Multi-objective hierarchical optimization design of compound electromagnetic linear actuator

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

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.

In this paper the Six-speed transmission with belt overdrive gear of one automobile transmission system will be taken as research object, automobile energy utilization ratio and standing start continuous shift acceleration time will be regarded as objective function, the multi-objective optimization model of automobile transmission system will be established. The improved congestion degree calculation and choose operation method will be put forward according to the problem that poor population diversity when NSGA-II algorithm was used in the transmission optimization, the improved NSGA-II algorithm will be used to implement multi-objective optimization design on the automobile transmission system. Optimization results show that Pareto optimal solutions obtained from the improved algorithm are more evenly distributed and algorithms are more efficient. The improved NSGA-II algorithm used in this paper is also suitable for other areas of computing multi-objective optimization problem.

ABSTRACTTo address multiobjective, multi constraint and time-consuming structural optimization problems in a vehicle axle system, a multiobjective cooperative optimization model of a vehicle axle structure is established. In light of the difficulty in the nondominated sorting of the NSGA-II algorithm caused by inconsistent effects of the uniformity objective function and physical objective function, this paper combines a multiobjective genetic algorithm with cooperative optimization and presents a strategy for handling the optimization of a vehicle axle structure. The uniformity objective function of the sub discipline is transformed to its self-constraint. Taking the multiobjective optimization of a vehicle axle system as an example, a multiobjective cooperative optimization design for the system is carried out in ISIGHT. The results show that the multiobjective cooperative optimization strategy can simplify the complexity of optimization problems and that the multiobjective cooperative optimization method based on an approximate model is favorable for accuracy and efficiency, thereby providing a theoretical basis for the optimization of similar complex structures in practical engineering.

This paper proposes a multi-objective optimization design method with the discrete variables for synchronous buck converter. This method defines three objective factors: minimize cost, minimize area and maximize efficiency, and a multi-objective optimization problem can be drawn with the objective function of assessment models of cost, area and loss and the constraint of the component database built by the parameter of MOSFETs, inductors and capacitors. This paper uses the NSGA-II algorithm to process the problem of a multi-objective optimization with discrete variables. The NSGA-II algorithm can find the Pareto optimal solution of a very large solution space which has hundreds of thousands feasible combinations of components, and the designers can make the reasonable choice of components by performing the trade-off analysis for the optimal solution when selecting the components. The simulation results demonstrate the feasibility of multi-objective optimization design method in this paper.

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.

Bi-level multi-objective fuzzy design optimization of energy supply systems aided by problem-specific heuristics

A multi-objective optimal PID control for a nonlinear system with time delay

A multiobjective design optimization (MDO) study has been conducted to characterize and maximize the performance of the downscaled cusped field thruster with respect to thrust, total efficiency, and specific impulse characterized by common design parameters: anode voltage, anode current, mass flow rate, and geometric configuration. Particle-in-cell (PIC) simulations have been performed for the selected design points identified in MDO study for verification by accurately accounting for phenomena and performance losses that originate from uncertainties and complexities associated with the thruster design and physics. The fidelity of the models employed in MDO has been enhanced owing to the new physical insights gained from the detailed analysis of the PIC results. The prediction errors associated with uncertainties such as the beam current and divergence angle have been reduced to within 5%.

Cemented carbide circular saw blades are widely used for wood cutting, but they often suffer from vibration and noise issues. This study presents a multi-objective optimization method that integrates ANSYS and MATLAB to optimize the design of noise reduction slots in circular saw blades. A mathematical model was developed to correlate the emitted sound power with the overall vibration intensity. A multi-objective optimization model was then formulated to map the slot shape parameters to the deformation, equivalent stress, and vibration intensity during sawing. The ABAQUS thermal–mechanical coupling analysis was used to determine the sawing force and temperature field. The NSGA-II algorithm was applied on the ANSYS–MATLAB platform to iteratively compute slot shape parameters and conduct optimization searches for a globally optimal solution. Circular saw blades were fabricated based on the optimization results, and experimental results showed a significant reduction in sawing noise by 2.4 dB to 3.0 dB on average. The noise reduction effect within the specified frequency range closely agreed with the simulation results, validating the method’s efficiency. This study provides a feasible and cost-effective solution to the multi-objective optimization design problem of noise reduction slots for circular saw blades.

:A robust multi-objective wing design optimization procedure using CFD is presented in this work. Instead of directly applying CFD to wing design optimization, a Kriging aerodynamic model that approximates CFD result is proposed to save computational cost. By introducing 6σ robust approach as a sub-objective function, multi-objective wing design problems can be solved with aerodynamic robustness. Non-Uniform Rational B-Spline curves (NURBS) are introduced to depict the wing geometry in design optimization process. The most important parameters of the wing geometry can then be screened by design of experiment and treated as design variables due to the local variation property of NURBS. Under this formulation, a multi-objective genetic algorithm based on non-dominated sorting is employed to handle multiple flight conditions in wing design. The optimum wing geometry is selected according to trade-off among design objects on the non-dominated front. To validate the proposed approach, two robust design optimization cases are studied for ONERA-M6-Wing. It turns out that the drag coefficient is insensitive to Mach number between Ma0.8–Ma0.9 after robust optimization. The result also verifies the effectiveness of our method in boosting performance and robustness of multiple flight conditions: the lift curve slope (Ma0.3) of optimum wing and the 6σ objective function of transonic drag (Ma0.8–Ma0.9) increase by 11.9% and 25.4%, respectively. Observations in the optimization cases are concluded as follows: 1) For wing aerodynamic design problems, the multi-objective robust optimization can both improve the performance at different flight conditions and provide robustness. 2) The Kriging aerodynamic model derived from CFD result can satisfy the precision requirement of wing design. 3) Even though the optimization result is subject to the weights of the 6σ function in sub-object, the influence is not comparable to the trade-off among design objects. 4) The optimum solution obtained by proposed approach is superior to gradient based optimization method, while the computational cost is acceptable.

A preliminary design optimization approach of axial flow compressors is developed. Loss correlations associated with airfoil geometry are introduced to relax the stringent requirement for the designer to prescribe the stage efficiency. In face of the preliminary design complexity resulted from the large number of design variables together with their stringent variation ranges and multiple design goals, the multi-objective optimization algorithm is incorporated. With such a developed preliminary design optimization method, the design space can be then explored extensively and the optimum designs of both high level overall efficiency and wide stall margin can be readily achieved. The preliminary design optimization method is validated in two steps. Firstly, an existing 5-stage compressor is redesigned without optimization. The obtained geometries and flow parameters are compared to the existing data and a good consistency is achieved. Then, the redesigned compressor is used as initial design and optimized by the developed multi-objective preliminary design optimization method, and significant performance gains are obtained, which demonstrates the effectiveness of the developed optimization methods.

Integration of multi-objective reliability-based design optimization into thermal energy management: Application on phase change material-based heat sinks

Multiobjective optimization is one of the key challenges in engineering design process. Since the answer to such problem is not unique, a set of evenly distributed solutions is particularly important for a designer. The Directed Search Domain (DSD) method is a numerical optimization approach that has proven to be efficient enough to tackle such optimization problems. In this paper, we propose two modifications to the DSD approach which make the solution algorithm simpler for program implementation. These modifications are related to the control of the search domain and reformulation of the appropriate single objective optimization problem. As a result, the computational efficiency of the method is increased due to the lower number of objective function evaluations. The capabilities of the new approach are demonstrated on a set of test cases.

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.