Slide 9 of 19
Notes:
-While there was no clearly dominant global optimization method, RANDLO (random local optimization) and SALO (ASA atop local optimization) generally performed most impressively for this set of test functions. RANDLO and SALO seem best suited for functions with few and many local minima respectively.
-Using local optimization as a subroutine is generally beneficial for this class of problems, as it effectively "flattens" and simplifies each search space. For instance, a parabola modulated with sinusoidal hills and valleys is roughly transformed into a parabola of plateaus. We'll touch on this point again later.
-Also, local optimization often doesn't lead us to the "nearest" optimum. This can sometimes work against the usefulness of local optimization for global optimization.
-It is interesting that, although global optimization usually takes place within a bounded space, test functions in the literature (including those I’ve chosen) very rarely have global minima at or even somewhat close to the bounds of the space. Our motivating stepper motor test function, however has all minima along the bounds of the search space. That test function was the focus of the next phase of the study.