Algorithm Optimisation Championship. - page 98

 
Andrey F. Zelinsky:
Are there moderators on the forum?
Why are you yelling like... Are you in pain or something? Get out of here.
 
Andrey Dik:
Of course, you must. If there are no function suggestions from you, I will post the final version of the codes and then proceed to the second step of the championship.
I may be able to offer some of my own feature suggestions after I see your example. If that would be considered legitimate...)
 
Реter Konow:
Perhaps I can suggest some variant of the function of my own after I see your example. If that would be considered legitimate...)

Yeah, sure, no problem.

pow(cos(0.2e1 * 0.3141592654e1 * x2 * x2) + cos(0.1884955592e1 * y2) - 0.11e2, 0.2e1) + pow(cos(0.1256637062e1 * x2) + cos(0.2e1 * 0.3141592654e1 * y2 * y2) - 0.7e1, 0.2e1)

и

0.3e1 * (double) (int) pow((double) (1 - x3), (double) 2) * exp((double) (-x3 * x3 - (int) pow((double) (y3 + 1), (double) 2)) - 0.10e2 * (0.2e0 * (double) x3 - (double) (int) pow((double) x3, (double) 3) - (double) (int) pow((double) y3, (double) 5)) * exp((double) (-x3 * x3 - y3 * y3)) - exp((double) (-(int) pow((double) (x3 + 1), (double) 2) - y3 * y3)) / 0.3e1;

Here are two examples of functions like f(x1, x2).

 
Andrey Dik:

Yeah, sure, no problem.

pow(cos(0.2e1 * 0.3141592654e1 * x2 * x2) + cos(0.1884955592e1 * y2) - 0.11e2, 0.2e1) + pow(cos(0.1256637062e1 * x2) + cos(0.2e1 * 0.3141592654e1 * y2 * y2) - 0.7e1, 0.2e1)

и

0.3e1 * (double) (int) pow((double) (1 - x3), (double) 2) * exp((double) (-x3 * x3 - (int) pow((double) (y3 + 1), (double) 2)) - 0.10e2 * (0.2e0 * (double) x3 - (double) (int) pow((double) x3, (double) 3) - (double) (int) pow((double) y3, (double) 5)) * exp((double) (-x3 * x3 - y3 * y3)) - exp((double) (-(int) pow((double) (x3 + 1), (double) 2) - y3 * y3)) / 0.3e1;

Here are two examples of functions of the form f(x1, x2).

You can see some discontinuity in the writing of functions...

The correct format is: fy = (x1 + x2 + ...xn) provides the left and right parts of the equation. The number of parameters in these scraps of formulas is obviously small. I thought it would be 500 or more...

 
Реter Konow:
I may be able to suggest some variant of the function of my own after I see your example. If that would be considered legitimate...)

There is only one point which I would like to discuss before publishing the testbench sources.

The point is that I don't know functions which would be interesting enough in terms of complexity for the algorithm over the whole range of its definition at [-DBL_MAX; DBL_MAX] parameters. As far as we all know, double numbers can have 17 digits (16 decimal places) and if we take the [-DBL_MAX; DBL_MAX] range, functions will become insensitive to changes of parameters (because we'll have to scale the range of input values into the functions' sensitivity range) because the step will not be continuous and uniform.

Therefore I propose to use the range [-2.0; 2.0] in steps of 0.0. In fact, due to limitations of number double we get the step 0.0000000000000001, which is interesting in terms of complexity of the problem, so we can fully use all opportunities of number double (number of parameter steps will get 4E16, and if we consider that the parameters are 500, it is clear that there are many variants of FF values, to put it mildly).

 
Реter Konow:

There seems to be some discontinuity in the writing of the functions...

The correct format is: fy = (x1 + x2 + ...xn) provides the left and right sides of the equation. The number of parameters in these scraps of formulas is obviously small. I thought it would be 500 and more...

This is an example of two functions of the form f(x1, x2). The championship FF will consist of 255 such functions, the parameters will be mixed up with each other, all these individual functions will become dependent and affect each other (how exactly - the referee will generate a sequence of calls to individual functions and a sequence of calls to parameters).

If you can, give me an example of such a function of the form f(x1, x2) and I will include it in the general FF.

 
Andrey Dik:

There is only one point which I would like to discuss before publishing the testbench sources.

The point is that I don't know functions which would be interesting enough in terms of complexity for the algorithm over the whole range of its definition at [-DBL_MAX; DBL_MAX] parameters. As far as we all know, double numbers can have 17 digits (16 decimal places) and if we take the [-DBL_MAX; DBL_MAX] range, functions will become insensitive to changes of parameters because the step will not be continuous.

That's why I suggest using the range [-2.0; 2.0] in increments of 0.0. In fact, due to limitations of double number we'll get a step of 0.0000000000000001, which is interesting in terms of complexity of the task, so we can fully use all possibilities of double number.

I don't get it. Step 0.0 means no step...

Well, to use all the possibilities of double number, the range should be [-DBL_MAX; DBL_MAX], with step 0.0000000000000001.

However much we may have overdone it...

 
Реter Konow:

I don't get it. Step 0.0 means no step...

Well, to take full advantage of the number double, the range should be [-DBL_MAX; DBL_MAX], with a step of 0.0000000000000001.

However much we may have overdone it...

Step 0.0 and means step 0.00000000000000000001. As for the range, I described above. I couldn't find any functions that fit the range [-DBL_MAX; DBL_MAX] and are guaranteed to work on this range (it would require research to check, which I don't have time for).

Think about it until tomorrow, it's important to realise that.

 
Andrey Dik:

This is an example of two functions of the form f(x1, x2). The championship FF will consist of 255 similar functions, the parameters will be mixed together, all these individual functions will become dependent and will influence each other (how exactly - the referee will generate a sequence of calls to individual functions and a sequence of calls to parameters).

If you can, provide an example of such a function of the form f(x1, x2) and I will include it in the general FF.

As I understand it, you will combine 255 similar scraps of analytic functions into a single equation. The problem is to find its maxima for the minimum number of calls to the FF.

All you need to know is range, step, number of parameters.

I don't think my personal mathematical surrealism is needed here) I will accept your formulas .

 
Andrey Dik:

Step 0.0 and means step 0.00000000000000000001. As for the range, I described above. I couldn't find any functions that fit the range [-DBL_MAX; DBL_MAX] and are guaranteed to work on this range (it would require research to check, which I don't have time for).

Think about it until tomorrow, it's important to realise that.

I will think about it.