Robust and Multi-Objective Pareto Design of a Solenoid

The optimization of the design of a practical electromagnetic device involves many challenging tasks for new algorithms, especially those involving numerical modeling codes in which objective function calls must be minimized for practical design processes. The Compumag Society provides openly accessible, challenging benchmark problems (TEAM problems) for testing novel numerical solvers. This paper deals with a novel solution for the multi-objective TEAM benchmark problem. This solenoid design test problem aims to search for the optimal shape of a coil, which ensures a uniform field distribution in the control region, while the sensitivity and the mass/DC loss of the coil are also considered in the context of robust design. The main differences from the previously published solutions are that the proposed methodology optimizes all three objectives together, not only as two independent two-dimensional sub-problems. We considered the asymmetrical cases in the solution and found that the symmetrical solutions always produced better uniformity and sensitivity measures. However, the difference between the symmetrical and asymmetrical solutions is insignificant for these objectives. Despite the fact that the cheapest solutions are symmetrical setups, they perform worse than the cheapest asymmetric ones in these uniformity and sensitivity criteria. Therefore, some asymmetric solutions that were previously neglected from the solution space can be competitive and interesting for practical design.