Slide 17 of 19
For our first set of test functions, the results of trials performed to date with MLLO-RIQ are very encouraging. The question marks indicate problems with a Matlab constrained minimization routine which prevented us from performing all trials by the time of this talk. For every other test function which can be minimized with quasi-Newton local optimization, MLLO-RIQ gives the strongest results yet. (Note the uniform failure of these methods for test function CMMR, the discontinuities of which were understandably troublesome to our chosen quasi-Newton local optimization. In our study, the only successful trials for CMMR were those of methods not dependent on local optimization.)
For simple test functions, bottom level local optimization quickly finds the global minimum and terminates the search. This is in contrast to methods such as MLSL or genetic algorithms which have a startup sampling cost. For more complex test functions with many minima, MLLO-RIQ efficiently searches the "flattened" search space to find the global minimum.