Recent advances in rapid multiobjective optimization of expensive simulation models in microwave and antenna engineering by Pareto front exploration

Abstract

Practical engineering design problems are inherently multiobjective, that is, require simultaneous control of several (and often conflicting) criteria. In many situations, genuine multiobjective optimization is required to acquire comprehensive information about the system of interest. The most popular solution techniques are population‐based metaheuristics, however, they are not practical for handling expensive electromagnetic (EM)‐simulation models in microwave and antenna engineering. A workaround is to use auxiliary response surface approximation surrogates but it is challenging for higher‐dimensional problems. Recently, a deterministic approach has been proposed for expedited multiobjective design optimization of expensive models in computational EMs. The method relies on variable‐fidelity EM simulations, tracking the Pareto front geometry, as well as response correction. The algorithm sequentially generates Pareto‐optimal designs using a series of constrained single‐objective optimizations. The previously obtained design is used as a starting point for the next iteration. In this work, we review this technique and its modification based on space mapping surrogates. We also propose new variations exploiting adjoint sensitivities, as well as response features, which can be attractive depending on availability of derivatives or the characteristics of the system responses that need to be handled. We also discuss several case studies involving various antenna and microwave components.

Locating Pareto optimal designs of antenna through parallel multiobjective evolutionary algorithm

“…For many antenna designs, there are several performance characteristics to be synthesized 1‐11 . It is hard to find a single design to trade off all design objectives because a design improving one performance characteristic might destroy another one 1 .…”

“…Pareto set (PS) is composed of all Pareto optimal designs, and Pareto front (PF) is its mapping in range. For antenna practitioners, it is much important to identify the best possible trade‐offs (ie, Pareto set in optimization community 1 ) among all design specifications for making application‐dependent decisions 1‐15 . A final design could be selected from the candidate designs according to the designer's preference 1 .…”

“…3. Electromagnetic (EM) simulation for objective function evaluation of one design is computationally expensive 5‐11 …”

“…In addition, certain engineering experience of the MOPs is required, and it is difficult to select the suitable type and parameters of the surrogate models for engineers 19‐21 . Another kind of popular method for solving MOPs is population‐based multiobjective metaheuristic due to its global searching capabilities regardless of the complexity of design objectives and the ability of obtaining an entire set of Pareto optimal designs in a single run 1‐15 . However, expensive computational time caused by thousands or tens of thousands of objective function evaluations through full‐wave EM simulation makes it difficult to be implemented in practical applications 5‐11 .…”

“…Another kind of popular method for solving MOPs is population‐based multiobjective metaheuristic due to its global searching capabilities regardless of the complexity of design objectives and the ability of obtaining an entire set of Pareto optimal designs in a single run 1‐15 . However, expensive computational time caused by thousands or tens of thousands of objective function evaluations through full‐wave EM simulation makes it difficult to be implemented in practical applications 5‐11 . Parallelization could fully exploit the hardware resources and assign the overall computational cost to multiple threads or several slave computers 22‐25 .…”