Multi-objective Optimization Research Articles

Multi-objective Optimization in EDM Process Using Backpropagation Neural Network-Genetic Algorithm (BPNN-GA)

Multi-objective Optimization in EDM Process Using Backpropagation Neural Network-Genetic Algorithm (BPNN-GA)

Human-in-the-loop Multi-objective Bayesian Optimization for Directed Energy Deposition with in-situ monitoring

Directed Energy Deposition (DED) is a free-form metal additive manufacturing process characterized as toolless, flexible, and energy-efficient compared to traditional processes. However, it is a complex system with a highly dynamic nature that presents challenges for modeling and optimization due to its multiphysics and multiscale characteristics. Additionally, multiple factors such as different machine setups and materials require extensive testing through single-track depositions, which can be time and resource-intensive. Single-track experiments are the foundation for establishing optimal initial parameters and comprehensively characterizing bead geometry, ensuring the accuracy and efficiency of computer-aided design and process quality validation. We digitized a DED setup using the Robot Operating System (ROS 2) and employed a thermal camera for real-time monitoring and evaluation to streamline the experimentation process. With the laser power and velocity as inputs, we optimized the dimensions and stability of the melt pool and evaluated different objective functions and approaches using a Response Surface Model (RSM). The three-objective approach achieved better rewards in all iterations and, when implemented in a real setup, allowed to reduce the number of experiments and shorten setup time. Our approach can minimize waste, increase the quality and reliability of DED, and enhance and simplify human-process interaction by leveraging the collaboration between human knowledge and model predictions.

A decomposition-based many-objective evolutionary algorithm with Q-learning guide weight vectors update

When dealing with regular, simple Pareto fronts (PFs), the decomposition-based multi-objective optimization algorithm (MOEA/D) performs well by presetting a set of uniformly distributed weight vectors. However, its performance declines when faced with complex and irregular PFs. Many algorithms address this problem by periodically adjusting the distribution of the weight vectors, but these methods do not take into account the performance of the population and are likely to update the weight vectors at the wrong time. In addition, for the SBX crossover operator, the setting of its distribution index will largely affect the exploration and convergence ability of the algorithm, so a single parameter setting will have negative impacts. To tackle these challenges, this paper proposes a method to simultaneously adaptively update weight vectors and optimize SBX parameter via Q-learning(RL-MaOEA/D). In order to make the strategies made by Q-learning more accurate, Two different metrics (CD and NCD) are proposed that capture diversity and convergence of individual and population respectively. RL-MaOEA/D is compared with seven state-of-the-art algorithms on different problems, and the simulation results reflect that the proposed algorithm has better performance.

Optimizing Organic Rankine Cycle (ORC) configurations integrated with transient industrial waste heat: a multi-objective approach

Decarbonizing heat-intensive industries by reusing the waste heat for power or combined heat and power systems is becoming increasingly important to address global warming. The Organic Rankine Cycle has shown a high level of feasibility and performed efficiently for utilizing medium-to-low-grade heat from renewable resources and heat-intensive industries for direct power generation. This study contributes to the field by conducting a techno-economic investigation of various Organic Rankine Cycle configurations to enhance energy conversion when real-life transient waste heat sources are available. These configurations were optimized to maximize energy output along with economic benefits. The non-linear programming by quadratic Lagrangian, a computational unintensive yet accurate optimization algorithm, was utilized for the multi-objective optimization. The optimized cycle configurations showed a 12.57% enhancement of turbine efficiency. Combining regeneration and recuperation enhanced the superheating by 32%, and the optimized air preheater cycle improved the overall objective by 64.2% compared to the pre-optimized conventional cycle, leading to a feasible 1.72-year payback period.

Transferring knowledge by budget online learning for multiobjective multitasking optimization

Multiobjective multitasking optimization (MO-MTO) has attracted increasing attention in the evolutionary computation field. Evolutionary multitasking (EMT) algorithms can improve the overall performance of multiple multiobjective optimization tasks through transferring knowledge among tasks. Negative transfer resulting from the indeterminacy of the transferred knowledge may bring about the degradation of the algorithm performance. Identifying the valuable knowledge to transfer by learning the historical samples is a feasible way to reduce negative transfer. Taking this into account, this paper proposes a budget online learning based EMT algorithm for MO-MTO problems. Specifically, by regarding the historical transferred solutions as samples, a classifier would be trained to identified the valuable knowledge. The solutions which are considered containing valuable knowledge will have more opportunity to be transfer. For the samples arrive in the form of streaming data, the classifier would be updated in a budget online learning way during the evolution process to address the concept drift problem. Furthermore, the exceptional case that the classifier fails to identify the valuable knowledge is considered. Experimental results on two MO-MTO test suits show that the proposed algorithm achieves highly competitive performance compared with several traditional and state-of-the-art EMT methods.

Optimum Planning of Carbon Capture and Storage Network Using Goal Programming

Carbon capture and storage (CCS) is a critical technology used for mitigating climate change by capturing carbon dioxide emissions from industrial sources and storing them underground to prevent their release into the atmosphere. Despite its potential, optimizing CCS systems for cost-effectiveness and efficiency improvement remains a significant challenge. In this paper, the optimization of CCS systems through the development and application of two mathematical optimization techniques is introduced. The first technique is based on using a superstructure optimization model, while the second technique relies on applying a goal programming optimization model. These models were solved using LINGO software version API 14.0.5099.166 to enhance the efficiency and cost-effectiveness of CCS systems. The first model, seeking to maximize the exchange of CO2 flowrate from sources to sinks, achieved a CO2 capture rate of 93.36% with an annual total cost of USD 1.175 billion. The second model introduced a novel mixed-integer non-linear programming (MINLP) approach for multi-objective optimization, targeting the minimization of total system cost, alternative storage, and unutilized storage while maximizing CO2 load exchange. The application of the second model, when prioritized to maximize CO2 flowrate exchange using the goal programming technique, resulted in a cost reduction of 36.46% and a CO2 capture rate of 75.87%. In contrast, when the second model prioritized minimizing the total annual cost, a 48% cost reduction was achieved, and the CO2 capture rate was decreased by 68.37%. A comparison of the two models’ results is presented. The results showed that the second model, with the priority of maximizing CO2 capture, provides the best economic–environmental objective balance, which offers notable cost reductions while keeping an efficient CO2 capture rate. This study highlights the potential of advanced mathematical modeling in increasing the feasibility of CCS as one of the very important strategies of mitigating climate change and reducing global warming.

Topology-optimized terahertz real-time reconfigurable multifunctional liquid-crystal-coding metasurface

In this paper, a reflective terahertz reconfigurable multifunctional coding metasurface based on topology optimization using liquid crystal (LC) is presented. First, the LC metasurface unit is topologically optimized using the NSGA-II multi-objective optimization algorithm. By applying the bias voltage to dynamically adjust the dielectric constant of the LC, the metasurface unit is capable of 2-bit coding at the frequency of 0.67 THz. Then, based on the designed metasurface unit, the array arrangements of the coding metasurface are reversely designed, which makes the metasurface realize flexible control and dynamic switching between beam assignment and vortex beam generation. The results show that for the beam assignment, the single-beam and multi-beam control can be realized with the reflected electromagnetic waves at continuous arbitrary angles in the range of elevation angle of 40° and azimuth angle of 360°. Moreover, the elevation angle and azimuth angle of each beam in the multi-beam can be controlled independently. Using the Fourier convolution addition operation, the control range of the single-beam elevation angle can be expanded. For the vortex beam, the single vortex beam and the multi-vortex beam can be generated in the range of elevation angle of 40° and azimuth angle of 360° with topological charges l=±1, ±2, ±3 at arbitrary angles. This provides flexibility and diversity in the generation of vortex beams. Therefore, the proposed terahertz LC metasurface can realize flexible control of reconfigurable functions and has certain application prospects in terahertz communication, phased array radar, and vortex radar.

Multiobjective Optimisation of Flotation Variables Using Controlled-NSGA-II and Paretosearch

Finding the optimum operating points for the maximisation of flotation recovery and concentrate grade can be a very difficult task, owing to the inverse relationship that exists between these two key performance indicators. For this reason, techniques that can accurately find the trade-off are critical for flotation process optimisation. This work extracted well-assessed Gaussian process predictive functions as objective functions for a comparative multiobjective optimisation study using the paretosearch algorithm (PA) and the controlled elitist non-dominated sorting genetic algorithm (controlled-NSGA-II). The main aim was the concomitant maximisation of the copper recovery and the concentrate grade. Comparison of the two applied techniques revealed that the PA discovered the best set of the pareto-optimal solution for both the recovery (93.4%) and concentrate-grade (17.4 wt.%) maximisation.

Multi-Objective Optimization for Controlling Conflicts in Roadway Surrounding Rock Induced by Floor Stress-Relief Groove

This paper studies the effectiveness of the stress-relief groove on the floor of deep coal roadway and determines the influence of the stress-relief groove parameters on the surrounding rock through qualitative analysis. Based on the displacement conflict problem, evaluation indicators were established, and the optimal solution set was obtained. The innovations of this research include: 1. For geotechnical numerical simulations, novel stress monitoring and plastic zone monitoring techniques have been introduced to accurately reflect the condition of the surrounding rock; 2. The effects of floor relief grooves in deep roadway on surrounding rock have been analyzed, and the advantages and utilities of central and corner relief grooves have been determined; 3. The usability of small datasets has been enhanced by applying SEGA to optimize machine learning models with data augmentation techniques; 4. Multi-objective optimization algorithms have been applied to geotechnical engineering, providing valuable references for decision making. The results demonstrate that multi-objective optimization can significantly enhance the effectiveness of surrounding rock control, resolve conflicts, and achieve more reasonable construction plans. This research provides new theoretical foundations and practical guidance for deep mine roadway-surrounding rock control.

Full-color electrophoretic display with high halftone image quality, reduced power, and deep-learning-enabled fast implementation

The electrophoretic display (EPD) with low power consumption, good sunlight readability, and flexibility is ideal for the Internet of Things. However, color EPDs have very limited grayscales (typically 1-bit) because it is challenging to precisely control the electrophoretic particles of multiple colors. Thus, halftone is usually employed to achieve continuous-tonal full-color EPDs alternatively. Nevertheless, halftone achieves continuous tones at the expense of a significant increase in driving current. This study first proposes and experimentally verifies a model that can accurately predict a driving current from image content. Next, a multi-objective optimized (MOO) halftone algorithm based on MOEA/D (multi-objective evolutionary algorithm based on decomposition) is proposed to consider image quality and driving current simultaneously. As a result, Pareto optimality is achieved, i.e., no image simultaneously performs better in image quality and driving current. A mean driving current reduction of 33.8% concerning the traditional error-diffusion algorithm is experimentally verified on a seven-color EPD with maintained halftone image quality. Considering the high computational complexity of the iteration-based MOO algorithm, this study also discusses the real-time generation of optimal halftone images using a generative adversarial network (GAN). Compared with the optimal halftone images slowly generated by the MOO, the GAN achieves almost the same driving current and a mean absolute error of 2.04, in terms of CIE76 color difference. The proposed algorithm enables full-color EPDs with high-quality continuous tones, reduced power consumption, and a GAN-based real-time implementation.

Truck Transportation Scheduling for a New Transport Mode of Battery-Swapping Trucks in Open-Pit Mines

To address the scheduling challenges associated with the increasing deployment of battery-swapping trucks in open-pit mines, this study proposes a multi-objective scheduling optimization model. This model accounts for the unique characteristics of battery-swapping trucks by incorporating constraints related to battery swapping alerts, the selection of battery-swapping stations, and the impact of ambient temperature on battery capacity. The primary objective is to minimize the total haulage cost and total waiting time. Both a genetic algorithm and an adaptive genetic algorithm are applied to solve the proposed multi-objective scheduling optimization model. The aim is to identify an optimal scheduling solution without violating any model constraints. Results demonstrate that both the basic genetic algorithm and the adaptive genetic algorithm effectively achieve truck transportation scheduling. However, the adaptive genetic algorithm surpasses the basic genetic algorithm, reducing the total transportation costs by 5.6% and total waiting time by 17.4%. It also reduces the number of battery swaps and transportation distance by 15.8% and 1.2%, respectively. The proposed multi-objective scheduling optimization model successfully minimizes the waiting time and transportation costs of battery-swapping trucks while ensuring the completion of production tasks. This approach provides valuable technical support for improving the production and transportation efficiency of open-pit mining operations.

Multi-objective optimal configuration of CCHP system containing hybrid electric-hydrogen energy storage system

In order to cope with the increasing energy demand and achieve the “double carbon “goal of China’s 14th Five-Year Plan,” combined with hydrogen energy storage technology, it has the characteristics of zero pollution, high efficiency and rich source. In the context of reducing energy consumption and the vigorous development of hydrogen energy storage technology, a multi-objective optimization configuration model with economy, energy consumption index and carbon emission index is proposed, which takes into account the working characteristics of the hydrogen energy storage system, and the exothermic heat release from the electrolysis tanks and fuel cells when they are working to provide the loads with an additional heat source of the Combined Cooling, Heating and Power (CCHP) system, to reduce energy consumption and carbon emission. Finally, taking a region as an example, a multi-objective optimization algorithm based on decomposition is used to solve the model, so as to obtain a series of alternatives with better optimization effect. At the same time, the two-way projection method based on interval intuitionistic fuzzy information is used to make decisions, and the scheme that optimizes the economy, energy consumption index and carbon emission index is obtained, which verifies the feasibility of the system proposed in this paper.

Lightweight aircraft design: Integrating biomechanics and algorithm optimization for drone construction using paper materials

Lightweight aircraft design emphasizes materials like composites, alloys, and advanced polymers to reduce weight while ensuring structural integrity. Streamlined aerodynamics, efficient propulsion systems, and optimized component layout further enhance performance. The purpose of this research is to develop an innovative aircraft design model for drones, integrating algorithm optimization techniques and lightweight materials to enhance the performance and efficiency of drones with the utilization of open-source software. We apply this structure to the construction of drones with fixed-wing (FW) and vertical take-off and landing (VTOL) configurations. The aircraft’s body is constructed using lightweight materials such as glass fiber fabric (Gff) and extruded polystyrene foam (XPS), employing a vacuum-assisted wet layup technique for fabrication. Multi-objective Co-evolving Ant Colony Optimization (MC-ACO) was used to improve the construction of drones with VTOL and FW capabilities. This strategy enabled it to be easier to achieve the trade-offs required for a generalist drone design, such as range, payload capabilities, and swarm operations, which were then evaluated against commercially available software to evaluate the effectiveness. Incorporating biomechanics into the design method permits higher consideration of user interaction with drones. The findings indicate that low-fidelity architecture is a suitable starting point for prototyping under limited time frames. The paper concludes with a discussion of the technical constraints of employing free software, as well as some practical concerns for flight testing drones with hybrid configurations.

Multi-objective optimisation of ORC–LNG systems using the novel One-shot Optimisation method

Optimisation is drawing more and more attention in the organic Rankine cycle (ORC) research field. However, as the complexity of the ORC scenarios increases, it poses challenges on operational parameter, working fluid, and configuration optimisation levels. This work first proposes an improved optimisation method, termed the One-shot Optimisation (OSO) method, which can simultaneously optimise the working fluid and configuration. Then, a two-objective optimisation is performed using the OSO method in combined ORC–LNG systems, considering up to eight operational parameters, 11 working fluids, and 16 system configurations to maximise energy efficiency and minimise the electricity production cost (EPC). Finally, the result of the optimisation is divided according to the thermodynamic weight (W1), and two typical conditions are analysed in detail: the maximum case (W1 = 1) and the balanced case (W1 = 0.5). The results show that the OSO method is capable of identifying the optimal working fluid and optimal configuration within a single optimisation process. The basic ORC configuration is preferred when W1 is lower while the recuperative ORC is preferred when W1 is higher. The balanced case can achieve an energy efficiency comparable to that of the maximum case but with a significantly lower EPC. The balanced case can achieve as much as 87. 48% of energy efficiency, requiring only 19.77% of the EPC compared to those of the maximum case.

Multi-objective optimization of activated cold metal transfer welded AA 6063-MgAZ31B dissimilar alloy joint using Taguchi and particle swarm algorithm

Multi-objective optimization of activated cold metal transfer welded AA 6063-MgAZ31B dissimilar alloy joint using Taguchi and particle swarm algorithm

LCL APF control strategy based on model predictive control

In order to further control harmonic current in distribution network, a LCL APF control strategy based on model predictive control is proposed. Firstly, APF mathematical model is established. Then, a multi-objective optimization model predictive control strategy (MPC) is proposed, which comprehensively considers the performance of AC side and DC side of APF. This strategy solves the delay problem existing in the existing MPC strategy: while improving the performance of APF, there is no need to set weight factor; Then, Kalman filter is used to predict the inverter current, thus simplifying the APF measurement system. Finally, the simulation results show that the proposed control strategy can simplify the measurement system and make APF have stronger harmonic suppression ability when it only participates in power conversion and better active filter performance when it participates in harmonic control.

Multi-objective planning of distribution network based on distributionally robust model predictive control

The uncoordinated integration of numerous distributed resources poses significant challenges to the safe and stable operation of distribution networks. To address the uncertainties associated with the intermittent output of distributed power sources, we propose a multi-objective planning strategy for distribution networks based on distributionally robust model predictive control (MPC). Initially, an error fuzzy set is established on a Wasserstein sphere using historical data to enhance out-of-sample performance. Next, a multi-objective optimization framework is constructed, balancing returns and risks, and is subsequently converted into a single-objective solution using value-at-risk conditions. This is followed by the implementation of multi-step rolling optimization within the model predictive control framework. We have linearized the proposed model using the linearized power flow method and conducted a thorough validation on an enhanced IEEE 37-node test system. Distributionally robust optimization (DRO) has been shown to reduce costs by a significant 29.16% when compared to an RO method. Moreover, the energy storage capacity required has been notably reduced by 33.33% on the 29-node system and by 20% on the 35-node system. These quantified results not only demonstrate the substantial economic efficiency gains but also the enhanced robustness of our proposed planning under the uncertainties associated with renewable energy integration.

A Comprehensive Multi-objective Optimization Framework for Balanced Distribution System Planning

A Comprehensive Multi-objective Optimization Framework for Balanced Distribution System Planning

Optimized design of energy absorption of aluminum foam filled CFRP thin-walled square tube based on agent model

PurposeAluminum foam-filled thin-walled unit structures have received much attention for their excellent energy absorption properties. To improve the energy absorption effect of car energy absorption box under axial compression, this paper optimizes the fiber lay-up sequence, fiber angle and aluminum foam density of aluminum foam filled carbon fiber reinforced plastic (CFRP) thin-walled square tubes.Design/methodology/approachDesign of sample points required to construct the proxy model using design of experiments (DOE) method, and the data sample points of different models are obtained through Abaqus simulation and test. A double high-precision proxy model with the maximum specific energy absorption (SEA) and the minimum initial peak crash force (PCF) as the evaluation index is constructed based on the response surface function method. The NSGA-II multi-objective genetic algorithm was used to optimize the design parameters and obtain the optimal solution for the Pareto front, and the results were verified by using the multi-objective optimization toolbox in design-expert.FindingsThe results show that the optimal solution to the multi-objective optimization problem with the inclusion of the lay-up sequence is ρ = 0.5g/cm3 for a fiber lay-up angle varying in the range ±15–90° and an aluminum foam density varying in the range 0.2g/cm3-0.5g/cm3, with a lay-up method of [±87°/±16°/±15°/±89°]. The two optimization methods correspond to SEA and PCF errors of 2.109% and 4.1828%, respectively. The optimized SEA value is 18.2 J/g and the PCF value is 18,230 N. The optimized design reduces the peak impact force and increases the specific energy absorption, which improves the energy absorption effect of thin-walled energy-absorbing boxes for automobiles.Originality/valueIn this paper, the impact resistance of CFRP thin-walled square tubes filled with aluminum foam is optimized. Based on numerical simulations and experiments to obtain the sample point data for constructing the dual-agent model, we investigate the effect of filling with different densities of aluminum foam under the simultaneous change of fiber lay-up angle and order on its mechanical properties in this process, and carry out the multi-objective optimization design with NSGA-II algorithm.

A Multimodal Multi-Objective Coati Optimization Algorithm Based on Spectral Clustering

Multimodal multi-objective problems refer to situations where more than one Pareto set in the decision space corresponds to the same Pareto front in the objective space. In this paper, we propose a multimodal multi-objective coati optimization algorithm based on spectral clustering (MMOCOA-SC) for use in multimodal multi-objective problems. The algorithm starts by creating stable subpopulations via a spectral clustering method, grouping similar individuals within each subpopulation. Then, an improved coati optimization algorithm is proposed in order to increase the diversity of the population and continuously search for near-Pareto optimal solutions. Finally, we use an improved crowding distance method combined with a non-dominated sorting method to maintain and retain multiple near-Pareto optimal solutions. The MMOCOA-SC is evaluated alongside five state-of-the-art algorithms using the 2020 CEC test suite, IDMP test problems, and twelve classic engineering application problems. In comparison to the other five state-of-the-art algorithms, the experimental results show that MMOCOA-SC exhibits a superior performance when applied to the problems. This study explores multimodal multi-objective optimization algorithms with a focus on the concept of symmetry, which is crucial for multimodal multi-objective optimization problems in terms of achieving a balanced decision space and a diversity of solutions in the objective space.