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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.

Inverse problems in electromagnetism, namely, the recovery of sources (currents or charges) or system data from measured effects, are usually ill-posed or, in the numerical formulation, ill-conditioned and require suitable regularization to provide meaningful results. To test new regularization methods, there is the need of benchmark problems, which numerical properties and solutions should be well known. Hence, this study aims to define a benchmark problem, suitable to test new regularization approaches and solves with different methods.

To assess reliability and performance of different solving strategies for inverse source problems, a benchmark problem of current synthesis is defined and solved by means of several regularization methods in a comparative way; subsequently, an approach in terms of an artificial neural network (ANN) is considered as a viable alternative to classical regularization schemes. The solution of the underlying forward problem is based on a finite element analysis.

The paper provides a very detailed analysis of the proposed inverse problem in terms of numerical properties of the lead field matrix. The solutions found by different regularization approaches and an ANN method are provided, showing the performance of the applied methods and the numerical issues of the benchmark problem.

The value of the paper is to provide the numerical characteristics and issues of the proposed benchmark problem in a comprehensive way, by means of a wide variety of regularization methods and an ANN approach.