Multiminima Heuristic Methods for Antenna Optimization

Abstract

Two general approaches to multiminima optimization are considered. The first approach is based on repetition of a single minima method (e.g., the Nelder-Mead simplex applied to the best solution in a set of random trials). The second approach is based on a coarse estimation of local minima using initial set of points and local optimization starting from these local minima (e.g., random search as a generator of the initial set of points and Nelder-Mead simplex as a local optimizer). A comparison of various optimization algorithms has been done on one analytical problem and two well-known examples of antenna design. It is found that: a) the multiminima method based on coarse estimation enables finding more minima with smaller number of iterations than that based on repetition, b) the best multiminima methods are comparable with the best single minima methods in a number of iterations needed for finding the global minima, and c) the multiminima method based on coarse estimation restarted with different weighting coefficients of multiobjective cost function enables efficient Pareto optimization