دانلود رایگان مقاله بهینه سازی چند هدفه مدل های شبیه سازی الکترومغناطیسی گران

Abstract

Vast majority of practical engineering design problems require simultaneous handling of several criteria. For the sake of simplicity and through a priori preference articulation one can turn many design tasks into single-objective problems that can be handled using conventional numerical optimization routines. However, in some situations, acquiring comprehensive knowledge about the system at hand, in particular, about possible trade-offs between conflicting objectives may be necessary. This calls for multi-objective optimization that aims at identifying a set of alternative, Pareto-optimal designs. The most popular solution approaches include population-based metaheuristics. Unfortunately, such methods are not practical for problems involving expensive computational models. This is particularly the case for microwave and antenna engineering where design reliability requires utilization of CPU-intensive electromagnetic (EM) analysis. In this work, we discuss methodologies for expedited multi-objective design optimization of expensive EM simulation models. The solution approaches that we present here rely on surrogate-based optimization (SBO) paradigm, where the design speedup is obtained by shifting the optimization burden into a cheap replacement model (the surrogate). The latter is utilized for generating the initial approximation of the Pareto front representation as well as further front refinement (to elevate it to the high-fidelity EM simulation model level). We demonstrate several application case studies, including a wideband matching transformer, a dielectric resonator antenna and an ultra-wideband monopole antenna. Dimensionality of the design spaces in the considered examples vary from six to fifteen, and the design optimization cost is about one hundred of high-fidelity EM simulations of the respective structure, which is extremely low given the problem complexity.

4. Discussion and conclusion In the paper, we investigated cost-efficient design optimization of expensive computational electromagnetic (EM) models. We demonstrated that a suitable combination of various con-cepts borrowed from surrogate-based modeling and optimization such as utilization of variable-fidelity EM simulations, response correction techniques, as well as response surface approximation modeling, allows for expedited identification of Pareto-optimal designs at the cost corresponding to just a few dozen of high- fidelity EM model evaluations. Our methodology can be applied in various fields exploiting computational electromagnetics such as microwave and antenna engineering, wireless power transfer, microwave photonics, etc. We discussed several specific applications, including multi-objective design of a wideband impedance matching transformer and two antenna structures. A potentially high cost of evolutionary-algorithm-based optimization required to identify the Pareto front has been mitigated by executing the search at the level of a fast kriging interpolation model and subsequent Pareto set refinement (also realized with surrogate-based optimization). Design space reduction applied as the first stage of the process allows for handling higher-dimensional problems. Also, suitable statistical studies demonstrated that the potential issue of lack of repeatability of Pareto front identification with population-based metaheuristics is well controlled by the remaining stages of the optimization process. Overall, the framework discussed in this work may be considered as a step towards computationally-efficient automation of multi-objective design optimization processes involving expensive simulation models. Although showcased for problems in computational electromagnetics, it might also be useful for handling design tasks in other engineering fields.