Improved solutions to a TEAM problem for multi-objective optimisation in magnetics

New solutions to a recently proposed benchmark TEAM problem for Pareto optimisation are presented. In the benchmark, an air-cored solenoid of small size, which can be used, for example, for magnetic fluid hyperthermia, is considered. Two shape optimisations of the solenoid are proposed in the benchmark: synthesising a uniform magnetic field in a control region, considering also a sensitivity function (Problem 1) or synthesising a uniform magnetic field, simultaneously minimising the power losses (Problem 2). The benchmark is solved by means of three different nature-inspired algorithms and a genetic one, namely micro biogeography-inspired algorithm, wind-driven optimisation, and the cuckoo search, taking the genetic algorithm NSGA-II as a reference, because all these methods have proven to be effective in solving multi-objective optimisation problems.