prior studies have largely concentrated on the scalability of objective functions, with relatively less emphasis on the scalability of decision variables. However, in practical applications, complex optimization problems often involve multiple objectives and large-scale decision variables. To address these challenges, this paper proposes an innovative large-scale multi-objective evolutionary optimization algorithm. The algorithm utilizes clustering techniques to categorize decision variables and introduces a novel dominance relation to enhance optimization efficiency and performance. By dividing decision variables into convergence-related and diversity-related groups and applying distinct optimization strategies to each, the algorithm achieves a better balance between convergence and diversity. Additionally, the algorithm incorporates a new angle-based dominance relationship to reduce dominance resistance during the optimization process. Experimental results on multiple mainstream multi-objective optimization test sets, such as standard DTLZ and UF problem sets, indicate that CLMOAS achieves smaller IGD values relative to mainstream algorithms such as MOEA/D and LMEA, thereby demonstrating that the proposed algorithm outperforms several existing multi-objective evolutionary algorithms and showcases its effectiveness in solving complex optimization problems with multiple objectives and large-scale decision variables.

Purpose This paper aims to propose a structured method to support decision-making in complex operational contexts by improving the efficiency of multi-objective simulation optimization (MOSO). The focus is on helping managers and analysts handle large-scale decision problems with high-dimensional search spaces, often present in production and logistics systems. Design/methodology/approach The proposed method integrates Latin hypercube design (LHD) and data envelopment analysis with variable returns to scale (DEA-VRS), including super-efficiency analysis, to identify promising regions in the search space. The approach was applied to two real-world case studies in logistics and manufacturing environments. Findings The proposed method achieved a substantial reduction in the search space, ranging from 70% to 89%, and reduced the number of optimization experiments by up to 31%. In both case studies, the reduced search space led to improved outcomes across most optimization profiles. In the logistics case, costs decreased by up to 10%, and the quantity shipped increased by up to 219%. In the manufacturing case, lead time was reduced by up to 26% while maintaining the same production output, demonstrating enhanced computational efficiency without compromising solution quality. These results confirm that the method enhances computational efficiency without compromising solution quality in complex MOSO scenarios. Practical implications The method enabled the identification of high-quality solutions with significant operational benefits. These improvements were achieved using fewer simulation runs, up to 31% less, demonstrating the method’s ability to accelerate decision-making and reduce computational effort. Its integration with existing simulation platforms and consistent performance across diverse optimization profiles make it a valuable tool for supporting data-driven decisions in complex operational environments. Originality/value This study introduces a novel combination of LHD and DEA-VRS to enhance the performance of simulation optimization methods. It contributes to both the fields of operations research and operations management by offering a robust, interpretable and computationally efficient framework for solving complex MOSO problems in industrial applications.

The valve lift profile plays a crucial role in the gas exchange process of natural gas engines, as well as in the operational stability of the valve mechanism. Through optimization and design of the valve lift profile, it is possible to effectively reduce engine gas exchange loss, enhance engine power output, and improve the operational stability of the valve mechanism. This study establishes a simulation model for a natural gas engine, which is validated against experimental data. The impact of various parameters on engine performance is explored using a parametric method and experimental design. The paper focuses on optimizing the valve lift profile at a typical operating point, with targets of minimizing brake-specific fuel consumption and NOx emissions. The non-dominated sorting genetic algorithm was employed to optimize the valve lift profile. Given that the optimized lift curve alters the original kinematic characteristics, an impact-free function cam design method was adopted to perform the forward design of the optimized curve, followed by a comprehensive valve motion verification. The results show that the fullness coefficient of the optimized exhaust valve lift profile increased from 0.609 to 0.637, and the fullness coefficient of the intake valve lift profile improved from 0.578 to 0.608. The larger fullness coefficient indicates improved engine gas exchange performance. At 90.9% load, the brake-specific fuel consumption of the natural gas engine decreased by 2.76%, and NOx emissions were reduced by 22.93%. The valve lift profiles designed using the cam method with the impact-free function achieved third-order continuity in lift, velocity, and acceleration. This ensures smoother operation of the engine valve mechanism and prevents abnormal vibration.

Path planning for unmanned aerial vehicles (UAVs) in mountainous environments requires satisfying terrain clearance and obstacle avoidance constraints while optimizing path length, flight time, and energy consumption. To address these challenges, this paper proposes EC-MOPSO (Epsilon-dominance and Crowding-distance-based Multi-Objective Particle Swarm Optimization). Inspired by the principle of symmetry, the algorithm integrates an adaptive parameter adjustment mechanism with a ε− dominance–crowding archiving strategy to balance global exploration and local exploitation through spatially symmetric archive management. A safety-repairable B-spline trajectory model ensures smooth and feasible flight paths under complex terrain conditions. Simulation results show that EC-MOPSO reduces path length by 10–40%, improves normalized hypervolume by over 25%, and decreases performance variance by 20–25%, confirming faster convergence and higher robustness compared with representative multi-objective optimization approaches. Ablation studies further verify that both the adaptive parameter mechanism and the ε− dominance–crowding strategy significantly enhance convergence stability and overall optimization performance. Overall, EC-MOPSO provides an adaptive and reliable optimization framework for generating efficient, safe, and energy-aware UAV trajectories in real-world mountainous rescue missions.

With the progress of science and technology, how to optimise the production of electronic products has become a very important issue, because it can control the quality of parts and reduce the cost. This paper investigates the production optimization of electronic products and analyzes the defective parts rate and finished product rate of spare parts through Monte Carlo, binomial distribution and multi-objective optimization models. A hierarchical decision-making model is established to optimize the production stages, and the total cost and net profit for six cases are calculated by combining heuristic decision-making and iterative optimization. Finally, decision trees and multi-objective optimization were used to determine the optimal failure rate. It was found that spare parts should be rejected at 95% confidence level and acceptable at 90% confidence level, with case 5 having the highest net profit and the optimal failure rate threshold of 0.01, which helps to improve the quality of parts and reduce costs.

ABSTRACT In recent years, the use of Unmanned Aerial Vehicles (UAVs) for remote sensing and aerial photogrammetry has surged, owing to their affordability and ability to capture high-resolution data in hard-to-reach areas. However, the effectiveness of these platforms can be limited by environmental factors such as turbulence and wind gusts, which may destabilize the aircraft and compromise the proper exposure of images. To address this issue, this work presents a terrain survey planner that considers the environmental conditions derived from a meteorological forecast. The system employs Computational Fluid Dynamics (CFD) simulations to generate high-resolution wind predictions for a given study area. This data is integrated into a state-of-the-art UAV simulator to estimate aircraft behaviour at various locations. Additionally, it incorporates an empirically calibrated camera model to predict sensor performance based on solar radiation estimates. With this information, a multi-objective optimization is performed, computing the optimal path and camera settings to mitigate the impact of wind on photogrammetry. Results highlight the significant impact of wind and poor lighting on motion blur, emphasizing the need to carefully plan not only the inspection path but also the time and date for correct image exposure.

Abstract This paper focuses on the expansion train designed for the Compressed Air Energy Storage (CAES) concept under development in the EU-funded ASTERIx-CAESar project. The system integrates concentrated solar thermal energy from a high-temperature (800°C) volumetric central-receiver into a hybrid storage configuration, combining Low-Temperature Thermal Energy Storage (LT-TES) with Compressed Air Storage (CAS) and High-Temperature Thermal Energy Storage (HT-TES). Electricity from the grid powers compressors during low-price periods, storing compressed air and recovering compression heat in LT-TES. Solar heat is stored in HT-TES. During discharge, preheaters and reheaters supply stored energy to the expansion train. Residual energy in the exhaust of the low-pressure turbine reduces round-trip efficiency; therefore, a bottoming Waste Heat Recovery (WHR) unit based on Organic Rankine Cycle (ORC) technology is assessed. Multiple air-cooled configurations are modelled for Expander Exit Temperatures (EET) of 300-600°C, using organic fluids and steam in subcritical, transcritical and supercritical layouts. Scale effects on expander type (screw or axial) and isentropic efficiency are considered for capacities from 1 to 100 MWe. A multi-objective optimisation of the bottoming cycle considers technical and economic aspects to maximise efficiency and heat recovery by adjusting vapour generator pressure/temperature. A global optimisation of the expansion train identifies the optimal cycle configuration for each EET and scale, integrating the WHR system with a two-stage turbine. Recommendations to improve CAES system efficiency are provided.

A collaborative control strategy combining the hyperbolic sine-cosine optimization (SCHO) algorithm with fuzzy adaptive linear active disturbance rejection control is proposed to address the nonlinearity and uncertainties in the hydraulic position servo system of shock absorber test benches. First, based on the dynamic characteristics of the shock absorber fatigue test bench and the tested shock absorber, a linearized model of the valve-controlled hydraulic cylinder and its load was established. The coupling mechanism of system parameter perturbation and disturbance was also analyzed. A third-order LADRC (Linear Active Disturbance Rejection Control) was designed considering the linear model characteristics of the test bench hydraulic servo system model to quickly estimate internal system disturbances and perform real-time compensation. Secondly, a multi-objective optimization function was constructed by integrating system performance indicators and incorporating controller and observer bandwidths into the optimization objectives. The SCHO algorithm was used for the global search and optimization of key LADRC parameters. To enhance the controller’s adaptive capability of modeling uncertainties and external disturbances, a fuzzy adaptive module was introduced to adjust control gains online according to errors and their rates of change, further improving system robustness and dynamic performance. The results show that compared with traditional PID, under different working conditions, the proposed method reduced the maximum tracking error, overshoot, and system response time by an average of 45%, from 15% to 5%, and by approximately 30%, respectively. Meanwhile, the parameter combination obtained via SCHO effectively avoids the limitations of manual parameter tuning, significantly improving control accuracy and energy utilization. The simulation results indicate that this method can significantly enhance position-tracking accuracy compared with traditional LADRC, providing an effective solution for position-tracking control in hydraulic servo testing systems.

Abstract The stronger coupling between the turbomachinery and the air inlet becomes more relevant in next-generation turbofan engines with low-pressure ratio fans and compact nacelles. This study presents a numerical investigation of the interaction between a transonic fan and a short aero-intake in terms of intake geometric design and fan modeling. The inlet design space is first explored at cruise and take-off conditions, and the three-dimensional geometry is optimized in a multi-point and multi-objective formulation using a Bayesian solver to minimize the inlet distortion at take-off and the total pressure losses at cruise. Flow coupling at high incidence is ensured through a Body Force Model of the fan. The Pareto frontier highlights the conflicting nature of intake design between high incidence and high speed performance. A selected individual from the Pareto is further examined by running unsteady full-annulus sliding-mesh simulations at high angle of attack upon inlet separation. The detailed comparison of the flow structures and the turbomachinery performance indicates an accurate reproduction of the inlet flow coupling through the body force model. Although lacking in fully replicating specific flow features near the tip of the blade, the simplified method allows reconstructing the blade response to inlet distortion and capturing the main flow structures. The study thus highlights the suitability of the adopted approach to simulate the mutual interaction between the fan and the inlet flow and provides an efficient method for the optimization of short-intake designs.

Model-aware Deep Learning (DL) accelerators surpass generic ones in terms of performance and efficiency. These model-aware accelerators typically comprise multiple dedicated Compute Engines (CEs) to handle the varying computational characteristics of the operations within a DL model. Multiple-CE accelerators usually target Field-Programmable Gate Arrays (FPGAs), as FPGAs’ reconfigurability enables tailoring the CEs architectures to the varying computational characteristics of the model operations. The continuous evolution of DL models and their use in application domains with diverse optimization objectives, including low latency, high throughput, and energy efficiency, makes it challenging to identify highly optimized multiple-CE accelerator architectures. The design space of multiple-CE accelerators is vast, and the state of the art explores only limited parts of this space, which hinders the identification of accelerators with high performance and efficiency. To address this challenge, we propose a framework for exploring the design space of FPGA-based multiple-CE accelerators (MC E xplorer). MC E xplorer comprises a set of single and multiobjective optimization heuristics that target throughput, latency, energy efficiency, and trade-offs among these metrics. MC E xplorer searches for optimized multiple-CE accelerator architectures given a DL model, a hardware resource budget, and a single or multiple objectives. MC E xplorer explores a space beyond that explored in the literature by not restricting the accelerator inter-CE arrangements and exploring distinct configurations of individual CEs. We evaluate MC E xplorer with various DL models and hardware resource budgets. The evaluation shows that by exploring a search space beyond that in the literature, MC E xplorer identifies highly optimized multiple-CE accelerators. These accelerators achieve up to 2.8 × throughput improvement, 2.1 × speedup, and \(45\% \) energy reduction compared to the state of the art. Moreover, the evaluation demonstrates that broad space exploration is key to identifying multiple-CE accelerators with the best performance-efficiency trade-offs. MC E xplorer code is available at https://github.com/fqararyah/MCExplorer.

In this paper, the Probabilistic Multi-Objective Optimization method (PMOO) is applied to perform the optimal allocation of clean energy with multiple objectives. A solar photo-thermal system, wind energy, and a comprehensive energy storage system for photo-thermal power generation are involved. In PMOO, a new concept of "preferable probability" is put forward to address the preference degree of an attribute of a candidate and the corresponding evaluation method and attributes of the alternative scheme are divided into two types, i.e., beneficial type and unbeneficial (cost) type of attributes, and the corresponding evaluation algorithms of their partial preferable probability are formulated quantitatively. The total preferable probability of each alternative scheme is the product of all possible partial preferable probability, which is employed as the unique indicator to conduct the ranking of the optimization. In the application of optimum allocation problem of clean energy, the solar energy assurance rate and efficiency index of the heating system are the optimal criteria to be maximized, while the heat collecting area of solar collector, the heating capacity of heat pump and the volume of water tank for heat storage are used as input parameters. Especially, the range analysis of the total preferable probability of each alternative scheme is conducted using orthogonal experimental design. The result indicates the optimum configuration for this allocation of clean energy design. Alternatively, in the application of wind-photo-thermal power generation and storage comprehensive energy system problem, both carbon emissions and total operating costs are the optimization criteria to be minimized for the three scenarios, yielding an optimal configuration.

Background The rapid development of information technology has significantly propelled the integration and evolution of product design technologies and their related algorithms. This review systematically investigates the pivotal role of AI-driven product form generation technologies in promoting industrial design innovation and sustainable development. Methodology By employing bibliometric tools (Citespace) combined with visualization analysis, we propose a seven-stage technical framework encompassing “identification-extraction-analysis-generation-data mapping-decision-making-optimization.” Results The study traces the historical evolution, current research trends, and future development of product form generation design technologies. It highlights that artificial intelligence, as the core driving force, has substantially enhanced automated modeling and multi-objective optimization capabilities. However, challenges remain in areas such as data standardization deficits, limited dynamic adaptability, and insufficient cross-disciplinary collaboration. Future priorities should include: (1) strengthening algorithmic robustness to manage complex design scenarios; (2) integrating multimodal user feedback mechanisms to elevate interactive experiences; (3) constructing interpretable generative models to ensure design credibility; and (4) exploring green design-oriented intelligent algorithm deployment strategies with embedded ethical considerations.

Purpose This study aims to address the key challenges in multi-unmanned aerial vehicle (UAV) data sensing systems, where energy-constrained UAVs require real-time trajectory optimization to simultaneously maximize coverage efficiency and minimize energy consumption. Traditional centralized optimization approaches struggle with scalability and computational complexity due to the non-convexity and high dimensionality of the joint optimization problem. To overcome these limitations, the authors propose a distributed multi-agent deep reinforcement learning (MADRL) framework that leverages the autonomous decision-making capability of deep reinforcement learning to achieve distributed continuous action control of UAVs, thereby enabling efficient autonomous deployment. Design/methodology/approach This study proposes a multi-UAV energy-efficient data collection scheme (multi-UAV E2DC) based on an MADRL algorithm. The proposed approach enables UAVs to dynamically collect data from multiple ground sensors while accounting for practical constraints such as communication range, motion limits and energy consumption. To achieve this, the authors first construct a multi-objective optimization model by integrating an air-to-ground communication model with a UAV energy consumption model. Building on this foundation, the authors further develop an enhanced MADRL algorithm within a centralized training and decentralized execution (CTDE) actor-critic framework, which supports efficient continuous trajectory control and deployment of multi-UAV. Findings Extensive simulations demonstrate that the proposed approach achieves superior performance in multi-objective optimization compared to benchmark methods, including random policy, K-means clustering and multi-agent deep deterministic policy gradient. Specifically, the proposed method outperforms in terms of average coverage density, data volume and coverage energy efficiency index. Originality/value This study proposes an MADRL-based energy-efficient data collection framework for UAVs, which integrates air-to-ground communication and UAV energy consumption models to formulate a multi-objective optimization problem. By adopting a CTDE framework for continuous trajectory control, it effectively overcomes the computational challenges of traditional non-convex optimization methods in complex environments. The proposed approach offers a theoretically sound and practically applicable solution for distributed UAV sensing in extreme disaster scenarios.

Abstract Floating Zone (FZ) silicon crystal growth is essential for high‐power electronics and advanced detection systems. The increasing pressure to scale up the process is challenging due to competing objectives. This study presents a surrogate‐based optimization framework to address Multi‐Objective Optimization (MOO) in FZ growth, considering eight relevant objectives related to productivity, geometrical and growth parameters, and crystal quality. A Deep Ensemble (DE) of Neural Networks serves as a surrogate model, trained on numerical data from a Finite Element Model (FEM). Optimization is carried out using NSGA‐II and NSGA‐III, two variants of Genetic Algorithms that explore trade‐offs between competing objectives and identify high‐performing candidate solutions. Results show that NSGA‐II outperforms NSGA‐III. The optimal solutions correctly capture known trends, such as correlations between crystal size, pulling rate, and thermal stress. A subset of the more intricate solutions is validated through new simulations, showing excellent prediction performance. However, candidate solutions must still be verified by the FEM prior to experimental validation. This framework establishes a foundation for systematic, data‐driven process optimization in FZ growth and can be extended to accelerate improvements in other crystal growth methods.