Table 2 Algorithm setup (proposed and benchmark).
From: Rapid global antenna design by simplex regressors and multi-resolution simulations
Algorithm | Name | Outline |
|---|---|---|
This study | Variable-resolution simplex-based global search with gradient-based fine tuning (Sect. Global optimization with simplex regressors and variable-resolution models) | Control parameters: Fmax = 0.2 GHz, α = 0.2, γ = 0.5, Dmin = 1, ε = 10–3 and Mc = 10 (cf. Table 1) |
I | Particle swarm optimizer (PSO) | Swarm size N = 10, number of iterations: 50 (Version I) and 100 (Version II); conventional parameter setup (χ = 0.73, c1 = c2 = 2.05); |
II | Differential evolution (DE) | Population size N = 10, number of iterations set to 50 (Version I) and 100 (Version II); conventional parameter setup (CR = 0.5, F = 1)114; |
III | Trust-region (TR) gradient-based optimizer [107] | Random initialization, Jacobian matrix estimated by finite differentiation, termination: convergence in argument [115] |
IV | Machine-learning procedure | Algorithm setup: Initial surrogate set up to ensure relative RMS error less than 20% (max. number of training samples limited to 400); the algorithm operates in the original parameter space (no dimensionality reduction); infill criterion: minimization of the predicted objective function; surrogate model optimization using the particle swarm optimizer |
V | Simplex-based global search with gradient-based fine tuning | Algorithm setup: the same as for the proposed approach, except that the search process is conducted using Rf |
