Semi-Analytical Solution for a Multi-Objective TEAM Benchmark Problem

TL;DR

This paper introduces a semi-analytical solution for the multi-objective T.E.A.M benchmark problem, aiding the testing of optimization algorithms and numerical solvers in magnetic coil layout design.

Contribution

It presents a novel semi-analytical approach integrated into an open-source framework for optimizing coil layouts in magnetic field applications.

Findings

Semi-analytical solution achieves high precision compared to numerical methods.

The approach effectively optimizes coil layouts for uniform magnetic fields.

Validation shows competitive performance with hp-adaptive numerical solver.

Abstract

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 \=Artap, 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.