MLLO Example: Rastrigin Function

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Here we see MLLO-RIQ optimizing the Rastrigin function, a two-dimensional sinusoidally modulated function with a global minimum of zero at the origin. The plot at the right gives an overhead view of the algorithm at work. The green lines represent movement of the center of our search. Red circles indicate the search radius. Blue lines indicate quasi-Newton local optimizations, and magenta lines connect the starting points of those optimizations to the current search center. From our starting center point, the algorithm repeatedly finds new, lower centers. Even when the estimated gradient of quasi-Newton local optimization causes it to leap over the global minimum, our function evaluations so far still bias the search in the correct direction and the global minimum is soon found.