Constraints handling in Nash/Adjoint optimization methods for multi-objective aerodynamic design

Optimization problems in many industrial applications are very hard to solve. Many examples of them can be found in the design of aeronautical systems. In this field, the designer is frequently faced with the problem of considering not only a single design objective, but several of them, i.e., the designer needs to solve a Multi-Objective Optimization Problem (MOP). In aeronautical systems design, aerodynamics plays a key role in aircraft design, as well as in the design of propulsion system components, such as turbine engines. Thus, aerodynamic shape optimization is a crucial task, and has been extensively studied and developed. Multi-Objective Evolutionary Algorithms (MOEAs) have gained popularity in recent years as optimization methods in this area, mainly because of their simplicity, their ease of use and their suitability to be coupled to specialized numerical simulation tools. In this chapter, we will review some of the most relevant research on the use of MOEAs to solve multi-objective and/or multi-disciplinary aerodynamic shape optimization problems. In this review, we will highlight some of the benefits and drawbacks of the use of MOEAs, as compared to traditional design optimization methods. In the second part of the chapter, we will present a case study on the application of MOEAs for the solution of a multi-objective aerodynamic shape optimization problem.

This paper designs and optimizes a new structure hybrid material B‐pillar assembly. Establish a finite element analysis model for the side impact test of an electric vehicle to verify the model's accuracy. Construct a finite element model of the hybrid material B‐pillar assembly. Combined with the static performance analysis of the B‐pillar, the laminate design of the carbon fiber composite B‐pillar reinforcement plate and optimization. For the outer and inner panels of the B‐pillar, the surrogate model method and the multiobjective optimization method are combined to set 11 design variables and 13 responses. The optimal Latin hypercube design method was used to randomly sample each design variable and fit the radial basis function (RBF) approximate model. The modified second‐generation non‐dominated sorting genetic algorithm (MNSGA‐II) was used to carry out multiobjective optimization of the mixed material B‐pillar assembly, and the multicriteria decision‐making method was used to obtain the optimal solution for the Pareto solution set. A drop weight impact test was performed on the hybrid material B‐pillar assembly. The results showed that the peak collision force of the hybrid material B‐pillar was reduced by 43.7% compared with the original steel B‐pillar, the specific energy absorption was increased by 17.5%, and the side impact safety performance was better. After optimization, the weight of the mixed material B‐column was reduced by 26.44%. The improvement rates of the intrusion amount at P2 and the intrusion speed at P1 were 23.99% and 0.63%, respectively, and the lightweight effect and side impact safety were significantly improved.Highlights The finite element analysis parameters of carbon fiber composite materials were constructed through experiments, and the basis for simulation analysis under various working conditions of the B‐pillar based on performance‐driven optimization was established. A hybrid material B‐pillar design method is proposed, which consists of a variable‐thickness high‐strength steel B‐pillar outer plate, a variable‐thickness high‐strength steel B‐pillar inner plate, and a carbon fiber composite B‐pillar reinforcement plate. The super layer of the carbon fiber composite B‐pillar reinforcement plate was optimized and the laying plan of the carbon fiber composite B‐pillar reinforcement plate was determined. Performance‐driven optimization is adopted to realize the collaboration of multilevel design and optimization methods such as B‐pillar conceptual design, detailed design, and multiobjective optimization. A modified NSGA‐II algorithm was proposed and combined with the multicriteria decision‐making method and the entropy‐weighted gray relation analysis method to determine the Pareto optimal solution and the optimal design scheme for the mixed material B‐pillar.

Heuristic-based multi-objective optimization design for viscous dampers in RC frame structures considering soil-structure interaction

Surrogate-based method can dramatically reduce the number of expensive function evaluations in real-world multi- objective optimization problems (MOP). When the number of objectives is small, using surrogate models combined with expected hypervolume improvement (EHVI) infill sampling criterion (ISC) has been proved to be efficient to provide a set of solutions with good diversity and good proximity to the Pareto front (PF) in aerodynamic shape optimization. However, traditional hypervolume-based infilling strategies use only one kind of ISC to generate one or multiple sample points, the advantages of various kinds of ISC cannot be comprehensively utilized and the parallelization is not easy to implement. This paper proposes a combined multi-point infilling strategy based on Kriging models and develops an efficient global multi-objective constrained optimization method (EGMOCO) to solve multi- objective aerodynamic shape optimization with complex constraints. Multiple sample points are generated by using four ISC considering hypervolume at each iteration and then evaluated in parallel. Firstly, the performance of EGMOCO is compared with that of single criterion EHVI strategy on six benchmarks within the same computational budget to prove its effectiveness, and then EGMOCO is implemented in an aerodynamic shape optimization problem with complex constraints. The result shows that EGMOCO has good performance in balancing local exploitation and global exploration with faster convergence rate and high robustness, the whole PF can be fully explored in limited evaluations and the constraint handling is effective especially for real-world problems with complex and nonlinear constraints, the comprehensive aerodynamic performance of the airfoil is greatly improved. It can be confirmed that Kriging-based multi-objective optimization method combined with multi-point infilling strategy performs better than single infilling criterion EHVI, since different sample infilling criteria can complement with each other, both local exploitation and global exploration can be considered and well balanced.

Multi-objective optimization method for reactor shielding design based on SMS-EMOA

Due to the adversarial limitations between the output solutions in the multi-objective optimization stage, the energy efficiency optimization of large pumping stations has the disadvantage of difficult coordination between power consumption and efficiency. Therefore, a multi-objective Bayesian hyperparameter optimization algorithm design for energy efficiency optimization of large pumping stations has been carried out. A multi-objective optimization model for energy efficiency of large pumping stations was constructed by combining the input power of the main motor, transmission energy loss, transformer loss, and energy consumption of auxiliary equipment, with efficiency as the constraint. We extract sequence features that affect pump water demand, and use feature labels as hyperparameters for the multi-objective optimization model of energy efficiency in large pumping stations. We transform the multi-objective optimization problem into a hyperparameter optimization problem, avoiding adversarial output solutions. We iterate the query points collected by EI, so the output model reaches a convergent optimal solution. The test results show that the designed algorithm can improve the pumping efficiency of the pump station while controlling the power consumption of the pump station, achieving collaborative optimization of efficiency.

Although various optimization methods for solving single-objective problems have been developed in the last few decades, these methods have lost their eligibility due to the fact that today’s engineering problems are toward multiple objective optimization problems, in real applications. For single-objective optimization problems, for example, in case of a minimization problem, this value is the decision vector giving the smallest objective that can be achieved within the specified constraints. Hence the minimum decision vector within all possible (feasible) solution vectors is the so-called optimal solution and/or optimal design. However, in multi-objective optimization problems, since a different objective value is generated against each decision vector, the superiority of the solutions over each other is determined by considering the trade-off among the objective values. Therefore, the solution of multi-objective optimization problems, unlike single-objective problems, is a set of vectors rather than a single decision vector. In multi-objective optimization problems, especially if there are intricate objectives, the computational cost of the problem increases. In other words, while synchronously trying to maximize one of the objectives and to minimize another one makes it difficult to find the global optimum design. One of the important techniques used in multi-objective optimization problems is Pareto optimality which enables to select the global optimum solution taking into account the trade-off among all objectives. In this context, using of derivative-based methods has decreased, but the use of metaheuristic methods has increased due to the rapid availability of global optimum solution. This is because the improvements in the field of optimization are progressing in proportion to technology and varying according to the needs. In this chapter, one of the recent metaheuristic optimization methods based on swarm intelligence that is so-called a Pareto-based bat algorithm inspired by the behavior of determining the direction and distance of an object using the echo of the sound called the echolocation of bats is used in order to obtain optimum solutions for multi-objective engineering design problems. In this regard, a four-bar planar truss, a real-sized welded steel beam as well as a multi-layer radar absorber are selected as multi-objective engineering design optimization problems. In case the obtained results (optimal designs) are examined, the potency and the reliability of the proposed multi-objective Pareto-based bat algorithm are demonstrated.

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

A computationally efficient procedure for multiobjective design optimization with variable-fidelity models and response surface surrogates is presented. The proposed approach uses the multiobjective evolutionary algorithm that works with a fast surrogate model, obtained with kriging interpolation of the low-fidelity model data enhanced by space-mapping correction exploiting a few high-fidelity training points. The initial Pareto front generated by multiobjective optimization of the surrogate using the multiobjective evolutionary algorithm can be iteratively refined by local enhancements of the surrogate model. The latter are realized with a space-mapping response correction based on a limited number of high-fidelity training points allocated along the initial Pareto front. The proposed method allows us to obtain, at a low computational cost, a set of designs representing tradeoffs between the conflicting objectives. The current approach is illustrated using examples of airfoil design: one in transonic flow, involving aerodynamics tradeoffs; and another one in low-speed flow, involving tradeoffs between the aerodynamic and the aeroacoustic performances.

Groundwater management involves conflicting objectives as maximization of discharge contradicts the criteria of minimum pumping cost and minimum piping cost. In addition, available data contains uncertainties such as market fluctuations, variations in water levels of wells and variations of ground water policies. A fuzzy model is to be evolved to tackle the uncertainties, and a multiobjective optimization is to be conducted to simultaneously satisfy the contradicting objectives. Towards this end, a multiobjective fuzzy optimization model is evolved. To get at the upper and lower bounds of the individual objectives, particle Swarm optimization (PSO) is adopted. The analytic element method (AEM) is employed to obtain the operating potentio metric head. In this study, a multiobjective fuzzy optimization model considering three conflicting objectives is developed using PSO and AEM methods for obtaining a sustainable groundwater management policy. The developed model is applied to a case study, and it is demonstrated that the compromise solution satisfies all the objectives with adequate levels of satisfaction. Sensitivity analysis is carried out by varying the parameters, and it is shown that the effect of any such variation is quite significant. Copyright (c) 2015 John Wiley & Sons, Ltd.

This study presents a new method for aerodynamic optimization of a civil aircraft fuselage. Typically, the fuselage is designed for minimum drag force at cruise conditions, which is essential for determining the flight cost. Evolutionary optimization methods, as a powerful tool, require the accurate computations of flows around several hundreds of candidate geometries, which in turn are too costly and time-consuming. One strategy is to use two-dimensional simulations that reduce the computational cost by at least one order of magnitude. This approach was applied in the current work, and the results were obtained with the aim of minimizing the drag coefficient and maximizing the lift coefficient. A genetic algorithm (GA) was used for shape optimization, and the objective function evaluation was carried out using computational fluid dynamics (CFD). A fuselage shape parameterization method is presented that accounts for important flow features. The 150-seat aircraft model designed in Amirkabir University of Technology was considered as a reference body. In the first step, the optimization is carried out for the single objective of minimizing the drag coefficient. Then, the multiobjective optimization is performed with the simultaneous drag coefficient minimization and lift coefficient maximization. Finally, the two-dimensional (2D) side view of the optimum fuselages is used for generation of the corresponding three-dimensional (3D) geometry. The results show that such 3D optimum fuselage reduced the drag coefficient by about 11% while increasing the lift coefficient by 29% in comparison with the original geometry.

In the multi-objective optimization design of automotive seats based on Approximation-Based Design Optimization, a single approximation model may not adequately address the requirement of accurately fitting highly nonlinear feature data. For this reason, the Hybrid Approximation Models based on the Multi-Species Approximation Model (HAM-MSAM) is proposed to meet the requirement for high fitting accuracy. Subsequently, this study introduces a HAM-MSAM-based Approximation-Based Global Multi-Objective Optimization Design (ABGMOOD) strategy. This strategy is employed in the multi-objective optimization of the rear seat of a passenger car. HAM-MSAM was constructed from an experimentally validated finite element model and a training set generated through experimental design. The advantages of HAM-MSAM in capturing the highly nonlinear response under seat crash conditions were validated through comparison with hybrid model construction methods reported in existing literature. Finally, the optimization results obtained by the ABGMOOD strategy were compared to those of the classical local multi-objective optimization strategy, demonstrating the substantial advantages of the ABGMOOD optimization scheme in economy and weight reduction. In addition, the safety of the rear seats is slightly lower than that of the local optimization scheme but remains in compliance with regulatory requirements. The final optimized rear seat demonstrates notable improvements in safety, economy, and weight reduction, validating the feasibility of the ABGMOOD strategy and providing valuable insights for similar engineering optimization challenges.

Conventional electromagnetic linear actuators(ELA) have difficulty in balancing efficiency, response and accuracy, so a novel compound ELA is researched, featuring a coaxial integrated design of moving coil and moving iron actuators that switch between co-drive mode and separate drive mode based on service environment. In order to further enhance the comprehensive performance of the actuator and improve its adaptability to extreme working conditions, a multi-objective hierarchical optimization strategy was proposed based on NSGA-II algorithm by analyzing its structural principle, magnetic circuit characteristics and electromagnetic force characteristics. The moving coil actuator, as the main driving component, and the moving iron actuator, as the auxiliary driving component, are selected as the first and second layer optimization objects for multi-objective optimization design. Results indicate that the actuator achieves starting forces of 587.6N and 191.4N under cooperative drive mode and separate drive mode, respectively. Following optimization, these forces increased by approximately 2.2% and 22.4%, while the mover mass was reduced by about 7.2%. The actuator's thrust density, response speed, and structural compactness were effectively enhanced. The proposed approach can be used to solve the complex multi-objective optimization tasks in ELA designing.

This paper considers the combined use of a hybrid numerical method for the modeling of acoustic mufflers and a genetic algorithm for multiobjective optimization. The hybrid numerical method provides accurate modeling of sound propagation in uniform waveguides with non-uniform obstructions. It is based on coupling a wave based modal solution in the uniform sections of the waveguide to a finite element solution in the non-uniform component. Finite element method provides flexible modeling of complicated geometries, varying material parameters, and boundary conditions, while the wave based solution leads to accurate treatment of non-reflecting boundaries and straightforward computation of the transmission loss (TL) of the muffler. The goal of optimization is to maximize TL at multiple frequency ranges simultaneously by adjusting chosen shape parameters of the muffler. This task is formulated as a multiobjective optimization problem with the objectives depending on the solution of the simulation model. NSGA-II genetic algorithm is used for solving the multiobjective optimization problem. Genetic algorithms can be easily combined with different simulation methods, and they are not sensitive to the smoothness properties of the objective functions. Numerical experiments demonstrate the accuracy and feasibility of the model-based optimization method in muffler design.

Crushing analysis and multi-objective optimization design for bionic thin-walled structure