In this paper we focus on multi-objective optimization in electromagnetic problems with given priorities among the targets. The approach proposed in this paper is able to build a proper cost function capable to correctly implementing the design criteria and their priorities avoiding the evaluation of the Pareto front of the solutions, which is a very time consuming task required in the classic a-posteriori methods. The resulting function, named Quantized Lexicographic Weighted Sum (QLWS), can be used as cost function in a very large class of electromagnetic problems. In this paper we demonstrate its usefulness in two common situations in antenna array design: the synthesis of a sparse linear array and a sparse isophoric ring array.
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