Optimal design for electromagnetic devices: A synthesis approach using intervals and constraint-based methods

In electrical engineering, current methods show limits when it comes to complex design problems with heterogeneous and multidisciplinary requirements in the preliminary steps. Also, the setting and the solving of those problems is a simultaneous challenge that needs to be more explored. It may be necessary to recall the need to re-think the conventional design process when it comes to complex electrical systems. Particularly, by considering first the problem admissibility before its solving or optimization. Being able to detect an ill-posed or an over-constrained problem (causal analysis) can help in finding admissible solutions but also forces the designers to understand the meaning of the problem modeling. A synthesis point of view is proposed to ensure admissible and relevant solutions during the preliminary design (pre-design) process. Intervals and constraint-based methods are shown suitable for proposing efficient modeling, solving tools and addressing optimal design. This paper is illustrated by the case study of a benchmark transformer, taking into account multi-physical requirements. The optimal design includes mixed-type variables and tabulated constraints such as manufacturer datasheets. The computed results are then compared with solutions found in the literature and show the advantages of the implemented method in terms of solutions and computation time.