On EM-Driven Size Reduction of Antenna Structures With Explicit Constraint Handling

Abstract

Simulation-driven miniaturization of antenna components is a challenging task mainly due to the presence of expensive constraints, evaluation of which involves full-wave electromagnetic (EM) analysis. The recommended approach is implicit constraint handling using penalty functions, which, however, requires a meticulous selection of penalty coefficients, instrumental in ensuring optimization process reliability. This paper proposes a novel size reduction technique with explicit handling of design constraints. Our approach employs trust-region gradient-based procedure as an underlying optimization engine, and adjusts the search radius based on assessing the quality of representing constraints by auxiliary linear expansion models (versus their exact evaluation through EM analysis), rather than based on the quality of objective rendition. This unconventional utilization of trust region framework leads to a procedure that is demonstrably superior over implicit methods, as indicated by comprehensive numerical studies involving three broadband antennas, and benchmarking against state-of-the-art techniques. The two most attractive features of our methodology are simplicity, and no need to tune the algorithm for a specific problem at hand.

Optimization-Based High-Frequency Circuit Miniaturization through Implicit and Explicit Constraint Handling: Recent Advances

“…It should be noted, however, that implementation of these strategies is rather complex. Recently, a technique for explicit constraint control in high-frequency design has been presented [44], which operates on entirely different principles while enabling similar benefits as the procedures of [41,42]. This section outlines this approach and illustrates it using two examples.…”

“…The approach of [44] is embedded in the trust-region (TR) framework [54] briefly outlined in Section 3.1. In [44], the following model of the kth constraint S ineq.k (r(x)) is used:…”

“…, n ineq . The keystone of the procedure [44] is the updating scheme for the trust-region size d (i) . It has been explained in Figure 8.…”

“…Rule 3 overrides both Rules 1 and 2 if the actual violation at x (i+1) is lower than G k (i) . This allows for avoiding erratic behavior in the vicinity of the feasible region boundary [44]. Some examples of poor and good constraint prediction can be found in Figure 10.…”

“…Moreover, the entire adjustment procedure is problem-dependent and needs to be readjusted accordingly. A workaround has been proposed by implementing an explicit method of handling constraints [43,44] using the trust-region (TR) framework as the optimization engine. Therein, the TR search radius is adjusted based on a cheap linear approximation of the design constraints rather than based on the quality of the objective function.…”