Multi-objective Memetic Algorithm with Adaptive Weights for Inverse Antenna Design

TL;DR

The paper tackles inverse antenna design as a multi-objective optimization problem with conflicting metrics such as bandwidth, size, matching, and manufacturability. It introduces a multi-objective memetic algorithm with adaptive weights (MOMA-AW) that assigns weight vectors to agents and blends a gradient-based local search with NSGA-II to explore the Pareto front within a single run. Key contributions include a MO formulation with adaptive weights, a neighborhood-based weight update strategy, and a weight-to-solution association mechanism, yielding faster convergence and richer Pareto fronts compared to scalarization or vanilla MO approaches; the method is validated on four challenging antenna design problems. The approach provides a practical, data-rich tool for rapid exploration of design trade-offs and can serve as a data-mining platform for physics-informed machine learning in antenna design.

Abstract

This paper deals with discrete topology optimization and describes the modification of a single-objective algorithm into its multi-objective counterpart. The result is a significant increase in the optimization speed and quality of the resulting Pareto front as compared to conventional state-of-the-art automated inverse design techniques. This advancement is possible thanks to a memetic algorithm combining a gradient-based search for local minima with heuristic optimization to maintain sufficient diversity. The local algorithm is based on rank-1 perturbations; the global algorithm is NSGA-II. An important advancement is the adaptive weighting of objective functions during optimization. The procedure is tested on four challenging examples dealing with both physical and topological metrics and multi-objective settings. The results are compared with standard techniques, and the superb performance of the proposed technique is reported. The implemented algorithm applies to antenna inverse design problems and is an efficient data miner for machine learning tools.

Figures (17)

• Figure 1: Three parameter spaces used in this paper. (a) The design region is discretized, here into a set of triangles, and antenna $\varOmega_n$ is represented by vector $\mathbf{g}_n$, with zeros corresponding to a vacuum and ones corresponding to a metal. The values of vector $\mathbf{g}_n$ form the variable space. (b) The weighting sum method is used in this work to deal with multi-objective (MO) problems Ehrgott_MulticriteriaOptimization. The vector of weights $\mathbf{w}$ is assigned from a normalized barycentric coordinate system. (c) Antenna performance is studied in the objective space. The variables (shapes) and weights are set so that the Pareto front demonstrates the trade-off between optimized parameters.
• Figure 2: The flowchart of the proposed multi-objective memetic algorithm with adaptive weights (MOMA-AW) proposed in this paper. Here, $\mathbf{f}$ denotes the vector of objective function values, matrix $\mathbf{W}$ is the set of weighting vectors, $\mathcal{G}$ and $\mathcal{O}$ represent the sets of agents (generation) and offspring candidates, respectively.
• Figure 3: Association of weighting vectors $\mathbf{w}_i$ to solutions $\mathbf{g}_j \subset \mathcal{O}_t$ (dark blue circles) proposed by NSGA-II based on the previous generation $\mathcal{G}_{t-1}$ (orange plus markers). Weighting vector $\boldsymbol{w}_i$ is associated with solution $\boldsymbol{g}_j$ based on similarity angle $\nu_{i,j}$. The local algorithm then leads the proposed solutions to locally optimal solutions (red crosses) near the true Pareto front (black bold curve). The weighting vectors are convex, i.e., they form an $M$-dimensional simplex (green bold curve).
• Figure 4: Multi-objective topology optimization of the Q factor and the electrical size $ka$. The design region is a rectangular plate of the side aspect ratio 2:1 with $16 \times 8$ pixels ($744$ basis functions). The structure is fed by a discrete feeder in the middle of the longer edge, see Fig. \ref{['fig:ExA2']}. Different sets of markers represent different optimization methods. The method proposed in this paper (MOMA-AW) has the non-dominated solutions denoted by circles. The black dashed line shows the asymptote $1/(ka)^3$ normalized so that it is equal to the value $Q_{\mathrm{min}, ka=0.5}/Q_\mathrm{lb}^\mathrm{TM}=1.11$ at $ka=0.5$, where $Q_{\mathrm{min},ka=0.5}$ is the minimum Q factor value found by topology optimization. All traces are normalized to the Q factor lower bound evaluated for $ka = 0.5$ ($Q_\mathrm{lb}^\mathrm{TM} = 42.2$) with only TM modes considered Capek_etal_2019_OptimalPlanarElectricDipoleAntennas. Four diverse solutions are tagged by a letter, and the associated candidates are shown in Fig. \ref{['fig:ExA2']}. The best run out of 30 runs (in terms of maximum HV) is shown for all three optimization methods.
• Figure 5: Four Pareto-optimal candidates from Fig. \ref{['fig:ExA1']}, labeled A-D, are shown from left to right. Their normalized Q factor performance and electrical size are shown on the top. The electrical size of the smallest circumscribing sphere is highlighted by the black circle.