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I am studying hill climbing algorithm and this topic seems so confusing.

  1. What is ridge basically?

  2. Can you show an example while searching using hill climbing when ridge occurs?

I have researched in internet about this topic but it only left me with more confusions. It seems like ridge seems very similar to local maximum imo. In the sense there are some big hills later on. But it says a lot of other things which I found very confusing. Need some help here. Here is the pdf that I collected by studying from various sources.

I would like to visualize and understand this figure-:

enter image description here

I have collected some resources for studying this topic. If It is legal to share it here is it-:

https://jmp.sh/OMZtkWF

I first asked this in other forums here are responses from other forums that I didn't understand that deeply-:

enter image description here enter image description here

My confusion with this is that-:

if that's the case all of hill climbing is filled with ridge. i don't understand this. its name is hill climbing but it says that it can only travel in x or y directions. what does this mean..if we are in a steep hill then how can we travel only x direction or y direction, how can maxima and minima exists in that case if we are moving only in x or y direction? i don't quite get it. Also you say every direction we are allowed to move in sends us downhill. From which point are you talking can you show that in that above figure?

Sadly the guy could not elaborate further so I am here on stackexchange. That conversation is just for reference, no need to answer that, just to get you a view of what I am confused.

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Ridges are maxima that are very elongated in one direction. When you sample such a function, the sampling points will not fall exactly on the ridge line and will "fluctuate randomly", giving the impression of numerous local maxima.

enter image description here

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ridge [rɪdʒ] NOUN a long, narrow hilltop, mountain range, or watershed: "the North-East ridge of Everest" synonyms: mountain · hill · height · alp · aiguille · serac · puy · crag · tor · inselberg · [more]

by looking at the definition of "ridge" I think we can simply understand it as a hill. although we need to keep in mind that there could be more than one ridges in the plot. some of these ridges will be the local optimum (lower ridges) and only one can be the true optimum (highest ridge)

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