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We propose an innovative technique for dealing with optimal shape design problems that exploits the flexibility of the virtual element method (VEM) in handling meshes with general polygonal and polyhedral elements. The shape synthesis of a magnetic pole is considered as the case study.

In the framework of induction hardening, the coil design task is particularly suitable to be formulated as multi-objective optimization problem. In fact, the Pareto front estimation raises the issue of guaranteeing a satisfactory diversity and number of non-dominated solutions to be provided to the decision maker (DM). In this paper, a generative adversarial network (GAN) and a forward neural network (FNN), which is cascade connected to the GAN generator, produce additional Pareto optimal solutions starting from the results of a genetic algorithm (NSGA-II) used as training set. The FNN ensures an accurate prediction of the objectives of the added solutions, removing the need for further field analyses. This method is first tested against two analytical problems and subsequently validated on a 3-objective coil design task to illustrate its utility for a real-world case.

The double-layer approach (DLA) possesses superior features for the analysis of static electromagnetic problems. In this article, dealing with the magnetostatic analysis, we introduce two kinds of double layers: the first one on the surface of the magnetic body and the second one on the cut-surface within the exciting current loop. From the double layers on the cut-surface, we were able to derive a novel, unified exciting potential, which facilitates the treatment of any magnetostatic problem, including multiply connected problems. Furthermore, in this article, we use for the first time DLA for the analysis of magnetic forces acting on the magnetic bodies. The law of action and reaction provides a self-check function within DLA, enabling thus the simple and reliable tool for the confirmation if the computed results are adequate and accurate. This improved, DLA-based approach for the force analysis together with the introduced “action-reaction” principle for the self-checking of the force calculation are, to the authors' best knowledge, not known in the scientific community so far. Finally, we would like to emphasize that the presented DLA enables accurate, self-checked, generic analysis of the real-world devices, providing advanced treatment of both geometrical singularities (edges, corners) and materials used (high permeability, nonlinearities).

Magnetic Fluid Hyperthermia is a cancer therapy that requires a uniform magnetic field to heat nanoparticles localized in the treatment volume. The efficacy of nanoparticles heating is studied using cells cultured in Petri dishes. The automated optimal design of the inductor to generate the magnetic field to heat nanoparticles in cells cultured in Petri dishes is presented, exploiting field analysis and a new version of an optimization algorithm.

A new version of the biogeography-based optimization algorithm is proposed in order to consider multiple objectives. In fact, by exploiting non-dominated sorting of habitats, it is possible to approximate Pareto-optimal solutions in the objective space. The optimal shape design of an electrostatic micromotor, which is a benchmark in the Micro Electro-Mechanical Systems design, is considered as the case study.

This paper deals with the optimal design of a new synchronous motor particularly suitable for electric vehicles. The unique advantage of this motor is its possibility to realize field weakening at high speeds, which is the most important demand for such drives. The main design goal is to identify the dimensions of certain crucial regions of the machine in order to avoid saturation of the iron and to minimize the mass to volume ratio, while simultaneously maximizing the torque. The originality of the contribution is manifold: formulating the design problem in multiobjective terms, solving it by means of evolutionary computing, solving the associated direct problem based on a three-dimensional finite element analysis (3-D-FEA) field model, considering a reduced set of design variables by means of response surface method, referring to a real-life problem.

The design optimization of an induction heating device is considered. The non-linear multi-physics analysis is carried out by means of finite-element method, while the optimal design problem is solved by NSGA-II genetic algorithm. A comparison with the results obtained by a simplified linear analysis is shown. The original contribution of this paper is the Pareto front identification for a design problem in which the field analysis is multi-physics, dynamic, and non-linear.

A multiobjective optimization method is used to design a treatment planning based on electrochemotherapy (ECT). A penalty function technique is coupled to NSGA algorithm in order to identify the constrained Pareto front, so preventing unfeasible solutions.

This paper proposes the identification of the B-H curve of anisotropic magnetic laminations in the direction normal to the sheet surface. An automated procedure for linking an identification algorithm implemented in a Matlab environment with a commercial finite-element code Opera for 3-D magnetic field analysis has been used. In particular, an optimization procedure is proposed, where the computation time is reduced by adjusting the refinement of the FEM mesh. The use of a multiprocessor computer allowed to perform parallel computations and to realize the calculation in a reasonable time. The finite element mesh density is changed during operation of the procedure depending on the level of magnetic flux density difference between calculation and measurements.

A field source reconstruction of the dipoles modeling the activated area of the brain, while a subject performs the task of the voluntary motion of the hand, is solved. Experimental data resulting from fMRI are used for constraining the position of the equivalent dipole.

In this paper, the actual synthesis of the thermal field is proposed and solved as an inverse problem, considering a fully coupled magnetic-thermal analysis as for the direct problem. Reference is made to an air-cored inductor for magnetic fluid hyperthermia (MFH).

A magnetic fluid hyperthermia (MFH) inductor design using multiobjective evolution strategy techniques is proposed. Uniformity of the magnetic field and solution sensitivity are the objective functions chosen for the selection of the inductor geometry. After a 3-D finite-element analysis (FEA) of the thermal field, the coupled-field response of the synthesized inductor has been assessed.

The purpose of this paper is to focus on multiobjective optimization methods that are suitable for industrial electromagnetic design. In particular, a multiobjective optimization procedure is proposed, where the computation time is reduced by adjusting the refinement of the mesh, according to the accuracy required for the search in the design space rather than for the field analysis. A case study, dealing with the shape design of a small generator for automotive applications, is solved by comparing different procedures of optimization. Finally, a review of open problems is presented and discussed.

This paper deals with the shape design of the excitation unit of a magnetic induction tomography (MIT) system by means of a procedure of multiobjective design. As a result of the proposed method, a set of optimal geometries of the basic excitation structure was found.

The purpose of the paper is to demonstrate that the multicriteria formulation of an inverse problem fits well with current industrial electromagnetic design. The optimal shape design of a permanent-magnet (PM) generator is developed as the case study. Two well-known evolutionary algorithms, NSGA-II and MOESTRA, have been implemented and relevant results compared.

The optimal control of the geometry of a magnetic pole under step excitation has been formulated as a problem of multiobjective optimization in dynamic conditions. Accordingly, the nondominated solutions of the problem have been determined in the time domain. The scope of the paper is to prove the feasibility of dynamic multiobjective optimization in computational electromagnetism by solving a benchmark of inverse magnetic diffusion.

We have developed an automated method for optimizing the design of a coil for magnetic stimulation of peripheral nerves, acting on the current distribution of the coil. The method consists of these steps: 1 generating a 3-D finite-element model of a coil laid on a forearm; 2 solving the model for two parameters,f1 and f2 of the activating function, which is responsible for the peripheral nerve stimulation; and 3 starting from an existing prototype, applying an evolutionary algorithm to maximize f1 and minimize f2 . The final aim is to obtain a focused and strong stimulation. In order to determine robust solutions, the method considers a sensitivity constraint and obtains two solutions, one without the sensitivity constraint and the other taking it into account. In both cases, the objective functions are improved with respect to the existing prototype. In conclusion, we discuss the structure of the objective space.

A multi-objective optimization problem for Loney's solenoid consists of the determination of the current system which produces a uniform magnetic field within a domain of finite extent inside the solenoid and a low stray field outside it. In order to solve the multi-objective problem, four different approaches have been utilized and compared. In all cases evolution strategy (ES) techniques are utilized for the minimization procedure.

The basic ideas of IC-processed electrostatics are reviewed. The three-dimensional field model of a variable-capacitance electrostatic micromotor is then presented and the underlying analysis problem is solved by means of the finite element method. The micromotor, acting as a position actuator, is investigated at steady state and particular attention is paid in the calculation of the torque-angle curve featuring the device. The influence of stator geometry on the electromechanical performance is also investigated and design considerations are accordingly drawn. Finally, the step-transient response of the actuator is simulated. >

In the paper the optimal shape design of a dc torque motor is considered. Finite element models in 2D and 3D are examined, taking into account the magnetization curves of iron and permanent magnets. A stochastic optimizer of lowest order is then applied to identify the optimal shape of the device exhibiting the minimum cost, subject to a set of geometrical and behavioural constraints. An automatic procedure is set up interfacing optimizer and field simulator; remarks about the search of the global optimum are drawn. >

General problems of optimization of iron-core electromagnets are considered. The use of analytical and numerical methods are compared. Various models of electromagnets are examined, taking into account the magnetization curve of iron, operating conditions, the construction of coils, etc. The possibility of tackling the automatic design of iron-core electromagnets with cylindrical symmetry is demonstrated. The optimization procedure can also be used in the design of magnetic devices of complicated structure. >