In electromagnetic design, the traditional approach to multiobjective optimisation implies to set up a preference function, expressing a compromise among the various objectives and depending on weight coefficients or threshold values; successively, standard single-objective optimisation methods can be used to find the optimum of the preference function.
Although offering a friendly implementation, scalar formulation presents several drawbacks: first of all, the result of an optimisation gives a single solution, which is supposed to be globally optimal. A criticism is that it is not clear whether the solution found is a non-dominated one; moreover, even if it is dominated, it is not clear where the solution is located with respect to the PF.
Another criticism follows: solving a multiobjective optimisation problem gives rise to a variety of solutions, which are spread along the PF; in Chapter 7 it will be clarified that knowing this variety is useful for the designer, who is provided with a wide range of possibilities for a choice a posteriori. In order to obtain different solutions located on the PF, one could run successive single-objective optimisations after modifying the preference function, and then collect results in a comparative way. This strategy might work in some particular cases; in general, however, it is unattractive for a twofold reason; in fact, it might originate dominated solutions; moreover, it makes it difficult to generate solutions uniformly spaced on the PF.
Various scalar formulations, which are commonly used in electromagnetic design, are now presented.