Implement symbolic regression problem instances from "A multilevel block building algorithm for fast modeling generalized separable systems"

[gkronber]

See: ​https://arxiv.org/abs/1706.02281

This paper uses data from physical formulas as benchmark problems. The formulas are complex (complex non-separable terms, several variables and variable references, etc.). It also describes comparisons with experiments using the "Eureka" software (convenient for further papers!).

Interesting formulas are listed in Equation 2.1, 2.2 and 2.4, ranges for variable values are in the appendix. Ranges for values and "readable" formulas are given in the appendix.

[gkronber]

r16264: initial import of physics problems implemented by lkammere

[gkronber]

r16394: reviewed implementation and made some adjustments.

The "maximum lift of whole aircraft" is only described in the arXiv version of the paper but has been removed in the peer-reviewed version for ESWA. There seems to be an error in the pre-print (x5 and x6 stand for only one variable in the original formula and the ranges for valid values are missing).

I decided to keep the problem and assumed a rather large range to make the problem more interesting for benchmarking purposes. All differences to the published version of the problem instances are described.

[gkronber]

There were two significant changes made in r16394:

• for the lift coefficicent, I changed x1*(x2 - 2) + ... to C_L = C_La (a + 2) + ... because the paper states that a0 is set to -2° in C_La (a - a0)
• for the flow psi problem, I changed x1*x2*x5*(1 - x4²/x5²) + ... to V_inf r sin(th) (1 - R²/r²) + .... So it is now necessary to identify the function sin(th) as a factor.

[lkammere]

r16431: Fixed visibility of regression instance providers for physics benchmark problems.

[gkronber]

Reviewed r16431.

[gkronber]

r16495: merged r16264, r16394, r16431 from trunk to stable