A Lexicographic Approach for Multi-Objective Optimization in Antenna Array Design

Abstract

Abstract-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.

Multiobjective Optimization of a Rotman Lens through the QLWS Minimization

“…Moreover, D k x k is a function that maps each optimization objective x k onto a real number ranging within the interval I = 0, 1 : the smaller the value of D k x k , the closer the fulfilment of the target relevant to x k . Some examples of D k x k can be found in [14] and are not reported here for brevity. The weighted sum in (3) is inspired by the lexicographic ordering rules, from which it retains its name, that is, quantized lexicographic weighted sum, briefly QLWS.…”

“…The weighted sum in (3) is inspired by the lexicographic ordering rules, from which it retains its name, that is, quantized lexicographic weighted sum, briefly QLWS. Minimization of the QLWS in (3) has been introduced in [14] for the synthesis of sparse arrays; in particular, multiobjective global optimization was performed in that case. In the following section, we show that the QLWS can be exploited also to perform a multiobjective local optimization, as required for the synthesis of a Rotman lens.…”

“…The approach in [14] addresses such kind of problem through the minimization of a GCF built as follows:…”

“…In other words, we have to solve a multiobjective ("multicriteria" or "multiparameter" or "multitarget") problem. To do this, in the following, we set a priori the priorities among the different concurring targets listed above and exploit the method recently proposed in [14] for the multiobjective synthesis of sparse arrays. The method, which is based on the minimization of a properly defined GCF named QLWS and inspired by the lexicographic order rules, is briefly recalled in the next section; for further details, the reader can refer to [14].…”

“…More specifically, we carry out a multiobjective optimization of a Rotman lens, by exploiting the method recently proposed in [14] for the synthesis of sparse arrays. In particular, the method is based on the minimization of a properly defined global cost function (GCF) inspired by the lexicographic order rules and named quantized lexicographic weighted sum (QLWS).…”