Quasi-Gradient Nonlinear Simplex Optimization Method in Electromagnetics

Particle swarm optimization (PSO), genetic algorithm (GA), and nonlinear simplex optimization method (SOM) are some of the most prominent gradient-free optimization algorithms in engineering. When it comes to a common group of electromagnetic optimization problems wherein less than 10 optimization parameters are present in the problem domain, SOM features faster convergence rate vs PSO and GA. Nevertheless, PSO and GA still outperform SOM by having more accuracy in finding the global minimum. To improve the accuracy of SOM in problems with few optimization parameters, a quasi-gradient (Q-G) search direction is added to the conventional algorithm. An extra decision is made by the proposed algorithm to move alongside the reflection or quasi-gradient direction during the error-reduction operations. This modification will improve the accuracy of SOM, which otherwise fails in the examples presented in this article, to levels similar to PSO and GA, while retaining approximately 33% faster convergence speed with relatively small number of parameters, and 20% faster convergence speed with larger number of optimization parameters. Following a standard benchmark test verification, the proposed algorithm successfully solves a suite of electromagnetic optimization problems. Representative examples include the optimization of absorber dimensions in an anechoic chamber, and estimation of the properties of an unknown embedded object by scattered microwave signals.

Automated summary

Particle swarm optimization (PSO), genetic algorithm (GA), and nonlinear simplex optimization method (SOM) are popular gradient-free optimization algorithms in engineering. SOM has faster convergence rate than PSO and GA in electromagnetic optimization problems with less than 10 parameters, but PSO and GA outperform SOM in finding the global minimum. To improve the accuracy of SOM in problems with few parameters, a quasi-gradient (Q-G) search direction is added to the algorithm.