Multi-objective Optimization Method Research Articles

A staged diversity enhancement method for constrained multiobjective evolutionary optimization

Optimizing the convergence and diversity of solutions simultaneously under constraints is a challenge in solving constrained multiobjective optimization problems. In existing multiobjective optimization algorithms, general diversity maintenance mechanisms have difficulty determining all optimal solutions in discrete feasible regions. This paper proposes a staged constrained multiobjective optimization algorithm with a diversity enhancement method (SDEM), which can explore potential discrete feasible regions by retaining well-distributed offspring. Specifically, after solutions have converged to optimal feasible regions by niching-based constraint dominance in the early stage, the SDEM improves the diversity of solutions through a proposed diversity enhancement dominance principle in the mid-term. Finally, the optimize objective functions and constraints of all solutions are optimized under constraint dominance to balance convergence, diversity, and feasibility during the three stages. Experiments on four well-known test suites and six real-world case studies demonstrate that the SDEM is competitive with or comparable to seven state-of-the-art constrained multiobjective evolutionary algorithms.

Joint UAV Deployment and Task Offloading in Large-Cale UAV-Assisted MEC: A Multiobjective Evolutionary Algorithm

With the development of digital economy technologies, mobile edge computing (MEC) has emerged as a promising computing paradigm that provides mobile devices with closer edge computing resources. Because of high mobility, unmanned aerial vehicles (UAVs) have been extensively utilized to augment MEC to improve scalability and adaptability. However, with more UAVs or mobile devices, the search space grows exponentially, leading to the curse of dimensionality. This paper focus on the combined challenges of the deployment of UAVs and the task of offloading mobile devices in a large-scale UAV-assisted MEC. Specifically, the joint UAV deployment and task offloading problem is first modeled as a large-scale multiobjective optimization problem with the purpose of minimizing energy consumption while improving user satisfaction. Then, a large-scale UAV deployment and task offloading multiobjective optimization method based on the evolutionary algorithm, called LDOMO, is designed to address the above formulated problem. In LDOMO, a CSO-based evolutionary strategy and a MLP-based evolutionary strategy are proposed to explore solution spaces with different features for accelerating convergence and maintaining the diversity of the population, and two local search optimizers are designed to improve the quality of the solution. Finally, simulation results show that our proposed LDOMO outperforms several representative multiobjective evolutionary algorithms.

Multi-Objective Optimization towards Heat Dissipation Performance of the New Tesla Valve Channels with Partitions in a Liquid-Cooled Plate

The utilization of liquid-cooled plates has been increasingly prevalent within the thermal management of batteries for new energy vehicles. Using Tesla valves as internal flow channels of liquid-cooled plates can improve heat dissipation characteristics. However, conventional Tesla valve flow channels frequently experience challenges such as inconsistencies in heat dissipations and unacceptably high levels of pressure loss. In light of this, this paper proposes a new type of Tesla valve with partitions, which is used as internal channel for liquid-cooled plate. Its purpose is to solve the shortcomings of existing flow channels. Under the working conditions of Reynolds number equal to 1000, the neural network prediction-NSGA-II multi-objective optimization method is used to optimize the channel structural parameters. The objective is to identify the optimal structural configuration that exhibits the greatest Nusselt number while simultaneously exhibiting the lowest Fanning friction factor. The variables to consider are the half of partition thickness H, partition length L, and the fillet radius R. The study result revealed that the optimal parameter combination consisted of H = 0.25 mm, R = 1.253 mm, L = 0.768 mm, which demonstrated the best performance. The Fanning friction factor of the optimized flow channel is substantially reduced compared to the reference channel, reducing by approximately 16.4%. However, the Nusselt number is not noticeably increased, increasing by only 0.9%. This indicates that the optimized structure can notably reduce the fluid’s friction resistance and pressure loss and slightly enhance the heat dissipation characteristics.

Virtual Sound Image Reconstruction Method for Multi-objective Optimization of Folk Music Based on Evolutionary Algorithm

At present, the exchanges in various fields such as culture, economy, and politics are becoming more and more close in the world. From the perspective of the relationship between national music and cultural development, the development of national music has also received more and more attention, and it has become an inevitable trend in the development of today's era. The purpose of this paper was to perform virtual reconstruction of the sound image of folk music through multiple objective optimizations, and to model the virtual sound image of folk music as a multi-objective optimization problem. According to the research on sound image positioning, the relevant noise factors were removed, so as to achieve the playback of ethnic music that enhanced the surround effect and visual enjoyment. The evolutionary algorithm in this paper was mainly based on the multi-objective optimized sound image localization technology. For the music virtual sound image, an improved FCM algorithm and an evolutionary multi-objective optimization algorithm combining local and non-local information of the sound image were proposed, respectively. Through the analysis of the traditional sound image algorithm method, the accuracy of the sound image localization on the horizontal plane could be effectively improved. After the conversion, the audience could feel the better stereo image and surround feeling of the folk music. Through experimental analysis, it can be seen that the system can not only perform virtual conversion of audio-visual signals of different frequencies, but also provide data for different audio playback systems. The feature point registration error is low, and the reconstruction effect is good, especially the random delay processing in the range of 0∼20m, and the performance is better than the traditional method. Finally, virtual left and right surround sound image signals were obtained, which effectively improved the three-dimensional surround feeling of folk music.

Multi-objective optimization method for medium and long-term power supply and demand balance considering the spatiotemporal correlation of source and load

The medium and long-term supply-demand imbalance of the power system in the context of the new power system is becoming more and more prominent due to the fluctuation and intermittency brought about by the high proportion of new energy sources connected to the grid. In this regard, a multi-objective power supply-demand balance optimization method considering the spatiotemporal correlation of source and load is proposed in this work. First, the autocorrelation and inter-correlation characteristics of source and load are analyzed. On this basis, a multi-dimensional scenario set construction method considering the spatiotemporal correlation of source and load is proposed. Then, the planning capacity of each regional power source and the system operation under each scenario are taken as the optimization variables. Renewable energy electricity curtailment, equivalent annual total cost, and inter-region transmission electricity are taken as the optimization objectives. Various constraints such as power source planning and operation, power balance, inter-region power transmission, and renewable energy power curtailment rate are considered comprehensively. The optimization method for the medium and long-term power supply and demand balance is proposed. Finally, the method is applied to Hunan Province, China to guide power planning. The results show that compared with traditional multi-dimensional correlation scene construction methods, the average probability density functions error of wind turbine output, photovoltaic output, and load constructed in this work decrease by 44.08 %, 73.64 %, and 57.54 %, respectively. It takes into account the regional, temporal, temporal autocorrelation, and inter-correlation of the source and load, and has similar characteristics to historical data. Compared with traditional planning that only considers economy, the optimization plan for power supply and demand balance in this work reduces electricity curtailment and inter-region transmission by 97.04 % and 72.71 %, respectively, balancing renewable energy consumption, economy, and regional independent balancing indicators.

Experimental Investigation on Wire Electric Erosion Behaviour of Silicon Dioxide Particulate Reinforced Composite

The intend of current study was focused on the prediction of material removal rate (MRR) and surface roughness (SR) for the AA7050-SiO2 composite during wire electric erosion or discharge machining (WEDM) process using a brass (Br) wire electrode. Here, stir casting process was employed to develop the AA7050 matrix composite with inclusion of 10wt.% SiO2 particle reinforcement. The multi-objective optimization method of Technique for order preference by similarity to ideal solution (TOPSIS) approach has been applied to find out the optimal setting of input machining parameters such as peak current (Ip), pulse-on time (Ton) and pulse-off time (Toff). Furthermore, the significant effects of parameters were identified by analysis of variance (ANOVA). Taguchi L9 (33) orthogonal design has been formulated to perform the experimental work. TOP SIS results stated that the optimal setting of Ip at 30 amps, Ton of 130 μs and Toff of 55 μs provide the better MRR with lesser SR. The ANOVA results noticed that Ip has the prime noteworthy parameter over the adopted responses having a contribution of 45.67%, followed by Ton (32.34%) and Toff (12.26%), respectively. The confirmation test was carried out by the optimal parameters setting to verify the predicted results. Finally, the scanning electron microscopy (SEM) test was carried out for the machined surface of the composite specimen and it was reveals that the formation of craters and recast layer thickness in the machined surfaces.

Research on a Multi-Objective Optimization Method for Transient Flow Oscillation in Multi-Stage Pressurized Pump Stations

The long-distance multi-stage pressurized pump station water delivery system involves numerous valve closure parameters, complicating the rapid identification of an optimal valve closure scheme that satisfies multiple transient flow oscillation protection requirements. A hydraulic transient model was established based on transient flow calculation theory to address this challenge. Decision biases were identified using the Analytic Hierarchy Process and the Entropy Weight Method. A multi-objective optimization model, incorporating Support Vector Regression (SVR) and the Beluga Whale Optimization (BWO) algorithm, iteratively searches for optimal schemes under different biases. The results indicate that Support Vector Regression exhibits optimal performance, while Beluga Whale Optimization demonstrates excellent performance. The optimal schemes obtained from the multi-objective optimization model meet the transient flow protection requirements of the water delivery system. The study demonstrates that this model effectively solves the multi-objective optimization problem for water hammer protection in multi-stage pressurized pump station water delivery systems.

Prediction of frost resistance and multiobjective optimisation of low-carbon concrete on the basis of machine learning

The use of Portland cement is a major source of carbon dioxide emissions, causing considerable environmental pollution worldwide. Therefore, reducing carbon emissions in concrete is of paramount importance. This study presents a multiobjective optimisation method for low-carbon concrete mix design, combining the use of optimal machine learning models for prediction, with the aim of minimising the cost and carbon emissions of concrete. Several optimisation models, including SVR, CatBoost, RF, XGBoost, DBO-RF and VMD-DBO-RF, were employed to predict the frost resistance of low-carbon concrete. The research findings demonstrate that the VMD-DBO-RF optimisation algorithm achieves high prediction accuracy in terms of RDEM and MLR. For RDEM prediction, R2 = 0.9346, MSE = 0.0508, MAE = 0.1686, and RMSE = 0.2253. For MLR prediction, R2 = 0.9557, MSE = 0.0245, MAE = 0.1042, and RMSE = 0.1565. Furthermore, the model’s interpretability was improved by combining SHAP and PDP analyses.

A demand-based three-stage seismic resilience assessment and multi-objective optimization method of community water distribution networks

This paper proposes a three-stage resilience concept that takes into account reliability, vulnerability and recovery resilience of water distribution networks (WDNs) from three phases, namely, pre-disaster preparation (PDP) phase, disaster response (DR) phase and the post-disaster recovery (PDR) phase. Based on the three-stage resilience concept, the initial performance, robustness and multi-objective optimization recovery method are proposed. In PDP phase, based on the reliability concept and the user demand, the initial performance of WDNs is defined, and the method is proposed based on Monte Carlo simulation method combined with seismic fragility of pipelines. In DR phase, a comprehensive quantitative index is proposed to quantify the robustness of WDNs by integrating the structural attributes, topological attributes and operational characteristics of WDNs. Finally, on the basis of the previous two stages, the disaster recovery process of failed pipelines of WDNs is further analyzed, and a multi-objective recovery optimization model of failed pipelines with consideration of users’ demands under the resources constraints is proposed to achieve the resilience enhancement. Through a case, the three-stage resilience assessment optimization enhancement of WDNs is implemented using the improved NSGA-II. The proposed method can be used as a basis for disaster prevention planning and seismic measures.

Multi-objective optimization and sensitivity analysis of offset strip fin compact heat exchangers

In this study, the aerothermal performance of Offset Strip Fin Compact Heat Exchangers (OSF-CHE) is optimized with the multi-objective Particle Swarm Optimization method. Available empirical correlations for the Fanning factor and Colburn factor are utilized in the optimization process. Selected off-design Pareto-optimal solutions for compact heat exchanger configurations are reconstructed and simulated by Computational Fluid Dynamics simulations at various boundary conditions after extensive validation processes. Optimized OSF-CHE designs are shown to have improved aerothermal performances among comparable designs in the literature. It has been shown that a high Reynolds number in the range of 1,500–2,000 as a flow attribute provides the Fanning factor ranging from 0.0228 to 0.0619 and the Colburn factor between 0.0067 and 0.0122 and Re is more dominant than geometric design variables on the objective functions. Low and moderate Reynolds number flows at 500 and 1,000 offer a wider selection range for both objective functions on the Pareto-front.

Analyze of pipeline transport characteristics and optimization method of structural parameters in slurry shield circulation system with spiral structure

This study introduces the application of a spiral structure in pipeline transportation to enhance the pipeline capacity of a slurry shield circulation system. A numerical model of solid–fluid coupling in a pipeline with a double spiral structure was established based on computational fluid dynamics and the discrete element method (CFD–DEM) theory, and its validity was confirmed through comparison with experimental data. The characteristics of the spiral pipeline were evaluated by comparing them with those of a conventional smooth straight pipeline. A multi-objective optimization method for determining the structural parameters of a spiral pipeline in a slurry shield circulation system is proposed using the Kriging surrogate model. The optimized design of a spiral pipeline was demonstrated through a specific project, and the impact of the main structural parameters on the slurry transport characteristics of the pipeline was analyzed. The results indicated that the optimized structural parameters led to an 18.65% increase in the average flow rate of the slurry and a 19.13% reduction in the accumulation of stones in the pipeline.

Pricing Optimal Outcomes in Coupled and Non-convex Markets: Theory and Applications to Electricity Markets

The clearing of nonconvex markets poses unique challenges. The canonical market clearing, a Walrasian equilibrium, needs not exist when participants’ preferences display nonconvexities, for example, due to technical constraints. Then market clearing prices might not exist, and side payments may be required to compensate losses. Electricity markets are a prime example. Market operators in the United States use heuristic pricing rules to compute market prices; the magnitude of the side payments, potential lost opportunity costs, and the quality of network congestion signals in prices have all become a concern. In “Pricing Optimal Outcomes in Coupled and Non-Convex Markets: Theory and Applications to Electricity Markets,” Ahunbay, Bichler, and Knörr propose a multiobjective framework for pricing such markets. The design goals are shown to be inherently conflicting but may be balanced against each other through traditional methods in multiobjective optimization. Pricing rules used in practice are identified as prices for a suitably convexified market, which motivates a novel pricing method that drastically reduces side payments while maintaining congestion signals in realistic test cases.

Deep learning assisted optimization of Ka-band relativistic backward wave oscillator operating in TM03 mode with low guiding magnetic field

To accelerate the design of a high-power microwave device, a deep learning assisted multi-objective optimization method is used to optimize a Ka-band relativistic backward-wave oscillator (RBWO) operating with a low magnetic field. Particle-in-cell simulation results show that the optimized RBWO with a tooth-shaped slow wave structure (SWS) can generate microwave pulses with an output power of 1.24 GW and an operating frequency of 26.8 GHz under a diode voltage of 623.3 kV, and the diode current is 6.56 kA at a guiding magnetic field of 0.8 T. Compared with the original RBWO, the output power of the optimized RBWO has been increased by 201.2%, and the beam-to-microwave conversion efficiency has increased from 10.0% to 30.3%. The detailed analysis reveals that in an overmoded RBWO with low guiding magnetic fields, the introduction of a tooth-shaped SWS is beneficial to mode competition, improves output power, and decreases microwave starting time.

Co-optimization method for injection strategy of underground natural gas storage integrating aboveground and underground parts

Underground natural gas storage (UNGS) is an important infrastructure to overcome the imbalance between supply and demand of natural gas. During the gas injection period, gas is compressed aboveground and then transported to injection wells for injection into the underground reservoir. Reasonably formulating the compressor operation scheme and injection scheduling scheme is a crucial step. However, “Compressor-pipeline-injection well-reservoir" constitutes a synergistic whole. More efficient and practical operation schemes can only be proposed through the establishment of an optimization method that coordinates the entire gas injection process. A novel two-layer multi-objective collaborative optimization method is proposed to optimize the monthly operation scheme during the injection period. The upper-layer model focuses on optimizing injection volume allocation to minimize reservoir pressure deviation and total compressor energy consumption. The under-layer model optimizes the compressor operation scheme by considering the multi-stage compression (MC) and clearance adjustment (CA) equipped in reciprocating compressors. The synergistic relationship during the injection process is integrated into the traditional model through the interlayer iteration method. Furthermore, a high accuracy and efficiency proxy model based on machine learning algorithms (ML) is developed to predict compressor performance. The results of the case study indicate that, compared with traditional optimization method and the two-stage co-optimization method, the proposed method achieves an average energy consumption reduction of 9.54 × 106 kWh (10.79%) and 2.12 × 106 kWh (2.4%) respectively. The effective utilization of CA and MC can significantly alleviate the deviations between displacement and processing requirements, eliminating 22,120.5 × 104 Nm3(85.62%). The two-layer co-optimization method effectively integrates the aboveground and underground parts of UNGS, providing a solution for safe and efficient operation during the injection period.

Numerical two-dimensional optimization of a cylindrical fuselage for bioinspired unmanned aerial vehicle based on non-dominated sorting genetic algorithm-II

To achieve an aerodynamically efficient design of fuselage for bioinspired unmanned aerial vehicles (UAV), the development of a systematic method is of paramount need. This work presents a multiobjective optimization study for shape parameterization of a 2D fuselage of foldable flapping wing UAV in low Reynolds number (2e05) flight conditions. The novelty of the research work lies in integrating S1223 airfoil characteristics for predicting the efficient shape design of the fuselage. This paper offers four sections; (i) the validation of the ANSYS Fluent model with experiment, (ii) the exploration of design variables using Design of Experiment (Sparse Grid Initialization), (iii) the implementation of response surface method (Genetic Aggregation) to know about dimensional sensitivity among independent and dependent variables and (iv) the application of multiobjective optimization method i.e. NSGA II to optimize the drag and lift coefficient. To identify the superiority, a comparative study between the original and optimized fuselage is presented considering many parameters like pressure contours, velocity contours, pressure coefficients, and streamlines representations. It is evident from various results that the 2D optimum shape significantly minimizes the drag coefficient and increases the lift coefficient. This work also makes room for 3D shape optimization, which helps in prototype fabrication for real-time flight conditions.

Improved energy utilization in heavy-duty automatic transmission: Advanced modeling and multi-objective optimization

In the current research of electro-hydraulic actuators for heavy-duty automatic transmissions, achieving accurate output is proven to be insufficient to meet growing demand. Aiming at this deficiency, this paper proposes a dynamic model, which combines detailed loss analysis and multi-objective optimization to further improve energy efficiency. Firstly, considering the key resistance factors, including viscous damping coefficient, spring constant and supply pressure, a dynamic model is established. Subsequently, the overall response of the model is verified based on the existing experimental data. In addition, the accuracy and stability time are used as evaluation indexes to analyze the influence of resistance on the function pattern. Finally, a multi-objective optimization method is used to balance the relationship between energy utilization efficiency, accuracy and shift quality. The slight changes in mechanical energy and stable time lead to a significant decrease in jerk by 22.11 %, which makes the shifting process smoother and effectively improves the shifting performance.

Research on the construction of multi objective coupling model and optimization method of ship form

AbstractMulti‐objective optimization of ship form can effectively reduce ship energy consumption, and is one of the important research topics of green ships. However, the computational cost of numerical simulation based on computational fluid dynamics (CFD) theory is relatively high, which affects the efficiency of optimization. Traditional subjective weighting methods mostly rely on expert's experience, which affects the scientificity of optimization. This paper effectively integrates the CFD method, the improved multi‐objective optimization algorithm and the objective weighting method to build a ship form multi‐objective optimization framework. Conduct multi‐objective optimization research on resistance and seakeeping performance of a very large crude oil carrier (KVLCC) ship. The improved bare‐bones multi‐objective particle swarm optimization (IBBMOPSO) algorithm is used to obtain the pareto front, and the kernel principal component analysis (KPCA) method is used to objectively assign the weight of each target. Finally, the optimal ship form scheme with high satisfaction was obtained. The multi‐objective optimization framework constructed in this paper can provide a certain theoretical basis and technical support for the development of ship greening and digital transformation.

Controller Placement Approach with Criteria Balance in SDN networks

Software Defined Network (SDN) is an emerging technology that centralizes network control and automates network management by separating the data plane from the control plane. The control plane is a set of controllers that manage the network switches. The crucial problem of positioning these controllers is known as the Controller Placement Problem (CPP). The optimal controllers positioning is very constrained and affects the different network performance parameters, such as, controller-to-switch latency, inter-controller latency, number of hops between controller and switch and inter-controller. In this paper, we study the impact of optimizing some parameters on the others, we have developed different approaches, and each considers one or two parameters. Moreover, we propose a balanced optimization approach that considers the various network performance parameters. We formulate the problem as an Integer Linear Programming model that considers all parameters using the Lexicographic Multi-objective optimization method. By ensuring a balance between all parameters, network performance is significantly improved. The obtained results reveal that our approach is more inclusive and provides very interesting results.

Optimization of baffle and tapering integration in the PEM fuel cell flow field employing artificial intelligence

In this study, two surrogate models are developed to investigate and enhance the performance of parallel flow field Proton Exchange Membrane Fuel Cells (PEMFCs) with two modifications. The main channels are tapered, and baffles are inserted to enhance the mass transfer. A data set is generated by the multi-phase, three-dimensional CFD model. Two different data-driven models based on Artificial Intelligence (AI) and Modified Response Surface Methodology (MRSM) provide surrogate models. Subsequently, two multi-objective optimization methods are employed to reveal the optimum case. The results show that the AI model achieves superior accuracy, whereas the MRSM model has greater simplicity. An increased number of baffles and an optimal tapering ratio contribute to higher mass flux and improved uniformity in reactant distribution. The insertion of baffles and the tapering of main channels result in a remarkable 67 % increase in output power density. Optimum tapering also reduces pressure drop, whereas baffles, while improving performance, contribute to increased pressure drop and potential PEMFC degradation. The identified optimum configuration of baffles and tapering, along with the optimum values for voltage, pressure, and anode and cathode stoichiometries, results in an impressive output power density of 0.93 W cm−2 and a parasitic power ratio of 0.17, respectively.

Exploring the Power & Loads Paradigm: Tocha Farm Case Study

Wind energy plays a vital role in the European Union’s decarbonization and electrification efforts. The present study addresses wind farm control strategies exploring the design space of optimal solutions and understanding how these solutions vary when different objectives and meteorological scenarios are considered. The goal is to bridge the gap in existing literature by avoiding the simplification of the multi-objective optimization problem into single-objective using the weights method. This method was not chosen due to its various limitations, particularly its inability to deal with non-convex Pareto fronts. Instead, in this work, a multiobjective optimization method is adopted that overcomes these constraints and offers a set of solutions (the Pareto front) where the decision maker selects the most suitable solution. The methodology involves four main steps: flow calculation using FLORIS, aerodynamic load calculation with CCBlade, conversion of loads into damage equivalent moments (DEM), and multi-objective optimization using a direct multi-search (DMS) algorithm. By exploring various objectives, such as power and fatigue loads at different components, and different wind turbines, this study aims to explore the design space and quantify the potential improvement in terms of the defined cost-functions. The study utilizes data from Tocha Wind Farm in Portugal, that comprises five VESTAS wind turbines. Strain gauges, accelerometers, and meteorological measurements are used for data collection. Simulations under ‘greedy control’, where a turbine is affected by a wake, are compared with campaign data, considering a fixed wind speed and varying turbulence intensity. The optimization reveals Pareto-optimal strategies and the respective optimal yaw angles. Considering a wind velocity of 8 m.s −1 and a wind direction of 308°, power may improve up to 4.6%, and the blade root DEM and tower base DEM up to 5.7% and 84%, respectively. The study highlights the impact of considering multiple objectives and supports the selection of wind farm control strategies to effectively manage critical structural components, thereby extending the lifespan of the wind farm.