Benchmarking is essential for testing new numerical analysis codes. Their solution is crucial both for testing the partial differential equation solvers and both for the optimization methods. Especially, nature-inspired optimization algorithm-based solvers, where is an important study is to use benchmark functions to test how the new algorithm may perform, in comparison with other algorithms or fine-tune the optimizer parameters. This paper proposes a novel semi-analytical solution of the multi-objective T.E.A.M benchmark problem. The goal of the benchmark problem is to optimize the layout of a coil and provide a uniform magnetic field in the given region. The proposed methodology was realized in the open-source robust design optimization framework Ārtap, and the precision of the solution is compared with the result of a fully hp-adaptive numerical solver: Agros-suite. The coil layout optimization was performed by derivative-free non-linear methods and the NSGA-II algorithm.