Suppose we have a MxN grid with each cell having a particular (random) number. Also suppose that you are an organism capable of moving one cell left/right/up/down and accessing the number on the cell you are presently standing on. Moving takes away X units of energy/time and accessing the number takes Y units/time. You are assigned the task to search for a particular number NUM in the grid using the least amount of energy/time. You are allowed to choose the location (middle/corner/random) where you want to start searching. What will be your search strategy?

Will you do a systematic search or a clumsy search? Well, this is what I want to find out. I want to find out which is the best search strategy when there is a random chance of hitting upon the goal. Maybe, someone ( me, perhaps! ) should apply genetic programming to evolve agents who do this and then analyze their strategy.

This problem can be very exciting and can have huge applications.

I dare to say:

if the gird is totally randomized, there is not much you can do, except to make sure that you choose a path where you traverse and access every cell only once.

if the gird is not 100% random, it depends on how exactly the values of the cells relate to each other, and there might be an ideal algorithm.

can you agree?

Maybe, you are true. But in traversing each cell, there must be N number of strategies out of which one or more can be regarded as the best.

Assuming that you have N algorithms (A1 to An), and two different, totally random grids X and Y.

Maybe A1 will be best for X, and A2 best for Y. I see no possibility to say anything in advance if there is only random data. But if there is the slightest bit of non-random in your grid, and if you KNOW something about it, then there is a chance for on optimal algorithm that takes this information into account.