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The purpose of this paper is to describe main ideas and demonstrate results of the research activities carried out by the authors in the field of design concepts of induction mass heating technology based on multiple-criteria optimization. The main goal of the studies is the application of different optimization methods and numerical finite element method (FEM) codes for field analysis to solve the multi-objective optimization problem that is mathematically formulated in terms of the most important optimization criteria, for example, maximum temperature uniformity, maximum energy efficiency and minimum scale formation.

Standard genetic algorithm (GA), non-dominated sorting genetic algorithm (NSGA) and alternance method of parametric optimization based on the optimal control theory are applied as effective tools for the practice-oriented problems for multiple-criteria optimization of induction heaters’ design based on non-linear coupled electromagnetic and temperature field analysis. Different approaches are used for combining FEM codes for interconnected field analysis and optimization algorithms into the automated optimization procedure.

Optimization procedures are tested and investigated for two- and three-criteria optimization problems solution on the examples of induction heating of a graphite disk, induction heating of aluminum and steel billets prior to hot forming.

Solved problems are based on the design of practical industrial applications. The developed optimization procedures are planned to be applied to the wide range of real-life problems of the optimal design and control of different electromagnetic devices and systems.

The paper describes main ideas and results of the research activities carried out by the authors during past years in the field of multiple-criteria optimization of induction heaters’ design based on numerical coupled electromagnetic and temperature field analysis. Implementing the automated procedure that combines a numerical FEM code for coupled field analysis with an optimization algorithm and its subsequent application for designing induction heaters makes the proposed approach specific and original. The paper also demonstrates that different optimization strategies used (standard GA, NSGA-II and the alternance method of optimal control theory) are effective for real-life industrial applications for multiple-criteria optimization of induction heaters design.

An inductor for the uniform heating of the extremity of a ferromagnetic steel tube for stress relieving is considered. The main goal of the study is to investigate the possibility to achieve a reasonable design of the inductor when dealing with many design variables.

Genetic optimization algorithms are used for this purpose, demonstrating the applicability of these techniques to the design of induction heating inductors. Genetic algorithms provide to the designer several optimal solutions belonging to Pareto Front, and this way they allow choosing the solution that better fits the technological requirements. In any case, the designer has to adapt the chosen solution to fit in with the real possibilities in industrial application.

The study demonstrates that automatic optimization methods may help the designer of the induction heating system to solve complex problems with very conflicting technological requirements.

In the paper, a problem with a high number of design variables is solved. Moreover, the goals of the optimization process are strongly conflicting, and the proposed problem is a challenging one.

The purpose of this paper is to present a modified version of the non-dominated sorted genetic algorithm with an application in the design optimization of a power inductor for magneto-fluid hyperthermia (MFH).

The proposed evolutionary algorithm is a modified version of migration-non-dominated sorting genetic algorithms (M-NSGA) that now includes the self-adaption of migration events- non-dominated sorting genetic algorithms (SA-M-NSGA). Moreover, a criterion based on the evolution of the approximated Pareto front has been activated for the automatic stop of the computation. Numerical experiments have been based on both an analytical benchmark and a real-life case study; the latter, which deals with the design of a class of power inductors for tests of MFH, is characterized by finite element analysis of the magnetic field.

The SA-M-NSGA substantially varies the genetic heritage of the population during the optimization process and allows for a faster convergence.

The proposed SA-M-NSGA is able to find a wider Pareto front with a computational effort comparable to a standard NSGA-II implementation.

This paper aims to investigate different multi-objective optimization (MOO) approaches for design and control of electromagnetic devices. The main goal of MOO is to find the set of design variables or control parameters which will provide the best possible values of typical conflicting objective functions.

In the research studies, standard genetic algorithm (GA), non-dominated sorting GA (NSGA-II), migration NSGA algorithm and alternance method of optimal control theory are discussed and compared.

The test practical problems of multi-criteria optimization of induction heating processes with respect to chosen quality criteria confirm the effectiveness of application of considered MOO approaches both for the problems of design and control.

This paper represents and investigates different MOO approaches for design and control of electrotechnological systems.

The mixed variational formulation in two‐dimensional magnetostatics and the corresponding discretization are presented in a systematic way. The comparison between the mixed finite element approach and the classical one is shown with reference to some case studies; numerical results are reported.

This paper aims to present the optimal design of an inductor used to heat a magnetic nanoparticle fluid injected in a cell culture inside a Petri dish.

The inductor design is driven by means of a multi-objective optimization algorithm that generalizes the migration-non-dominated sorting genetic algorithm (NSGA); it is called self-adapting migration-NSGA.

The optimized device is able to synthesize a uniform magnetic field in a nanoparticle fluid, substantially helping its heating capability. The ultimate scope is to assist the cancer therapy based on magnetic fluid hyperthermia (MFH).

The optimal design of an inductor for MFH applications has been carried out by applying an improved version of migration-based NSGA-II algorithm including automatic stop and a self-adapting concept. The modified optimization algorithm is suitable to find better optimal solutions with respect to a standard version of NSGA-II.

Introduces papers from this area of expertise from the ISEF 1999 Proceedings. States the goal herein is one of identifying devices or systems able to provide prescribed performance. Notes that 18 papers from the Symposium are grouped in the area of automated optimal design. Describes the main challenges that condition computational electromagnetism’s future development. Concludes by itemizing the range of applications from small activators to optimization of induction heating systems in this third chapter.

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.

The purpose of this study is to develop a method to reduce the computation time necessary for the automated optimal design of dual-band wearable antennas. In particular, the authors investigated if this can be achieved by the use of a hierarchical optimization paradigm combined with a simplified human body model. The geometry of the antenna under consideration is described via eight geometrical parameters which are automatically adjusted with the use of an evolutionary algorithm to improve the impedance matching of an antenna located in the proximity of a human body. Specifically, the antennas were designed to operate in the ISM band which covers two frequency ranges: 2.4-2.5 GHz and 5.7-5.9 GHz.

During the studies on the automated design of wearable antennas using evolutionary computing, the authors observed that not all design parameters exhibit equal influence on the objective function. Therefore, it was hypothesized that to reduce the computation effort, the design parameters can be activated sequentially based on their influence. Accordingly, the authors’ computer code has been modified to include this feature.

The authors’ novel hierarchical multi-parameter optimization method was able to converge to a better solution within a shorter time compared to an equivalent method not exploiting automatic activation of an increasing number of design parameters. Considering a significant computational cost involved in the calculation of the objective function, this exhibits a convincing advantage of their hierarchical approach, at least for the considered class of antennas.

The described method has been developed for the design of single- or dual-band wearable antennas. Its application to other classes of antennas and antenna environments may require some adjustments of the objective functions or parameter values of the evolutionary algorithm. It follows from the well-recognized fact that all optimization methods are to some extent application-specific.

Computation load involved in the automated design and optimization can be significantly reduced compared to the non-hierarchical approach with a heterogeneous human body model.

To the best of the authors’ knowledge, the described application of hierarchical paradigm to the optimization of wearable antennas is fully original, as well as is its combination with simplified body models.

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.

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).

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.

The paper gives a good guide to the designers of electric motors, focussed on a shape design optimization.

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.