Question

In my program i have a loop which computes integer values and put it one after another into an arraylist.
The higher the computetd integer value is, the better it is.
Now i want to continue to compute until it seems to be that there will not come any better integer value. That is, when the computed integer decreases over a range, or it does not change anymore. I’m thinking of, comparing the current computed value with the last x (how much value do i have to concern?) If it is always smaller or equals than any of the last x elements I stop computing. But with this strategy i have no guarantee that this is the global maximum, but just a local….

What is a good strategy to do that?

EDIT:
I know that there can’t be a guarantee to find the global maximum.
But i know a little about the behaviour of the function:
The more values i have already computed the more unlikely it is that the global maximum will appear.

Answer 1

Well, it seems that you need to assume some heuristics to assess when to stop. Since you cannot say “I stop now, as I found my max”, you can proceed in one of the following fashions:

• Keep current maximum and compare the next value with the current one, if it is smaller, increase the counter. If the counter reaches X (your parameter) you stop
• Use a probablity distributionfunction which has probability of 1 at 0, and 0 at +inf. this can be tailored to your liking. Then, you simply increment the number of seen values, or a counter of smaller values, and using that counter you estimate the probability using that function. If prob < X (your param again) you stop.

Hope this gives you some idea