random expression generation

[Gasper Slapnicar]

Hello everyone.

I am rather new to both symbolic regression and sympy. I am trying to use expressions (mathematical equations) to represent individuals in a genetic algorithm population. However, i came across the following issue:

When trying to create an initial population, i have to create equations/expressions/trees from a fixed set of Symbols and operations. I do not know how to combine them into random combinations representing complete expression trees.

Here is my code snippet:

# Symbols
x1, x2 = symbols('x1, x2')
# Functions
operations = [Add, Mul, Rational, Pow, sin, cos, tanh, log]
for i in xrange(100):
    random_operation = randint(0, 7)
    print operations[random_operation]

With this i manage to get a random operation as described here: http://docs.sympy.org/dev/tutorial/manipulation.html

However, i would like to create complete examples of equations/expressions/trees, including my symbols, so that i can represent them as trees. My ultimate goal is to evolve this population by substituting certain operations/symbols for the new population (crossover, mutation, etc). For example, i would like to have (many different random combinations):

>>> expr = (Symbol('x1')+Symbol('x2'))**2 / 3

>>> srepr(expr)

Mul(Rational(1,3),Pow(Add(Symbol(′x1′),Symbol(′x2′)),Integer(2)))

Any help much appreciated.

Thank you and kind regards,

Gasper

[Richard Fateman]

This strikes me as a rather weak idea from a genetic algorithms point of view.

but you can create expressions by a recursive algorithm  (given some chosen maximum length) from the root

by picking an operation at each level, knowing the number of operands each takes.

[Francesco Bonazzi]

By just looking up on google:

http://mathematica.stackexchange.com/questions/11632/how-to-generate-a-random-tree

Anyway, if you do go on with your code, would you feel like sharing it? We could merge into SymPy a random expression generator, it can always be useful.

Easiest way, recursive function picking a random element each time. If it's an atom, stop, otherwise call the function recursively on the children elements.

You could easily store your node elements in a dictionary, telling you how many children there are.

[Francesco Bonazzi]

Maybe also this could help:
https://en.wikipedia.org/wiki/Random_tree