Discussion about formulations and resolution techniques of electrical machine design problems

In this paper, we discuss, through a simple example, the impact of two different but equivalent formulations used by standard local optimization solvers (here fmincon of MatLab). We show that even if the two formulations are equivalent in a mathematical sense (no loss of global optima) it is not completely true in a numerical way; using 1000 starting points, we show that it is quite difficult for the designer to find a starting point yielding a convergence of the algorithm to a local minimum and to find better points yielding the global solution (previously found using a global optimization algorithm). Furthermore, we discuss how to deal with the insertion of the integer variable p, representing the number of pole pairs of the machine, inside the problem of design which uses a standard local continuous optimization code to be solved.