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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 paper deals with an evolutionary method for solving many-objective optimization problems exhibiting a high-dimensionality objective space, which is a challenging problem. An application in the optimal synthesis of Compensation Networks (CNs) of wireless power transfer systems for charging the batteries of electric vehicles is developed. This design problem is characterized by a set of multiple objectives in mutual conflict, which should be simultaneously considered. The optimization aims to the maximization of both the efficiency and the transferred power; a further criterion selects the networks with a suitable profile of impedance vs. frequency. Moreover, the minimization of current and voltage values relevant to inductors and capacitors in the networks, respectively, is pursued. These five design criteria are optimized exploiting the concept of the degree of conflict, which is the core of the proposed method, named “EStra-many”. The method is applied by considering two approaches: the single-objective one, based on the degree of conflict function only, and the bi-objective approach in which the tradeoff between the degree of conflict function itself and another objective function (in turn, the efficiency, the transferred power, the distance of the resonance frequency from the supply frequency, the maximum value of the inductance current, the maximum value of the capacitor voltage, the distance from the Utopia point, and the number of inductors in the CN), is searched for. This way, all in one, seven different optimization problems are solved. The main element of novelty of the paper is a method to solve an optimization problem characterized by a high number of objective functions. In view of this, instead of considering a weighted sum of the objectives, a preference function inspired by the concept of least-conflict solution is formulated accordingly, the preference function is minimized by a cost-effective evolutionary algorithm of lowest order.

In computational electromagnetism there are manyfold advantages when using machine learning methods, because no mathematical formulation is required to solve the direct problem for given input geometry. Moreover, thanks to the inherent bidirectionality of a convolutional neural network, it can be trained to identify the geometry giving rise to the prescribed output field. All this puts the ground for the neural meta-modeling of fields, in spite of different levels of cost and accuracy. In the paper it is shown how CNNs can be trained to solve problems of optimal shape synthesis, with training data sets based on finite-element analyses of electric and magnetic fields. In particular, a concept of multi-fidelity model makes it possible to control both prediction accuracy and computational cost. The shape design of a MEMS design and the TEAM workshop problem 35 are considered as the case studies.

In the paper an original approach to efficiency map optimal synthesis is presented. A permanent magnet motor, working as controlled AC motor of synchronous type (PMSM), is selected as a case study. The first target of this research is to derive a lumped-parameter model of the motor (low-fidelity model), validated by magnetic field analysis (high-fidelity model). In turn, the end target is these two models application in a cost-effective optimisation procedures, where the goal is to identify the motor geometry maximizing the map area which is encompassed by a prescribed value for the motor efficiency.

A numerical twin model for the magneto-thermal analysis of an induction heating device is proposed. The non-linearity of magnetic permeability against temperature – which characterizes the workpiece – is captured by the model, while the use of a Convolutional Neural Network (CNN), trained by a number of finite-element analyses, makes it possible to solve the following inverse problem: given a temperature map in the workpiece section, identify current and relevant frequency in the inductor coil, as well as the time instant at which the map refers to. The TEAM problem 36 is considered as the case study.

In the paper, a Finite Element (FE) Analysis for investigating the electric properties of a Wireless Power Transfer System (WPTS) devoted to charging the batteries of electric vehicles is performed. In particular, the dynamic-WPTS, which is challenging because of the position-varying properties of the system, is considered. The field analysis is computationally heavy because of thin conductive layers modelling the car chassis: an effective analytical approximation for the field calculation in thin layers is applied to both the car frame bottom and the shielding aluminum layer. This approach allows for an accurate solution and, meanwhile, for a reduction in the computational costs, making the repeated simulations feasible.

Purpose This paper aims to deal with the optimal shape design of a class of permanent magnet motors by minimizing multiple objectives according to an original interpretation of Pareto optimality. The proposed method solves a many-objective problems characterized by five objective functions and five design variables with evolution strategy algorithms, classically used for single- and multi-objective (two objective functions) optimization problems. Design/methodology/approach Two approaches are proposed in the paper: the All-Objectives (AO) and the Many-Objectives (MO) optimization approach. The former is based on a single-objective optimization of a preference function, i.e. a normalized weighted sum. In contrast, in the MO a multi-objective optimization algorithm is applied to the minimization of a weight-free preference function and simultaneously to a maximization of the distance of the current solution from the prototype. The optimizations are based on an equivalent circuit model of the Permanent Magnet (PM) motor, but the results are assessed by means of finite element analyses (FEAs). Findings An extensive study of the solutions obtained by means of the different optimization approaches is provided by means of post-processing analyses. Both the approaches find non-dominated solutions with respect to the prototype that are substantially improving the initial solution. The points of strength along with the weakness points of each solution with respect to the prototype are analysed in depth. Practical implications The paper gives a good guide to the designers of electric motors, focussed on a shape design optimization. Originality/value Considering simultaneously five objective functions in an automated optimal design procedure is challenging. The proposed approach, based on a well-known and established optimization algorithm, but exploiting a new concept of degree of conflict, can lead to new results in the field of automated optimal design in a many-objective context.