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This paper aims to use the crankshaft-bearing system of a four-cylinder internal combustion engine as the studying object, and develop a multi-objective optimization design of the crankshaft-bearing. In the current optimization design of engine crankshaft-bearing, only the crankshaft-bearing was considered as the studying object. However, the corresponding relations of major structure dimensions exist between the crankshaft and the crankshaft-bearing in internal combustion engine, and there are the interaction effects between the crankshaft and the crankshaft-bearing during the operation of internal combustion engine.

The crankshaft mass and the total frictional power loss of crankshaft-bearing s are selected as the objective functions in the optimization design of crankshaft-bearing. The Particle Swarm Optimization algorithm based on the idea of decreasing strategy of inertia weight with the exponential type is used in the optimization calculation.

The total frictional power loss of crankshaft-bearing and the crankshaft mass are decreased, respectively, by 26.2 and 5.3 per cent by the multi-objective optimization design of crankshaft-bearing, which are more reasonable than the ones of single-objective optimization design in which only the crankshaft-bearing is considered as the studying object.

The crankshaft-bearing system of a four-cylinder internal combustion engine is taken as the studying object, and the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system is developed. The results of this paper are helpful to the design of the crankshaft-bearing for engine. There is universal significance to research the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system. The research method of the multi-objective optimization design of crankshaft-bearing based on the crankshaft-bearing system can be used to the optimization design of the bearing in the shaft-bearing system of ordinary machinery.

The purpose of this paper is to investigate the strategies and algorithms for expedited design optimization of microwave and antenna structures in multi-objective setup.

Formulation of the multi-objective design problem-oriented toward execution of the population-based metaheuristic algorithm within the segmented search space is investigated. Described algorithmic framework exploits variable fidelity modeling, physics- and approximation-based representation of the structure and model correction techniques. The considered approach is suitable for handling various problems pertinent to the design of microwave and antenna structures. Numerical case studies are provided demonstrating the feasibility of the segmentation-based framework for the design of real-world structures in setups with two and three objectives.

Formulation of appropriate design problem enables identification of the search space region containing Pareto front, which can be further divided into a set of compartments characterized by small combined volume. Approximation model of each segment can be constructed using a small number of training samples and then optimized, at a negligible computational cost, using population-based metaheuristics. Introduction of segmentation mechanism to multi-objective design framework is important to facilitate low-cost optimization of many-parameter structures represented by numerically expensive computational models. Further reduction of the design cost can be achieved by enforcing equal-volumes of the search space segments.

The study summarizes recent advances in low-cost multi-objective design of microwave and antenna structures. The investigated techniques exceed capabilities of conventional design approaches involving direct evaluation of physics-based models for determination of trade-offs between the design objectives, particularly in terms of reliability and reduction of the computational cost. Studies on the scalability of segmentation mechanism indicate that computational benefits of the approach decrease with the number of search space segments.

The proposed design framework proved useful for the rapid multi-objective design of microwave and antenna structures characterized by complex and multi-parameter topologies, which is extremely challenging when using conventional methods driven by population-based metaheuristics algorithms. To the authors knowledge, this is the first work that summarizes segmentation-based approaches to multi-objective optimization of microwave and antenna components.

In line with computational technological advances, obtaining optimal solutions for engineering problems has become attractive research topics in various disciplines and real engineering systems having multiple objectives. Therefore, it is aimed to ensure that the multiple objectives are simultaneously optimized by considering them among the trade-offs. Furthermore, the practical means of solving those problems are principally concentrated on handling various complicated constraints. The purpose of this paper is to suggest an algorithm based on symbiotic organisms search (SOS), which mimics the symbiotic reciprocal influence scheme adopted by organisms to live on and breed within the ecosystem, for constrained multi-objective engineering design problems.

Though the general performance of SOS algorithm was previously well demonstrated for ordinary single objective optimization problems, its efficacy on multi-objective real engineering problems will be decisive about the performance. The SOS algorithm is, hence, implemented to obtain the optimal solutions of challengingly constrained multi-objective engineering design problems using the Pareto optimality concept.

Four well-known mixed constrained multi-objective engineering design problems and a real-world complex constrained multilayer dielectric filter design problem are tackled to demonstrate the precision and stability of the multi-objective SOS (MOSOS) algorithm. Also, the comparison of the obtained results with some other well-known metaheuristics illustrates the validity and robustness of the proposed algorithm.

The algorithmic performance of the MOSOS on the challengingly constrained multi-objective multidisciplinary engineering design problems with constraint-handling approach is successfully demonstrated with respect to the obtained outperforming final optimal designs.

This paper aims to investigate deterministic strategies for low-cost multi-objective design optimization of compact microwave structures, specifically, impedance matching transformers. The considered methods involve surrogate modeling techniques and variable-fidelity electromagnetic (EM) simulations. In contrary to majority of conventional approaches, they do not rely on population-based metaheuristics, which permit lowering the design cost and improve reliability.

There are two algorithmic frameworks presented, both fully deterministic. The first algorithm involves creating a path covering the Pareto front and arranged as a sequence of patches relocated in the course of optimization. Response correction techniques are used to find the Pareto front representation at the high-fidelity EM simulation level. The second algorithm exploits Pareto front exploration where subsequent Pareto-optimal designs are obtained by moving along the front by means of solving appropriately defined local constrained optimization problems. Numerical case studies are provided demonstrating feasibility of solving real-world problems involving expensive EM-simulation models of impedance transformer structures.

It is possible, by means of combining surrogate modeling techniques and constrained local optimization, to identify the set of alternative designs representing Pareto-optimal solutions, in a realistic time frame corresponding to a few dozen of high-fidelity EM simulations of the respective structures. Multi-objective optimization for the considered class of structures can be realized using deterministic approaches without defaulting to evolutionary methods.

The present study can be considered a step toward further studies on expedited optimization of computationally expensive simulation models for miniaturized microwave components.

The proposed algorithmic solutions proved useful for expedited multi-objective design optimization of miniaturized microwave structures. The problem is extremely challenging when using conventional methods, in particular evolutionary algorithms. To the authors’ knowledge, this is one of the first attempts to investigate deterministic surrogate-assisted multi-objective optimization of compact components at the EM-simulation level.

Strategies for accelerated multi-objective optimization of compact microwave and RF structures are investigated, including the possibility of exploiting surrogate modeling techniques for electromagnetic (EM)-driven design speedup for such components. The paper aims to discuss these issues.

Two algorithmic frameworks are described that are based on fast response surface approximation models, structure decomposition, and Pareto front refinement. Numerical case studies are provided demonstrating feasibility of solving real-world problems involving multi-objective optimization of miniaturized microwave passives and expensive EM-simulation models of such structures.

It is possible, through appropriate combination of the surrogate modeling techniques and response correction methods, to identify the set of alternative designs representing the best possible trade-offs between conflicting design objectives in a realistic time frame corresponding to a few dozen of high-fidelity EM simulations of the respective structures.

The present study sets a direction for further studied on expedited optimization of computationally expensive simulation models for miniaturized microwave components.

The proposed algorithmic framework proved useful for fast design of microwave structures, which is extremely challenging when using conventional methods. To the authors’ knowledge, this is one of the first attempts to surrogate-assisted multi-objective optimization of compact components at the EM-simulation level.

There are process uncertainties and material property variations during laminated steel sheet forming, and those fluctuations may result in non-reliable forming quality issues such as fracture and delamination. Additionally, the optimization of sheet forming process is a typical multi-objective optimization problem. The target is to find a multi-objective design optimization and improve the process design reliability for laminated sheet metal forming. The paper aims to discuss these issues.

Desirability function approach is adopted to conduct deterministic multi-objective optimization, and response surface is used as meta-model. Reliability analysis is conducted to evaluate the robustness of the multi-objective design optimization. The proposed method is implemented in a step-bottom square cup drawing process. First, forming process parameters and three noise factors are assumed as probability variables to conduct reliability assessment of the laminated steel sheet forming process using Monte Carlo simulation. Next, only two forming process parameters, blank holding force and frictional coefficient, are considered as probability variables to investigate the influence of the forming parameter deviation on the variance of the response using the first-order second-moment method.

The results indicate that multi-objective design optimization using desirability function method has high efficiency, and an optimized robust design can be obtained after reliability assessment.

The proposed design procedure has potential as a simple and practical approach in the laminated steel sheet forming process.

This paper aims to assess control parameter setup and its effect on computational cost and performance of deterministic procedures for multi-objective design optimization of expensive simulation models of antenna structures.

A deterministic algorithm for cost-efficient multi-objective optimization of antenna structures has been assessed. The algorithm constructs a patch connecting extreme Pareto-optimal designs (obtained by means of separate single-objective optimization runs). Its performance (both cost- and quality-wise) depends on the dimensions of the so-called patch, an elementary region being relocated in the course of the optimization process. The cost/performance trade-offs are studied using two examples of ultra-wideband antenna structures and the optimization results are compared to draw conclusions concerning the algorithm robustness and determine the most advantageous control parameter setups.

The obtained results indicate that the investigated algorithm is very robust, i.e. its performance is weakly dependent on the control parameters setup. At the same time, it is found that the most suitable setups are those that ensure low computational cost, specifically non-uniform ones generated on the basis of sensitivity analysis.

The study provides recommendations for control parameter setup of deterministic multi-objective optimization procedure for computationally efficient design of antenna structures. This is the first study of this kind for this particular design procedure, which confirms its robustness and determines the most suitable arrangement of the control parameters. Consequently, the presented results permit full automation of the surrogate-assisted multi-objective antenna optimization process while ensuring its lowest possible computational cost.

The work is the first comprehensive validation of the sequential domain patching algorithm under various scenarios of its control parameter setup. The considered design procedure along with the recommended parameter arrangement is a robust and computationally efficient tool for fully automated multi-objective optimization of expensive simulation models of contemporary antenna structures.

This paper aims to propose a double-sided switched reluctance linxear generator (DSRLG) exclusively for wave power generation. The initial dimensions are given through design experience and principles. To ameliorate comprehensive performance of the DSRLG, the multi-objective optimization design is processed.

The multi-objective optimization design of the DSRLG is processed by adopting a modified entropy technique for order of preference by similarity to ideal solution (TOPSIS) algorithm. First, sensitivity analyzes on geometric parameters of the DSRLG are conducted to determine several pivotal geometric parameters as optimization variables. Then, the multi-objective optimization is conducted on the basis of initial dimensions. After determination of synthetical evaluation value of each structure parameter, the best dimension scheme of the DSRLG is concluded.

After verification by finite element method simulation and dynamic simulation, the final dimension scheme proves to perform better than the initial scheme. Finally, experiments are conducted to verify the accuracy of both the stable finite element DSRLG model and dynamic simulation system model so that the conclusion of this paper proves to be reliable and compelling.

This paper proposes an improved structure of the DSRLG, which is superior for wave power generation. Meanwhile, a novel modified entropy TOPSIS algorithm is applied to the field of electrical machine multi-objective optimal design for the first time.

The purpose of this paper is performance enhancement of ferrite-assisted synchronous reluctance (FASR) motor using multi-objective differential evolution (MODE) algorithm, considering the significant geometric design parameters.

This work illustrates the optimization of FASR motor using MODE algorithm to enhance the performance of the motor considering barrier angular positions, magnet height, magnet axial length, flux barrier angles of the rotor and air gap length. In the optimization routine to determine the performance parameters, generalized regression neural network-based interpolation is used. The results of MODE are validated with multi-objective particle swarm optimization algorithm and multi-objective genetic algorithm.

The design optimization procedure developed in this work for FASR motor aims at achieving multiple objectives, namely, average torque, torque ripple and efficiency. With multiple objectives, it is essential to give the designer the tradeoff between different objectives so as to arrive at the best design suitable for the application. The results obtained in this work justify the application of the MODE approach for FASR motor to determine the various feasible solutions within the bounds of the design.

Analysis, design and optimization of synchronous reluctance motor has been explored in detail to establish its potential for variable speed applications. In recent years, the focus is toward the electromagnetic design of hybrid configurations such as FASR motor. It is in this preview this work aims to achieve optimal design of FASR motor using multi-objective optimization approach.

The results of this work will supplement and encourage the application of FASR motor as a viable alternate for variable speed drive applications. In addition, the application of MODE to arrive at better design solutions is demonstrated.

The approach presented in this work focuses on obtaining enhanced design of FASR motor considering average torque, torque ripple and efficiency as performance measures. The posteriori analysis of optimization provides an insight into the choice of parameters involved and their effects on the design of FASR motor. The efficacy of the optimization routine is justified in comparison with other multi-objective algorithms.

The optimality objectives are the structure weight and embodied energy as well as calculating the cost and embodied carbon of the resulting optimum options. Three optimality algorithms developed in MATLAB, namely, genetic algorithms (GA), particle swarm optimisation (PSO) and harmony search algorithm (HSA), were used for structural optimisation to compare the effectiveness of the algorithms. Two life-cycle stages were considered, production and construction stages, which include three boundaries: materials, transportation and erection. In the formulation of the optimum design problem, 107 universal steel beams (UKB) and 64 columns (UKC) sections were considered for the discrete design variables. The imposed behavioural constraints in the optimum design process were set according to the provision of Eurocode 3 (EC3). The study aims to find the optimum solution of 2D steel frames whilst considering weight and embodied energy, investigate the performance of the analysis integrated with MATLAB and provide three examples to which all these are applied to.

Undoubtedly, in structural engineering, the best design of any structure aims at the most economical and environmental option, without impairing the functional and its structural integrity. In the paper, multi-objective stochastic search methods are proposed for optimum design of three two-dimensional multi-story frames.

Results showed that the optimised designs obtained by HSA are better than those found by the GA and PSO with an average difference of 16% from GA and PSO, where this difference increases at larger frame structures. It was, therefore, concluded that the integration of the analysis, design and optimisation methods employed in MATLAB can be effective in obtaining prompt optimum results during the decision-making stage.

There may be some possible limitations in the study. Due to the time constraints, only three meta-heuristic approaches were investigated, where more methods should be investigated to fully understand their effectiveness in multi-objective problems.

Investigating the performance of three optimisation methods in multi-objective problems developed in MATLAB. More importantly, developing optimisation models for evaluation of embodied energy, embodied carbon and cost for steel structures to assist designers, during the initial stages, to evaluate design decisions against their energy consumption and carbon impacts.