Multi-objective optimization of synchronous buck converter based on NSGA-U algorithm

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.

Antenna plays an important role in modern communication. Accurate calculation of antenna structure to obtain reasonable electromagnetic characteristic parameters is an important part of antenna design. With the increasing complexity of the antenna structure, a large number of numerical calculations are required in the design process to determine the optimal structure size. Therefore, it’s necessary to study the fast optimization algorithm of antenna multi-objective (antenna bandwidth, gain, polarization characteristics, etc) optimization design method. In this paper, a new adaptive BF neural network is proposed to optimize the resonant frequency and size structure of dual frequency circular polarization microstrip antenna, so as to improve the efficiency of antenna design.

Multi-objective optimization problems (MOP) are frequently encountered in practice. In some cases, different computationally expensive analyses may be independently used for computing different objectives of the MOP. Additionally, the analyses may be executed to obtain estimates with different fidelity, typically higher fidelity requiring a longer run-time. For instance, in automotive design, the aerodynamic drag is computed using computational fluid dynamic (CFD) analysis and its crashworthiness/strength is assessed using finite element analysis (FEA). Both the objectives can be independently computed and the underlying fidelity of each analysis can also be controlled using different mesh sizes/thresholds on the residual errors. While there exist a number of generic MOP benchmark problems in the literature, there is scarce work on constructing MOPs with multi-fidelity (MF) analyses to support the development of multi-fidelity, multi-objective optimization algorithms. The existing MF benchmarks are limited to unconstrained, single-objective optimization problems only. Towards addressing this gap, in this paper, we introduce a test suite for multi-objective, multi-fidelity optimization (MOMF). The problems are derived by combining existing unconstrained, multi-objective design optimization problems with resolution/stochastic/instability errors that are common manifestations of MF simulations. The method allows for the construction of any number of low-fidelity functions with desired level of correlations for a given high-fidelity objective function. We hope that the test suite would motivate novel algorithmic developments to support optimization involving computationally expensive and independently evaluable objectives.

Improvement of bubble distribution characteristics through multi-objective optimization of flow characteristics of a swirling flow type microbubble generator with fixed blades

In addition to the development of micro hydro turbine, the challenge in micro hydro turbine design as sustainable hydro devices is focused on the optimization of turbine runner blade which have decisive effect on the turbine performance to reach higher efficiency. A multi-objective optimization method to optimize the performance of runner blade of propeller turbine for micro turbine has been studied. For the initial design of planar blade cascade, singularity distribution method and the combination of the Bezier curve parametric technology is used. A non-dominated sorting genetic algorithm Ⅱ(NSGA Ⅱ) is developed based on the multi-objective optimization design method. The comparision with model test show that the blade charachteristics is optimized by NSGA-II has a good efficiency and load distribution. From model test and scale up calculation, the maximum prototype efficiency of the runner blade reaches as high as 90.87%.

Modern aerodynamic optimization design methods for the industrial axial compressor cascade mainly aim at improving both design point and off-design point performance. In this study, a multi-point and multi-objective optimization design method is established for the cascade, particularly aiming at widening the operating range while maintaining good performance at the acceptable expense of computational load. The design objectives are to maximize the static pressure ratio and minimize the total pressure loss coefficient at the design point, and to maximize the operating range for the positive and negative incidences. To alleviate the computational load, a design of experiment (DOE)-based GA–BP-ANN model is constructed to rapidly approximate the cascade aerodynamic performance in the optimization process. The artificial neural network (ANN) is trained by the genetic algorithm (GA) technique and back propagation (BP) algorithm, where the training cascades are sampled by the DOE method and analysed by the computational fluid dynamics method. The multi-objective genetic algorithm is used to search for a series of Pareto-optimum solutions, from which an optimal cascade is found out whose objectives are all better than (ABT) those of the original design. The ABT cascade is characterized by the lower camber and higher turning angle, leading to better aerodynamic performance in a widened operating range. Compared with the original design, the ABT cascade decreases the total pressure loss coefficient by 1.54 per cent, 23.4 per cent, and 7.87 per cent at the incidences of 5°, −9°, and 13°, respectively. The established optimization design method can be extended to the three-dimensional aerodynamic design of axial compressor blade.

The simulation of thermal–fluid–solid coupling in turbines is critically important for design optimization. Historically, most research on thermal–fluid–solid coupling has been conducted in three-dimensional, often with computational speeds that do not meet practical expectations. This study proposes a one-dimensional performance prediction and multi-objective optimization design methodology for turbines, integrating aerothermodynamics and structural strength, to facilitate rapid multidisciplinary coupling design optimization at a low-dimensional level. Initially, a multidisciplinary coupled turbine performance prediction model is established, incorporating the combined effects of turbine aerothermodynamics and structural mechanics. This model links the thermodynamics of the blade passage with the stress and strain of the blade. The predictive accuracy of this model is validated against experimental data from a four-stage axial flow turbine, showing a maximum error of 1.56% for the total temperature ratio and 1.69% for the total expansion ratio. Subsequently, using blade parameters, degree of reaction, load coefficient, and flow coefficient as optimization variables and targeting the turbine's overall isentropic efficiency and power as optimization objectives, a rapid Non-dominated Sorting Genetic Algorithm II and the Technique for Order Preference by Similarity to an Ideal Solution are employed to optimize the last stage of the four-stage axial flow turbine. The optimized turbine demonstrates an increase in overall isentropic efficiency by 1.333% and an increase in overall power by 3.329%, while satisfying structural strength requirements. The novelty of this study lies in its rapid optimization design and performance prediction method for the coupled aerothermodynamics and structural mechanics at a one-dimensional level.

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 deals with the multi-objective optimization of tire reinforcement structures such as the tread belt and the carcass path. The multi-objective functions are defined in terms of the discrete-type design variables and approximated by artificial neutral network, and the sensitivity analyses of these functions are replaced with the iterative genetic evolution. The multi-objective optimization algorithm introduced in this paper is not only highly CPU-time-efficient but it can also be applicable to other multi-objective optimization problems in which the objective function, the design variables and the constraints are not continuous but discrete. Through the illustrative numerical experiments, the fiber-reinforced tire belt structure is optimally tailored. The proposed multi-objective optimization algorithm is not limited to the tire reinforcement structure, but it can be applicable to the generalized multi-objective structural optimization problems in various engineering applications.

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.

Multi-objective robust optimization of a solar power tower plant under uncertainty

A new approach in multi-objective evolutionary optimization is decomposition. Decomposition is a basic method in old multi-objective optimization which in evolutionary multiobjective optimization, has not been widely used. Using this method, a multi-objective optimization problem is converted into a number of scalar subproblems, and all the subproblems are simultaneously optimized. In this paper, the performance and efficiency of the algorithm MOEA/D (multi-objective evolutionary algorithm based on decomposition) with the performance of two algorithms NSGA-II and MOPSO (evolution optimization methods based on dominance) for solving constrained portfolio optimization in Tehran Stock Exchange, has been compared. Portfolio return and its risk, has been considered as the optimization objectives and CvaR has been considered as a risk measure. The results indicate the high potential of these algorithms for constrained portfolio optimization. Also, the results indicate that the optimization algorithm based on decomposition has lower computational complexity, and Pareto front is more extensive than the other two methods. (Abstract)

Three-way spatial fluid channel (TSFC) is commonly used in spatial fluid channels of the high hydraulic integrated system. However, the mathematic model of TSFC pressure loss is not clear, and what TSFC structural parameters in a certain space can get the minimum pressure loss and weight is also vague. Therefore, TSFC pressure loss mathematic model and multi-objective optimization about pressure loss, axis path length, and mass are studied in this paper. First, the mathematic model of TSFC pressure loss is established based on the response surface methodology and pressure loss models of fluid dynamics. Then, the optimized mathematic model for the TSFC structural parameters is built by the multi-objective optimization design method to achieve low pressure loss, short axis path length, and lightweight. According to the simulation, the results of optimized structure model show that the mass has been reduced 5.68%, and the pressure loss has been reduced 70.75% compared with the original model. Besides, the optimized TSFC structure model is manufactured by additive manufacturing, and the experiment is carried out to measure TSFC pressure loss. It shows that the error of pressure loss between the mathematic model and the experiment is only 1.6%, which verifies the accuracy of mathematic model of the pressure loss. This research lays a foundation for the design and optimization of the spatial flow channel in highly integrated hydraulic systems.

In a real life situation, due to the complexity of the industrial systems and non-linearity of their behavior, it is very difficult to achieve optimum performance of system for desired industrial goals using uncertain, vague and imprecise data. Herein, an approach has been proposed through which the behavior of the system is analyzed in the form of well- known six reliability indices by using triangular fuzzy numbers which allow the consideration of expert opinions, linguistic variables, operating conditions in reliability information. Using their behavior analysis a fuzzy multi-objective optimization problem (FMOOP) has been formulated. Due to the conflicting nature of the multiple objectives, the decision making is difficult and it leads to the Pareto optimal solutions instead of single optimal solutions. Many evolutionary algorithms (EAs) already exist in the literature for solving a multi-objective optimization problem (MOOP), and are termed as multi-objective evolutionary algorithms (MOEAs). Particle swarm optimization (PSO) is one of such MOEA which demonstrates the ability to identity a Pareto-optimal front efficiently. Here, a crisp optimization problem is reformulated from FMOOP by taking into account the preference of decision maker (DM) and then PSO is applied to solve the resulting fuzzified MOOP. The presented approach is applied in order to solve the multi-objective series-parallel system reliability optimization problem for a crystallization unit of a urea plant.

The present work focuses on obtaining optimal operational policies of an industrial scale penicillin fed-batch fermentation process using dynamic optimization (DO). The three process objectives considered in this work include, maximization of total penicillin formed (J 1), minimization of total biomass formed (J 2), and minimization of fed-batch operation time (J 3). The control variables for the optimization study include, the feed flowrates of sugar, soyabean oil, and phenylacetic. We perform a single-objective optimization study with J 1 as the objective function and showcased the importance of DO. Consequently, we solve three multi-objective optimization (MOO) problems corresponding to all the pairwise combinations of the aforementioned three objectives. Outcomes of MOO problems are presented in terms of several non-dominated Pareto-optimal solutions. Furthermore, descriptive analysis of three representative Pareto points for all the MOO problems is presented, which highlights the importance of MOO study of the penicillin bio-reactor.