Multi-objective Structural Optimization Research Articles

Improved Monte Carlo tree search formulation with multiple root nodes for discrete sizing optimization of truss structures

This article proposes a novel reinforcement learning algorithm using an improved Monte Carlo tree search (IMCTS) formulation for the discrete optimum design of truss structures. IMCTS with multiple root nodes includes the update process, best reward, accelerating technique and terminal condition. The update process means that once a final solution is found, it is used as the initial solution for the next search tree. The best reward is used in the backpropagation step. The accelerating technique is introduced by decreasing the width of the search tree and reducing the maximum number of iterations. The agent is trained to minimize the total structural weight under various constraints until the terminal condition is satisfied. The optimal solution is the minimum value of all solutions found by the search trees. Numerical examples show that the agent can find the optimal solution with low computational cost, stably produces an optimal design, and is suitable for multi-objective structural optimization and large-scale structures.

Design and optimization of annular gap in a nozzle for dyeing machines

The annular nozzle is an important part of the dyeing machine as its impact and traction performance directly affect the quality and efficiency of dyeing. The annular gap forms the core of the nozzle. In this paper, the performance differences between six nozzles with different annular gap shapes were analyzed under various conditions using numerical simulation. The results indicate that the performance of the cone straight nozzle is more stable than other nozzle shapes under various conditions. To further enhance the performance of the nozzle, a multi-objective optimization of the cone straight nozzle structure was performed using a backpropagation neural network and a non-dominated sorting genetic algorithm, thereby obtaining the optimal combination of structural parameters. Finally, the optimization results were verified via experiments and numerical simulations. The results show that the pulling force of the optimized cone straight nozzle is more than 10% higher than that before optimization.

Failure Probability-Based Optimal Seismic Design of Reinforced Concrete Structures Using Genetic Algorithms

Artificial intelligence (AI) has enabled several optimization techniques for structural design, including machine learning, evolutionary algorithms, as in the case of genetic algorithms, reinforced learning, deep learning, etc. Although the use of AI for weight optimization in steel and concrete buildings has been extensively studied in recent decades, multi-objective optimization for reinforced concrete (RC) and steel buildings remains challenging due to the difficulty in establishing independent objective functions and obtaining Pareto fronts. The well-known Non-Dominated Sorting Genetic Algorithm II (NSGA-II) is an efficient genetic algorithm approach for multi-objective optimization. In this work, the NSGA-II approach is considered for the multi-objective structural optimization of three-dimensional RC buildings subjected to earthquakes. For the objective of this study, two function objectives are considered: minimizing total cost and the probability of structural failure, which are obtained via several nonlinear seismic analyses of the RC buildings. Beams and columns’ cross-sectional dimensions are selected as design variables, and the Mexican Building Code (MBC) specifications are imposed as design constraints. Pareto fronts are obtained for two RC-framed buildings located in Mexico City (soft soil sites), which demonstrate the efficiency and accuracy of NSGA-II for structural optimization.

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.

Failure analysis and structural optimization of unequal-parameter metal bellows in resistance to bending and torsional composite deformation

In practical engineering applications, metal bellows are subjected to complex environmental conditions, and they usually deform under the combined effects of tension, bending and torsion. In this paper, the bending and torsion composite deformation of unequal parameter metal bellows arranged alternately by large wave and wavelet is studied. Firstly, the finite element model of metal bellows is constructed, and the finite element simulation analysis of its mechanical properties is carried out. Taking the simulation results as samples, the multi-objective structural optimization of unequal parameter metal bellows under the condition of bending and torsion composite deformation is carried out. Combined with the bending-torsion composite deformation test and fracture microscopic characterization, the bending-torsion composite deformation characteristics and fracture failure mechanism of equal-parameter metal bellows (EPMB) and unequal-parameter metal bellows (Un-EPMB) were compared and analyzed. The results show that under the same deformation conditions, compared with the EPMB, the elastic limit bending line displacement and elastic limit torsion angle displacement of Un-EPMB are increased by 52.94 %, and the bending and torsional stiffness are greatly improved, moreover, the alternating waveform arrangement led to relatively gradual stress transfer through the Un-EPMB during the bending-torsion composite deformation process, thereby reducing stress concentration. Thus, the Un-EPMB exhibited more favorable mechanical properties. Unlike in the EPMB, which underwent fracture along the grain boundary, the cracks in the Un-EPMB appeared in the middle layer and propagated to both sides in a wavelike pattern. The dimples were distributed in the middle layer of the fracture, which indicates ductile behavior.

An interactive reference-point-based method for incorporating user preferences in multi-objective structural optimization problems

Although multi-objective evolutionary algorithms (MOEAs) are often used to solve multi-objective structural optimization problems (MOSOPs), the incorporation of decision-maker (DM) preferences into MOEAs to search for regions of interest from the Pareto front has received limited attention in these problems. Recently, three MOEAs have shown promising results in solving MOSOPs incorporating DM’s preferences based on a priori reference points. However, providing this information can be challenging as the DM may not know an initial reference point for the MOSOP. Therefore, this study analyzes three interactive multi-objective optimization (IMO) algorithms, called I-NSGA-II, I-GDE3, and I-GDE3+APM, in which the reference points are progressively incorporated during the search process. These IMOs are applied to benchmark MOSOPs and evaluated using well-known performance indicators. The results demonstrate that I-NSGA-II outperforms I-GDE3 and I-GDE3+APM, which have similar overall performances. Additionally, the IMOs considered here outperformed their respective a priori approaches in MOSOPs where the reference points are located at the central sector of the Pareto front. Also, we identified the performance indicators in which the approaches considered in this work performed better than their corresponding a priori ones. Furthermore, the research findings suggest that these IMOs can generate good results without defining a priori reference points, making them a promising approach for solving MOSOPs and enabling DMs to make better and more reliable decisions.

Optimal truss design with MOHO: A multi-objective optimization perspective.

This research article presents the Multi-Objective Hippopotamus Optimizer (MOHO), a unique approach that excels in tackling complex structural optimization problems. The Hippopotamus Optimizer (HO) is a novel approach in meta-heuristic methodology that draws inspiration from the natural behaviour of hippos. The HO is built upon a trinary-phase model that incorporates mathematical representations of crucial aspects of Hippo's behaviour, including their movements in aquatic environments, defense mechanisms against predators, and avoidance strategies. This conceptual framework forms the basis for developing the multi-objective (MO) variant MOHO, which was applied to optimize five well-known truss structures. Balancing safety precautions and size constraints concerning stresses on individual sections and constituent parts, these problems also involved competing objectives, such as reducing the weight of the structure and the maximum nodal displacement. The findings of six popular optimization methods were used to compare the results. Four industry-standard performance measures were used for this comparison and qualitative examination of the finest Pareto-front plots generated by each algorithm. The average values obtained by the Friedman rank test and comparison analysis unequivocally showed that MOHO outperformed other methods in resolving significant structure optimization problems quickly. In addition to finding and preserving more Pareto-optimal sets, the recommended algorithm produced excellent convergence and variance in the objective and decision fields. MOHO demonstrated its potential for navigating competing objectives through diversity analysis. Additionally, the swarm plots effectively visualize MOHO's solution distribution of MOHO across iterations, highlighting its superior convergence behaviour. Consequently, MOHO exhibits promise as a valuable method for tackling complex multi-objective structure optimization issues.

Multi-objective optimization of forest structure for broadleaf mixed forest under different CMIP5 scenarios

Climate change is an important global research topic and one of the most pressing issues facing the world today. It significantly impacts forest distribution, species composition, stand structure, growth, and other functions, therefore, it is crucial to simulate the dynamic changes of forest structure under future climate change and develop optimized solutions to adapt to it. Combined with the various stand structural parameters, based on the equal or unequal weights of each parameter at the stand level, to establish a dynamic stand spatial structure multi-objective optimization index (L-index) under different climate changes, and to implement broadleaf mixed forest spatial structure optimization research in Yanan Forest Farm under RCP 2.6, RCP 4.5, RCP 8.5 climate scenarios after 5 years. The results indicated that the L-index showed an increase ranging from 13.8 % to 35.7 % under equal weights in different climate scenarios. Additionally, the optimal harvesting intensity ranged from 13.2 % to 20.5 %, with the highest intensity observed in the RCP4.5 climate scenario; compared to the RCP4.5 and RCP8.5 climate scenarios, the RCP2.6 scenario shows the largest trend and magnitude of change in the indicators, suggesting that the state of stand growth is more sensitive under the RCP2.6 scenario. The L-index showed an increase ranging from 13.7 % to 34.4 % under the unequal weights in different climate scenarios, in which the optimal harvesting intensity ranged from 14.6 % to 19.8 %. More importantly, it should be noted that the values of the increases in the L-index and the relative increased proportion (RIP) were both higher than those when unequal weights were employed. Moreover, it should be highlighted that the increments in the L-index and RIP were both greater than those observed when unequal weights were applied for all three plots under different climate scenarios. Overall, the adjusted the complete mixing degree index (Mc) increased, angle index (W), dominance ratio index (U), and Hegyi competition index (CI) decreased compared to before optimizing with the equal or unequal weights of the stand structural variable, which is evident that the adjustments made to the stand’s structure have resulted in a significant improvement. Thus, the multi-objective optimization for forest spatial dynamics constructed is both reasonable and effective, and it more scientific forest management under different climatic scenarios.

Multi-objective Structural Optimization of Column based on Topology Optimization and NSGA-Ⅱ Algorithm

Multi-objective Structural Optimization of Column based on Topology Optimization and NSGA-Ⅱ Algorithm

Multiobjective Structural Layout Optimization of Tall Buildings Subjected to Dynamic Wind Loads

Multiobjective Structural Layout Optimization of Tall Buildings Subjected to Dynamic Wind Loads

Multi-objective structure optimization for interior permanent magnet synchronous motors under complex operating conditions

Multi-objective structure optimization for interior permanent magnet synchronous motors under complex operating conditions

Multi-level and multi-objective structural optimization for hypersonic vehicle design

This research introduces a novel methodology for optimizing the structural design of a full-scale hypersonic aircraft, integrating a multifaceted approach across different levels of modelling detail to enhance a variety of performance metrics. The proposed approach is capable of reduce the vehicle mass, while meeting the necessary operational requirements and maintaining an acceptable computational cost. The methodology, based on a coupled bi-level size optimization and denoted as single-objective bi-level optimization (SOBLO), is applied to the passenger cabin of the STRATOFLY MR3 hypersonic cruiser vehicle. This results in a substantial reduction in the baseline concept design weight, estimated to be more than half on average. The procedure is extended to incorporate a multi-objective optimization approach (MOBLO), which generates a Pareto frontier that provides significant information for selecting the optimal trade-off design, considering manufacturability constraints. The outcomes underscore the efficacy of the proposed methodology and highlight its usefulness in sizing complex aircraft configurations, particularly under the demanding loads imposed by a hypersonic flight regime. This approach has the potential to improve the overall production process and enable designers to attain feasible structural design solutions during early stages of development.

Multi-objective optimization of a novel phase-change thermal storage unit based on theoretical modeling and genetic algorithm

Phase-change thermal storage technologies are becoming increasingly indispensable in the field of renewable energy, and researchers have been striving to achieve high thermal storage performance in storage devices. To enhance the application potential of phase-change thermal storage units based on micro heat pipe arrays, theoretical analysis is applied to optimize the operating parameters and the fin structure, addressing the research gap caused by insufficient theoretical analysis. Therefore, an accurate thermal resistance network model is developed, and machine learning algorithms are employed for the multi-objective optimization of the fin structure. The optimal heights, widths, and thicknesses in two directions of the fins are 42.2, 3.7, 0.3, and 0.8 mm, respectively, resulting in a 15.8 % increase in charging power compared to the initial structure without increasing metal consumption. Additionally, it is recommended that the design flow rate be increased by 26 kg/h for each additional thermal storage unit connected in series. Finally, a phase-change thermal storage device is designed for a solar water heating system, and its applicability is simulated and analyzed. This study provides design guidance for this novel thermal storage device and promotes its application in the field of renewable energy.

Modeling and Optimization of the Air-Supported Membrane Coal Shed Structure in Ports

The air-supported membrane coal shed is widely used in bulk cargo terminals. It not only effectively protects goods from adverse weather conditions but also helps reduce coal dust and harmful gas emissions, promoting the green and sustainable development of ports. However, in practical engineering, the design parameters of the coal shed are often based on experience, making it difficult to accurately assess the quality of the structural design. The flexibility of the membrane material also makes the structure susceptible to deformation or tearing. This paper mainly focuses on modeling and solving the optimization design issues of air-supported membrane coal shed structures. According to the evaluation criteria for the form of air-supported membrane coal sheds, a multi-objective structural optimization model is established to minimize the maximum stress on the membrane surface, ensure uniform stress distribution, maximize structural stiffness, and minimize costs. The study utilizes a combined optimization approach using ANSYS 19.0 and MATLAB 2016a, incorporating an improved NSGA-II algorithm program developed in MATLAB into ANSYS for structural form analysis and load calculation. The research results indicate that the optimal solution reduces the maximum stress on the loaded membrane surface by 5.36%, shortens the maximum displacement by 30.3%, and saves on economic costs by 9.85%. Compared to traditional empirical design methods, the joint use of MATLAB and ANSYS for optimization design can provide more superior solutions, helping ports to achieve environmental protection and economic efficiency goals.

A compliant constant-force mechanism with sub-Newton force and millimeter stroke output

Force control technology plays a pivotal role in manipulating vulnerable objects. This paper presents a new compliant mechanism with constant-force output characteristics, which can prevent force damage due to displacement overshoot. Due to its unique passive structure, it is exempted from intricate sensors and complicated controllers. The quasi-static constant-force mechanism is obtained by the parallel combination of positive- and negative-stiffness mechanisms. Such a straightforward method facilitates a rapid development and implementation process. The procedures of architectural arrangement selection, theoretical model establishment, parameter sensitivity evaluation, and multi-objective structural optimization are carried out to achieve specified constant-force characteristics. Moreover, the prototype fabrication and performance testing of a constant-force mechanism have been performed. The results demonstrate that the mechanism delivers a constant output force of 339 mN in the motion range of 1.84 mm. The constant-force feature is solely governed by the actuating displacement and is independent of driving speed and acceleration. The promising application of the constant-force mechanism has been demonstrated by manipulating small force-sensitive objects such as biological eggs.

A machine learning-based method for co-design and optimization of microwave-absorbing/load-bearing multifunctional structures

Simultaneously considering the absorption performance and load-bearing capability is a trend in the design of multifunctional structures. Nevertheless, the collaborative design and optimization involved in this process present a challenging problem. Herein, guided by multifunctionality, a lightweight microwave-absorbing/load-bearing multifunctional structure is intelligently inversely designed based on machine learning. A co-design scheme is developed to address the contradiction between the absorption performance and load-bearing performance. An approach for rapid inverse design of metamaterial absorbers containing multilayered frequency-selective surfaces is proposed. The simulation results obtained using multi-objective optimization based on surrogate models indicate that the optimized multifunctional structure achieves more than 90% absorption in the frequency range of 2.5 GHz–18.0 GHz and simultaneously exhibits superior load-bearing performance with an out-of-plane Young’s modulus of 334.8 MPa and an out-of-plane compressive strength of 4.95 MPa, demonstrating the effectiveness of the co-design scheme. Finally, the experimental results are analysed. This study provides a reference for co-design and multi-objective optimization of similar multifunctional structures.

A robust machine learning-based framework for handling time-consuming constraints for bi-objective optimization of nonlinear steel structures

In structural design, multi-objective optimization of nonlinear steel structures simultaneously considers various design (often conflicting) purposes during the stage of construction to the operation of projects. Such optimization generally requires excessive computational efforts for the evaluation of time-consuming constraints. To overcome this drawback, this paper presents an efficient machine learning-based (ML) method to perform bi-objective optimization of nonlinear steel structures describing two conflicting objectives, namely minimization of structural weight and nodal displacements, simultaneously. The proposed method combines a nondominated sorting genetic algorithm-II (NSGA2) with an extreme gradient boosting (XGBoost) surrogate-assisted model. Furthermore, a multi-objective comparison technique (MulCT) is implemented, where a safety parameter t is introduced to reduce errors in the predictive ML model. To demonstrate the efficiency of the proposed method, two robust design examples, including a planar 10-bar truss and 47-bar transmission tower structures, are provided. In comparison with various ML algorithms, numerical results illustrate that the XGBoost model is superior in performance and requires significantly less training time. The MulCT technique enhances computational efficiency, leading to a 20% reduction in computing resources as when it was implemented with NSGA2. The proposed method by integrating both MulCT and XGBoost models with NSGA2 can save more than 50% of computational efforts, while maintaining good accuracy, as can be achieved by NSGA2.

Multi-objective structural optimization and degradation model of magnesium alloy ureteral stent

BackgroundMg alloys have attractive properties, including biocompatibility, biodegradability, and ideal mechanical properties. Moreover, Mg alloys are regarded as one of the promising candidates for manufacturing ureteral stents. This study proposed a multi-objective optimization method based on the Kriging surrogate model, NSGA-Ⅲ, and finite element analysis to improve the degradation performance of Mg alloy ureteral stents. MethodsThe finite element model for the degradation of Mg alloy ureteral stents has been established to compare the degradation performance of the stents under different parameters. Latin hypercube sampling was adopted to generate train sample points in the design space. Meanwhile, the Kriging surrogate model was constructed between strut parameters and stent degradation behavior. The NSGA-Ⅲ was utilized to determine the optimal solution in the global design space. ResultsThe optimized stent achieved 5.52 ​× ​degradation uniformity (M), 10 ​× ​degradation time (DT), and 4 ​× ​work time (FT). The errors between the Kriging surrogate model and the finite element calculation results were less than 6%. ConclusionThe optimized stent achieved better degradation performance. The degradation behavior of stents was dependent on the design parameters. The multi-objective optimization method based on the Kriging surrogate model and finite element analysis was effective in stent design optimization problems.

Multi-objective optimization and theoretical analysis of re-entrant structure with enhanced mechanical properties

In response to the challenge of low stiffness and energy absorption capacity, various designs of negative Poisson's ratio (NPR) structures have emerged. However, these designs often lack a comprehensive analysis of other mechanical properties, leading to subpar mechanical performance. Previous studies have explored the mechanical properties response of enhanced re-entrant honeycombs (ERH) under impact conditions, revealing limitations in optimizing the structure's performance with a single objective. Therefore, this study aims to enhance ERH structural parameters to achieve superior mechanical performance through theoretical derivations and geometric optimizations. The results demonstrate that the proposed theoretical model is consistent with finite element analysis and response surface (RS) predictions. Expressions for Young's modulus, specific energy absorption, and compressive strength are proposed, facilitating the identification of structural parameters that meet specific requirements during reverse design. Furthermore, a multi-objective optimization approach optimizes the geometric parameters based on maximum energy absorption and compressive strength. The mechanical behavior of the optimized ERH is investigated using the finite element method, revealing the energy absorption capacity of 13.78 J/g while maintaining Poisson's ratio at -1.06. Additionally, the deformation mode of the optimized structure showcases enhanced stability compared to traditional honeycomb structures. The theoretical model and RS method were used to guide the design of ERH and promote the application of NPR structures.

Multi-objective optimization of composite sandwich structures using Artificial Neural Networks and Genetic Algorithm

Sandwich structures offer significant opportunities to improve the performance of many industrial applications such as aerospace, automotive, and marine. The design of a composite sandwich structure is often challenging because it is driven by the balance between the weight and cost of these structures. In this paper, a multi-objective optimization model using a Genetic Algorithm (GA) and an Artificial Neural Network (ANN) is presented to evaluate a new optimization approach in terms of weight and cost minimization for the composite sandwich structures. Classical lamination and beam bending theories were used, along with Monte Carlo simulation, to generate the design data for the proposed composite sandwich structure, which is applied as a floor panel for a high-speed train. Multilayer feedforward neural networks were used for predicting safety factors, cost, and weight of the designed structure based on the following inputs: core density, core thickness, face sheet materials’ combinations, and applied load. The trained Neural Network model was able to predict the considered results with a good performance metric, namely the coefficient of determination (R2 = 0.99) and the Mean Square Error (MSE = 1.3·10−5).Multi-objective optimization for cost and weight minimization was performed with a Genetic Algorithm using the derived ANN model. The obtained Pareto front provided several non-dominated optimal points leading to insights on the optimization process. The Finite Element Method (FEM) was used to model the key points of the optimal designs (i.e. the design with the lowest cost, weight, and Pareto optimal points). The FEM and optimization results had a maximum deviation of about 8.9%, indicating a good agreement between the two techniques.The newly elaborated methodology demonstrates a new approach for obtaining the optimum design of the investigated composite sandwich structure constructed from honeycomb core and laminated face sheets in terms the cost and weight. The study concluded that the use of Carbon Fiber-Reinforced Plastic (CFRP) or Fiber-Metal Laminate (FML) face sheets results in significant weight savings of about 59.5% and 48.6%, respectively, compared to an all-aluminum sandwich structure.