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The purpose of this paper is to investigate a bi-objective optimization problem characterized by coupled field analysis. The optimal design of a pancake inductor for the controlled heating of a graphite disk is considered as the benchmark problem. The case study is related to the design of industrial applications of the induction heating of graphite disk.

The expected goal of the optimization process is twofold: to improve temperature uniformity in the disk and also electrical efficiency of the inductor. The solution of the relevant bi-objective optimization problem is based on multiphysics field analysis. Specifically, the direct problem is solved as a magnetic and thermal coupled problem by means of finite elements; a mesh-inspired definition of thermal uniformity is proposed. In turn, the Pareto front trading off electrical efficiency and thermal uniformity is identified exploiting evolutionary computing.

By varying the problem targets, different Pareto fronts are identified trading off thermal uniformity and electrical efficiency of the induction-heating device.

These results suggest how to improve the design of this kind of device for the epitaxial growth of silicon wafer; the advantage of using a magnetic concentrator placed close to the inductor axis is pointed out.

The coupling of a multiphysics direct problem with a multiobjective inverse problem is presented as a benchmark problem and accordingly solved. The benchmark provides a simple analysis problem that allows testing various optimization algorithms in a comparative way.

Magnetic fluid hyperthermia experiment requires a uniform magnetic field in order to control the heating rate of a magnetic nanoparticle fluid for laboratory tests. The automated optimal design of a real-life device able to generate a uniform magnetic field suitable to heat cells in a Petri dish is presented. The paper aims to discuss these issues.

The inductor for tests has been designed using finite element analysis and evolutionary computing coupled to design of experiments technique in order to take into account sensitivity of solutions.

The geometry of the inductor has been designed and a laboratory prototype has been built. Results of preliminary tests, using a previously synthesized and characterized magneto fluid, are presented.

Design of experiment approach combined with evolutionary computing has been used to compute the solution sensitivity and approximate a 3D Pareto front. The designed inductor has been tested in an experimental set-up.

The purpose of this paper is to show how the EStra-Many method works on optimization problems characterized by high-dimensionality of the objective space. Moreover, a comparison with a more classical approach (a constrained bi-objective problem solved by means of NSGA-II) is done.

The six reactances of a compensation network (CN) for a wireless power transfer system (WPTS) are synthesized by means of an automated optimal design. In particular, an evolutionary algorithm EStra-Many coupled with a sorting strategy has been applied to an optimization problem with four objective functions (OFs). To assess the obtained results, a classical genetic algorithm NSGA-II has been run on a bi-objective problem, constrained by two functions, and the solutions have been analyzed and compared with the ones obtained by EStra-Many.

The proposed EStra-Many method identified a solution (CN synthesis) that enhances the WPTS, considering all the four OFs. In particular, to assess the synthesized CN, the Bode diagram of the frequency response and a circuital simulation were evaluated a posteriori; they showed good performance of the CN, with smooth response and without unwanted oscillations when fed by a square wave signal with offset. The EStra-Many method has been able to find a good solution among all the feasible solutions, showing potentiality also for other fields of research, in fact, a solution nondominated with respect to the starting point has been identified. From the methodological viewpoint, the main finding is a new formulation of the many-objective optimization problem based on the concept of degree of conflict, which gives rise to an implementation free from hierarchical weights.

The new approach EStra-Many used in this paper showed to properly find an optimal solution, trading-off multiple objectives. The compensation network so synthesized by the proposed method showed good properties in terms of frequency response and robustness. The proposed method, able to deal effectively with four OFs, could be applied to solve problems with a higher number of OFs in a variety of applications because of its generality.

A novel method for modelling permanent magnets is investigated based on numerical approximations with rational functions. This study aims to introduce the AAA algorithm and other recently developed, cutting-edge mathematical tools, which provide outstandingly fast and accurate numerical computation of potentials and vector fields.

First, the AAA algorithm is briefly introduced along with its main variants and other advanced mathematical tools involved in the modelling. Then, the analysis of a circular Halbach array with a one-pole pair is carried out by means of the AAA-least squares method, focusing on vector potential and flux density in the bore and validating results by means of classic finite element software. Finally, the investigation is completed by a finite difference analysis.

AAA methods for field analysis prove to be strikingly fast and accurate. Results are in excellent agreement with those provided by the finite element model, and the very good agreement with those from finite differences suggests future improvements. They are also easy programming; the MATLAB code is less than 200 lines. This indicates they can provide an effective tool for rapid analysis.

AAA methods in magnetostatics are novel, but their extension to analogous physical problems seems straightforward. Being a meshless method, it is unlikely that local non-linearities can be considered. An aspect of particular interest, left for future research, is the capability of handling inhomogeneous domains, i.e. solving general interface problems.

The authors use cutting-edge mathematical tools for the modelling of complex physical objects in magnetostatics.

The paper aims to propose a a field-circuit method for investigating the magnetic behavior of a wireless power transfer system (WPTS) for the charge of batteries of electric vehicles. In particular, a 3D model for finite element analysis (FEA) for the field simulation of a WPTS is developed. Specifically, the effects of aluminum shield and steel layer, representing the car frame, on the self and mutual inductances are investigated. An equivalent electric circuit is then built, and the relevant lumped parameters are identified by means of the FEAs.

The finite element model is used to evaluate self and mutual inductances in several transmitting-receiving coil configurations and relative positions. In particular, the FEA simulates the aluminum and steel layers as shell elements in a 3D domain. The self and mutual inductance values in the aligned coil case are also used as input parameters in a circuit model to evaluate the onload current.

The use of shell elements in FEA substantially reduces the number of mesh elements needed to simulate the eddy currents in the steel and aluminum layer, so putting the ground for low-cost field analysis. Moreover, the FEA gives an accurate computation of the self and mutual inductance to be used in a circuit model, which, in turn, provides a fast update of the onload induced current.

To save computational time, the use of 2D shell elements to model thin conductive regions introduces a simplified FEA that could be used in the WPTS simulation. Moreover, the dynamic behavior of WPTS, i.e. the operation when the receiving coil is moving with respect to the transmitting one, is considered. Because of the lumped parameters’ dependence upon the relative positions of the two coils, the proposed method allows identifying the circuit parameters for several configurations so substantially reducing the computational burden.

The purpose of the study is to design the compensation network of a dynamic wireless power transfer system, considering the movement of the receiving coil along an electrified track with a large number of inductors buried on the road.

A finite element model has been developed to calculate the self-inductances of transmitting and receiving coils as well as the mutual inductances between the receiving coil and the transmitting ones in the nearby and for various relative positions. The calculated lumped parameters, self-inductances and mutual inductances depending on the relative positions between the coils, have been considered to design the compensation network of the active coils, which is composed of three capacitive or inductive reactances connected in the T form. The optimal values of the six reactances, three for the transmitting coils and three for the receiving one, have been calculated by resorting to the Genetic Algorithm NSGA-II.

In this paper, the results obtained by means of the optimizations have broadly discussed. The optimal values of the reactances of the compensation networks show a clear trend in the receiving part of the circuit. On the other hand, the problem seems very sensitive to the values of the reactances in the transmitting circuit.

Dynamic wireless power transfer system is one of the newest ways of recharging electric vehicles. Hence, the design of compensation networks for this kind of systems is a new topic, and there is the need to investigate possible solutions to obtain a good performance of the recharging system.

Fostered by the development of new technologies, micro-electro-mechanical systems (MEMS) are massively present on board of vehicles, within information equipment, as well as in medical and healthcare equipment. The purpose of this paper is to approach here the shape design of MEMS in terms of the optimization of a vector objective function, subject to a set of constraints. Objectives and constraints are non-linear, dependent on the unknown device shape. When multiple objective functions should be optimized simultaneously, the set of solutions minimizing the degree of conflict (Pareto front) can be searched for.

This paper proposes an automated optimal design method based on connecting the MATLAB surrogate modeling (SUMO) toolbox with COMSOL Multiphysics finite element analysis tool, and the evolutionary algorithm NSGA-II as well.

The efficiency of the optimization method proposed is approximately doubled in terms of runtime (5 vs 10 h for the referred platform), when compared with the same computational job without using surrogate models. This way, a cost-effective and accurate approximation of the Pareto front, trading off drive and levitation force components in a comb-drive electrostatic microactuator, was found.

More in-depth models of MEMS devices could be obtained by simulating multi-domain physical processes, i.e. encompassing a coupled-field analysis in the multiphysics sense.

Under this framework, the proposed approach lays the ground for a very general method devoted to the optimal shape design of any MEMS configuration; in fact, the application of multiobjective optimizations to these kind of devices is quite new.