Multi-objective Optimization Method Research Articles

Stochastic two-stage multi-objective unit commitment of distributed resource energy systems considering uncertainties and unit failures

Compared to centralized generation technology, distributed energy resource systems are susceptible to energy risks caused by boundary uncertainties and unit failures. This study introduces a stochastic two-stage multi-objective optimization method to address reliability-based unit commitment issues. In the day-ahead stage, operational state and reserve capacity are determined to minimize prescheduled operation costs based on forecasted parameters. In the real-time stage, a decision-dependent stochastic reliability method is proposed to simulate outage scenarios. Reserve resources within available units are allocated to mitigate forecasting errors and unit failures. Additionally, the grid interaction ratio and penalty cost are added to restrict the depth and frequency access to the grid. Four comparative cases analyze the effects of the proposed methodology. This method innovatively achieves the simulation of stochastic multi-unit outages and delete faulty units in the operation scheme. The optimal results show that the risks of electricity and cooling supply are underestimated, while the risks of heating are overestimated, compared to N-1 reliability. Furthermore, Pareto analysis of the multi-objective problem enhances independent operational capacity through utilization of reserve resources. Grid dispatch pressure is reduced since purchased power can be used as day-ahead planning. Thus, the methodology achieves collaborative optimization of reliability with a reduction of operation costs, offering effective guidance for engineering applications.

Data-driven multi-objective optimization of aerodynamics and aeroacoustics in dual Savonius wind turbines using large eddy simulation and machine learning

Savonius rotor is a popular form of vertical-axis wind turbine (VAWT) for small-scale and urban applications because of its straightforward design and self-starting ability. Dual VAWTs present challenges in terms of wake interactions and noise, particularly in urban areas. Optimizing these parameters is essential for future wind energy adoption. This research is the first to analyze how the interaction of wakes from adjacent rotors, combined with a deflector, affects both the aerodynamic performance and noise levels of dual Savonius rotors. Large Eddy Simulation is applied, as it effectively captures detailed turbulent wind flows and their interactions with wind turbines. A multi-objective optimization method combining Machine Learning and Computational Fluid Dynamics (CFD) is developed to optimize rotors for maximum power efficiency and minimum noise, considering their wake interactions with a unique deflector system. First, the influence of geometric parameters on aerodynamics and aeroacoustics characteristics of rotors is analyzed, and the database is generated using Design of Experiment approach. Next, the CFD model is replaced by Artificial Neural Network (ANN) model established for predicting rotor performances. A Multi-Objective Genetic Algorithm method is used to optimize aerodynamics and aeroacoustics characteristics of rotors. Finally, optimal design parameters are identified from the Pareto front using the technique for order of preference by similarity to ideal solution decision-making method. The ANN model demonstrated high accuracy with an RANN2 of 0.995 and 0.971 for the average power coefficient (CP) and overall sound pressure level (OSPL) predictions, respectively. Multi-objective optimization revealed the best configuration of the deflector with bleed jets, improving the average CP up to 57.5% and reducing OSPL to an almost 5.2% compared to the dual rotor case at TSR = 0.8.

A Novel Multi-objective Synthesis Method of Non-uniform Excitation Sparse Square Planar Transmitting Array Antenna for Microwave Wireless Power Transmission

A novel multi-objective optimal subarray partitioning synthesis method for non-uniformly excited sparse square planar array (NESSPA) antenna is proposed for the problems of maximizing beam collection efficiency (BCE) and minimizing excitation difference (diff) in microwave wireless power transmission (MWPT). The algorithm adopts the multi-objective particle swarm optimization algorithm based on the set of non-dominated solutions (NDSMOPSO) proposed in this paper, which determines the non-dominated solutions in the swarm according to the fitness value and updates the population during the evolution process; the array element positions and excitations are optimized simultaneously in each iteration. In addition, the performance parameter diff proposed in this paper can effectively measure the performance of the array; in general, the smaller the diff, the better the array performance. The effectiveness of the algorithm is demonstrated through a large number of simulations and, according to the method proposed in this paper compared with other two-step methods, a higher BCE can be obtained with fewer subarrays.

Methods of multi-criteria optimization of technological objects: a systematic review of scientific publications for the period 2013–2023

The article presents a systematic review of scientific articles devoted to applications of multi-criteria optimization methods, published in open sources in 2013-2023, conducted in accordance with the PRISMA recommendations. The main optimization methods with respect to a set of conflicting objective functions, such as energy efficiency, accuracy of achieving final states, economic feasibility, reliability of operation, compliance with environmental standards, etc. are considered. Particular attention is paid to the theoretical foundations and practical applications of these methods aimed at increasing the efficiency of technological processes and improving the quality of decisions. The main objective of the review is to analyze the current state of research in this area, to identify trends and limitations in the use of multi-criteria methods for optimization of specific technological processes and objects. The study showed that, despite significant progress in the development of the theoretical foundations of multi-criteria optimization, the number of works aimed at applying these methods to real technological problems remains limited. The article emphasizes the importance of further research and development aimed at adapting optimization methods to the specific features of technological processes. This review aims to provide a deeper understanding of current trends and issues related to the application of multi-objective optimization methods to improve technological processes, thereby contributing to the development of research in this promising area.

Multi-objective optimization method for building energy-efficient design based on multi-agent-assisted NSGA-II

This study develops a novel multi-agent augmented NSGA-II architecture specifically designed to efficiently handle high-dimensional multi-objective optimization challenges in building energy-efficient design. In this paper, the share Q method is abandoned, and a novel crowding evaluation and comparison mechanism is adopted to ensure comprehensive coverage of the quasi-Pareto frontier while maintaining the diversity of the population. After integrating fast non-dominated sorting, the computational pressure of the algorithm can be effectively reduced. The integration of elite strategies further expands the solution space and prevents the omission of optimal solutions, thereby improving the operating efficiency and stability of the algorithm. After an in-depth analysis of 50 actual building examples, the results show that compared with the conventional NSGA-II method, our method optimizes the quality and diversity of Pareto solutions, with an average improvement of 12% and 15% respectively, while significantly shortening the calculation time, bringing an innovative and efficient optimization path to the energy-saving practice of building design.

A dynamic migration route planning optimization strategy based on real-time energy state observation considering flexibility and energy efficiency of thermal power unit

New energy resources compromising intermittent and fluctuating natures have been integrated into the power grid on a large scale, and thermal power units are obliged to promote the depth of deep peak shaving and flexible response-ability to cope with this new scenario. The safety, flexibility, and high efficiency of coal-fired units are the ultimate goals of its transformation, and there is a mutual influence and mutual restriction relationship among these indicators. To exploit the flexibility of thermal power units, take into account efficiency and safety, and play a supporting role in the new power system, a control strategy that weighs various indicators needs to be developed. Based on heat flow model and dynamic state space model, and updated matrix in real time, the key process parameters affecting the flexibility of heat transfer can be fully characterized. By using the observed state and calculation, the load response index and the energy efficiency index are optimized under the boundary constraint. The results show that the multi-objective optimization methods can avoid over regulation, reduce the flue gas flow by 3.23%–3.59%, and reduce the fluctuation of state quantity under the premise of satisfying the load response rate, about 2.32%–2.52% away from the safety boundary of the design temperature parameter to achieve the flexibility of frequency modulation, high efficiency of energy transmission and operation safety.

Modeling solvation dynamics of transition metal redox ion through on-the-fly multi-objective Bayesian-optimized force field.

Modeling solvation dynamics and properties is crucial for developing electrolytes for electrochemical energy storage and conversion devices. This work reports an on-the-fly multi-objective Bayesian optimization (OTF-MOBO) method to parameterize force fields for modeling ionic solvation structures, thermodynamics, and transport properties using molecular dynamics simulations. By leveraging solvation-free energy and solvation radii as training data, we employ the data-driven OTF-MOBO algorithm to actively optimize the force field parameters. The modeling accuracy was evaluated in molecular dynamics simulations until the Pareto front in the parameter space was reached through minimized prediction errors in both solvation-free energy and solvation radii. Using transition metal redox ions (Fe3+/Fe2+, Cr3+/Cr2+, and Cu2+/Cu+) in aqueous solution as examples, we demonstrate that simple force fields combining the Lenard-Jones potential and Coulombic potential can achieve relative error below 2% in both solvation free energy and solvation radii. The optimized force fields can be further extrapolated to predict solvation entropy and diffusivities with relative error below 10% compared with experiments.

Robust retrofits for rural house envelope considering construction quality and occupant behavior uncertainties: A MOO-integrated Taguchi method

Due to the underdeveloped socio-economic environment, the uncertainties in construction quality and occupant behavior are more prominent for rural house than urban residential buildings. If these uncertainties are not considered, there are higher risks of inaccurate performance prediction, unrealistic retrofit decisions and causing serious performance gap. To address this challenge, this paper proposes a robust envelope retrofitting workflow that combine deterministic multi objective optimization (MOO) and Taguchi method. This workflow stands out for its utilizing mature deterministic MOO to fast approximate Alternative schemes, and utilizing Taguchi method to handle uncertainties, reducing some key disadvantages of traditional robust design optimization (RDO), such as heavy calculating burden, overly conservative solution and difficulty to predefine proper robust objectives or performance target value. The proposed workflow consists of four main steps, formulating Alternative schemes by deterministic MOO, screening highly sensitive uncertain parameters by uncertainty and global sensitivity analysis, formulating Typical uncertain scenarios by orthogonal experiments (OE) and calculating the comprehensive robustness indicators. Results show that by employing the proposed workflow, the selected robust optimal solution not only proves to be robust but also leads to preferable performance enhancements. Compared with the reference mode, the energy efficiency has been improved by 33.2% to 49.4%, the discomfort hours have been reduced by 0.4% to 26.5%, and the robustness has been enhanced by 36.1%.

Comprehensive analysis and thermo-economic optimization of the dry cooling system for supercritical CO2 power cycle

This paper presents a comprehensive analysis and optimization of the dry cooling system for the supercritical CO2 (sCO2) power cycle, a promising technology for generating electricity from renewable heat sources. Unlike prior studies that concentrated solely on specific cooling system components, this paper examines thermoeconomic factors and employs mathematical models to analyze how various operational parameters impact both the cooling system's performance and cost, as well as the overall power cycle. Additionally, the paper employs a multi-objective optimization method to determine the optimal parameter values across varying cooling capacities and ambient temperatures. The results show that the thermal efficiency of the power cycle does not increase linearly with the cooling capacity, due to the change in CO2's physical properties near the temperature and pressure where it behaves like both a liquid and a gas (the pseudo-critical point). Furthermore, optimal cooling system area varies based on cooling capacity and ambient temperature, leading to cost reduction and improved power system efficiency. This paper provides a useful tool and guidance for designing and operating the dry cooling system for the sCO2 power cycle.

An optimum structural design method for a torque sensor measuring the control moment of the micro flapping-wing robot

Abstract This paper presents an optimum structural design method for a sensor capable of measuring the control torque of the micro flapping-wing robot. Torque measurement in flapping-wing robots has special demands on the sensor bandwidth. The method in this paper focuses on the development of a multi-objective optimization method based on the surrogate model to solve the sensor indicator design issues, for example, increasing sensitivity while meeting bandwidth requirements. Initially, Latin hypercube sampling was applied to the choice of the characteristic parameters of the sensor. Based on finite element techniques, the surrogate models describing displacement and eigenfrequency were established to characterize the sensor indicators, and a multi-objective optimization was conducted. According to the optimization results, the sensor structure was manufactured, and a torque measurement platform was set up. Calibration experiments and frequency response experiments demonstrated a high level of consistency between the surrogate model and the experimental data. With the assistance of the eddy current displacement sensor, the actual displacement sensitivity coefficient of the torque sensor is determined to be 0.4325 mm mNm−1, consistent with the calculation of the surrogate model. The characteristic frequency is 488.5 Hz, with a relative error of 7.47% compared to the surrogate model. This indicates that the optimum structural design method can be utilized for the rapid design of torque sensors for special requirements, thus laying the foundation for the control torque measurement of micro flapping-wing robots.

An adaptive multi-objective optimization method for structure-connection-performance design of commercial vehicle cab

A variable screening-approximate model-adaptive multi-optimization algorithm integrated method is proposed to solve the high-dimensional nonlinear problems for lightweight optimization of cabs. Firstly, a full-parametric body-in-white model of the cab is established using implicit parameterization technology, and the simulation analysis of the bending and torsional stiffness, natural modal characteristics, and passive safety are established. Then, considering the structure and connection process parameters, the design variables are screened based on a gray relational analysis-TOPSIS (GRA-TOPSIS). Finally, integrated multi-objective optimization of cab structure-connection-performance is carried out by an adaptive RBF neural network optimization method, and the optimal solution is determined by the GRA-TOPSIS method. Compared with the initial model, the mass of cab is reduced by 3.28% after optimization design. It provides guidance for the lightweight design of body.

Optimizing underwater connectivity through multi-attribute decision-making for underwater IoT deployments using remote sensing technologies

The underwater Internet of Things (UIoT) and remote sensing are significant for biodiversity preservation, environmental protection, national security, disaster assistance, and technological innovation. Assigning tasks to autonomous underwater vehicles (AUVs) is a fundamental challenge in underwater technology and exploration. Remote sensing and AUVs are vital for pollution detection, disaster prevention, marine observation, and ocean monitoring. This work presents an optimized network connectivity using a multi-attribute decision-making approach for underwater IoT deployment. A feature engineering approach highlights the significant characteristics of underwater things, incorporating remote sensing data, and a multi-objective optimization method is used to select optimal UIoT for effective task allocation in deep-sea environments. A balance between data transmission, energy economy, and operational performance is necessary for efficient task distribution. Effective communication algorithms and protocols are needed to maintain environmental sustainability, protect marine ecosystems, and improve underwater monitoring enhanced by remote sensing technologies. Multi-criteria decision-making (MCDM) is beneficial for addressing various challenges in underwater technology, considering factors such as mission objectives, energy efficiency, environmental conditions, vehicle performance, safety, and much more. The proposed criteria importance through intercriteria correlation (CRITIC) methodology will assess technical competencies like communication, resilience, navigation, and safety in an underwater environment, leveraging remote sensing and aiding decision-makers in selecting appropriate undersea devices and vehicles for enhancing communication and transportation. This method prioritizes characteristics and aligns them with specific objectives, improving decision-making quality in the marine environment.

Knowledge hierarchy-based dynamic multi-objective optimization method for AUV path planning in cooperative search missions

This study focuses on path planning for Autonomous Underwater Vehicles (AUVs) in underwater cooperative search missions. The complexities of the ocean environment, the uncertainty of target movements, and limited communication capabilities render underwater cooperative search missions dynamic multi-objective optimization challenges. Studies focusing on communication-constrained search strategies still lack reliable metrics for assessing underwater communication quality and do not consider communication dead zones. Addressing these deficiencies, this paper introduces a novel communication optimization strategy utilizing packet error rate as a metric for assessing communication efficacy, complemented by a potential field-based method for navigating out of communication dead zones. To tackle the inherently dynamic nature of cooperative search missions for mobile underwater targets, we propose a dynamic multi-objective optimization algorithm that employs a knowledge hierarchy strategy. This method enhances the NSGA-II algorithm's efficiency by extracting effective gene segments from historical Pareto solution set and generating a new initial population through recombination, hierarchy, and prediction. Distinct from other advanced dynamic multi-objective optimization approaches that are limited to theoretical problems, our approach is directly applicable to practical scenarios. The effectiveness and practicality of the proposed method are validated through a series of simulation experiments considering the impact of underwater acoustic communication. These results demonstrate that this research is not only innovative in theory but also holds significant engineering value and practical prospects in real-world applications.

Multi-Objective Optimization Analysis of Electromagnetic Performance of Permanent Magnet Synchronous Motors Based on the PSO Algorithm

In order to optimize the electromagnetic performance of a permanent magnet synchronous motor (PMSM) during operation, this paper takes the size of the stator slot structure of the motor as the optimization variable and the peak cogging torque and no-load back electromotive force (EMF) amplitude of the motor as the optimization objectives. A multi-objective optimization method based on the particle swarm optimization (PSO) algorithm is adopted to obtain a structural parameter combination that minimizes the peak cogging torque and no-load back EMF amplitude while meeting the reasonable range requirements of magnetic flux density amplitude. The optimized motor structure design prototype is experimentally verified. The results show that through multi-objective optimization based on the PSO algorithm, the electromagnetic performance of the motor has been improved, with a reduction of 36.33% in peak cogging torque and 2.65% in peak no-load back EMF, indicating a reasonable magnetic flux density amplitude. The experimental results of the optimized prototype show that the difference between the theoretical simulation values and the experimental values is within a reasonable range, which verifies the effectiveness of the multi-objective optimization method.

A Review of Data-Driven Methods in Building Retrofit and Performance Optimization: From the Perspective of Carbon Emission Reductions

In order to reduce the contribution of the building sector to global greenhouse gas emissions and climate change, it is important to improve the building performance through retrofits from the perspective of carbon emission reductions. Data-driven methods are now widely used in building retrofit research. To better apply data-driven techniques in low-carbon building retrofits, a better understanding is needed of the connections and interactions in optimization objectives and parameters, as well as optimization methods and tools. This paper provides a bibliometric analysis of selected 45 studies, summarizes current research hotspots in the field, discusses gaps to be filled, and proposes potential directions for future work. The results show that (1) the building-performance optimization (BPO) process established through physical simulation methods combines the site, retrofit variables, and carbon-related objectives, and the generated datasets are either directly processed using multi-objective optimization (MOO) algorithms or trained as a surrogate model and iteratively optimized using MOO methods. When a sufficient amount of data is available, data-driven methods can be used to develop mathematical models and use MOO methods for performance optimization from the perspective of building carbon emission reductions. (2) The benefits of retrofits are maximized by holistically taking environmental, economic, and social factors into account; from the perspectives of carbon emissions, costs, thermal comfort, and more, widely adopted strategies include improving the thermal performance of building envelopes, regulating HVAC systems, and utilizing renewable energy. (3) The optimization process based on data-driven methods, such as optimization algorithms and machine learning, apply mathematical models and methods for automatic iterative calculations and screen out the optimal solutions with computer assistance with high efficiency while ensuring accuracy. (4) Only 2.2% and 6.7% of the literature focus on the impacts of human behavior and climate change on building retrofits, respectively. In the future, it is necessary to give further consideration to user behaviors and long-term climate change in the retrofit process, in addition to improving the accuracy of optimization models and exploring the generalization and migration capabilities of surrogate models.

Sustainable and efficient separation of ternary multi-azeotropic mixture butanone/ethanol/water based on the intensified reactive extractive distillation: process design, multi-objective optimization, and multi-criteria decision-making

It is of great significance and necessity to develop a sustainable and efficient separation scheme of butanone (MEK), ethanol (EtOH), and water, which are usually formed during the cinepazide maleate synthesis process. To the best of our knowledge, the systematic separation of this ternary multi-azeotropic mixture remains comparatively less studied, compounded by the significant challenges posed by its intricate composition comprising four azeotropes and three distillation boundaries. Therefore, a systematic approach by integrating the process design, multi-objective optimization, and multi-criteria decision-making (MCDM) methods was proposed to achieve the sustainable separation. Initially, three separation schemes, i.e., triple-column extractive distillation (TCED), double-column reactive extractive distillation (DCRED), and side stream intensified double-column reactive extractive distillation (SS-DCRED), were mainly explored via the thermodynamic and kinetic analysis. Subsequently, the multi-objective particle swarm optimization (MOPSO) algorithm was employed to optimize the process based on three objectives namely the total annual cost (TAC), CO2 emissions, and process route index (PRI). Finally, an efficient MCDM method combining CRITIC and TOPSIS was employed to rank the Pareto front solutions of the corresponding process design. Based on the comparison results, the optimal TCED process exhibits the lowest PRI with a decrease of 50.61% and 55.06% compared to that of the SS-DCRED and the DCRED, respectively. It also shows the best performance simultaneously considering economic, environmental, and safety criteria. Of note, the SS-DCRED separation process exhibited the lowest TAC, with a decrease of 60.67% and 11.45% compared to that of the TCED and the DCRED, respectively.

Performance-constrained multi-objective optimization of antennas for miniaturization design

The miniaturization of antennas is crucial as it improves the integration of wireless communication system. In order to achieve miniaturization of antennas, a performance-constrained multi-objective optimization method (PCMOM) considering the size and return loss is proposed. In the PCMOM method, an optimization strategy based on a multi-port network model is introduced, enabling the formation of antennas with various structures. Furthermore, we integrate the constraint of return loss performance into the non-dominated sorting genetic algorithm II (NSGA-II), eliminating solutions that do not meet performance requirements. Three pixel antennas are designed using the PCMOM method and two of them are fabricated. Experimental results demonstrate that the proposed PCMOM method can effectively address the complex trade-off issues in antenna miniaturization design.

Preparation of composites with integrated thermal insulation and mechanical properties using mixture design and multi-objective optimization methods

In order to break through the difficulty of balancing the thermal insulation and mechanical properties of composites, a mathematical model of the effects of thermal insulation fillers and reinforcing fibers on the thermal insulation and mechanical properties of composites was proposed using a mixture design approach. The synergistic interaction between fillers was investigated. Multi-objective optimization method was used to optimize the formulation under specific conditions. The optimized composites were prepared with a low thermal conductivity of 0.108 W m−1 K−1, and the compressive and flexural strengths reached 111.098 MPa and 26.985 MPa, respectively. Meanwhile, the tests showed that the composites had excellent thermal insulation effect and thermal stability.

Time-varying cost modeling and maintenance strategy optimization of plateau wind turbines considering degradation states

Plateau wind power has great potential in reducing carbon emissions; however, compared with other renewable energy, its economics still need to be improved. As an effective approach to enhance its economic feasibility, maintenance strategy optimization aims to reduce maintenance costs per kilowatt-hour and extend equipment lifespan. This paper proposes a multi-objective optimization model for the maintenance decision-making of plateau wind turbines that considers the degradation state. It incorporates: i) modeling the maintenance process of plateau wind turbines by combining time-based and state-based methods; ii) considering the time-varying maintenance costs in complex environments; and iii) employing a multi-objective optimization method to find the optimal strategy that meets maintenance requirements. The complexity considered in the model mainly includes the randomness of the operating duration for each equipment state, the temporal variability of equipment distribution and installation costs, and the uncertainty in maintenance effectiveness. The proposed optimization method is applied to a wind farm in the Yunnan-Guizhou Plateau, China.The results indicate that traditional maintenance strategies underestimate maintenance costs and equipment lifespan losses. Compared with conventional maintenance strategies, this method can reduce equipment maintenance costs by 24.07 % and extend its operating life by 11.58 %. Additionally, this paper has conducted a series of parametric analyses to enhance the generalization performance of the model. The proposed method effectively addresses the economic issues of plateau wind turbine maintenance and provides a valuable decision-making tool for guiding the long-term maintenance of wind turbines in complex environments.

Multi-objective topology optimization of macro structure and microtubule network structure for self-healing material

Abstract Self-healing materials possess the capability to promptly repair minor damages occurring during service, thereby effectively preventing safety accidents. This paper investigates a multi-objective topology optimization method for the macro structure and microtubule network of self-healing materials around pure epoxy resin materials, aiming to enhance the damage healing capability of the microtubule network while meeting the mechanical performance requirements of the macro structure. By introducing the design variables of macro structure and microtubule network, the corresponding topological description functions are established respectively. And study applies logical operations and post-processing techniques to generate an embedded microtubule network structure description. The objective functions include the flexibility of the macro structure, the along-travel head loss, and the total length of the microtubule network, with material volume serving as a constraint. In order to determine the head loss of the three-dimensional microtubule network structure, a Hardy-Cross method based on flow initialization and loop search is proposed. Multi-objective topology optimization is designed based on moving morphable components algorithm, enumeration method and Pareto principle. Develop iterative termination conditions by assessing the disparity between Pareto solution sets in each generation, thereby ensuring algorithm convergence. The numerical example of the Messerschmitt–Bölkow–Blohm (MBB) beamyields a flexibility of 0.059 without a carrier and 0.0728 with a carrier the macrostructural flexibility without a carrier is 81.0% compared to with a carrier, and the macrostructural profiles and the overall flexibility of the MBB beams with/without a carrier are close to each other. This method serves as a reference for optimizing large-scale self-healing structures.