initialize with a grid versus random initialization

While optimizing vectors for specific properties, I have been starting with random initialization and then optimizing the same for desired properties. However, I was hinted to start with a grid instead of random, as I am using a gradient method for optimizing and hence, every experiment ends up with a local minima. I have tried seeking more details on "starting with a grid", however, I am unable to find anything relevant and suitable. Can anyone point me in the right direction, a simple layman tutorial?