General

RILS-ROLS is metaheuristic-based framework to deal with problems of symbolic regression (and classification as of version 1.4).

All of its aspects (method description, empirical results, etc.) are explained in the paper named: "RILS-ROLS: Robust Symbolic Regression via Iterated Local Search and Ordinary Least Squares" by Aleksandar Kartelj and Marko Đukanović in the Journal of Big Data, Springer. The third author, who came later, is Ján Pigoš (https://github.com/janoPig). He was instrumental in improving the efficiency by almost three orders of magnitude (the module was rewritten in C++) and he also helped develop the symbolic classifier based on the symbolic regression algorithm as a backbone.

All RILS-ROLS resources can be found at https://github.com/kartelj/rils-rols

For the quickest start you can check the working colab notebook, with minimal working example here: https://colab.research.google.com/drive/1U8I92VTQao9UA9ErBK3VX9AbpIX1LLIv?usp=sharing

If you wish to run it locally, RILS-ROLS distribution is available as a pip package at https://pypi.org/project/rils-rols, so it can be easily installed with the following pip command on Windows (binaries available):

pip install rils-rols

On the Linux, the source must be build as a Pybind11 C++ module, so there are two commands in that case:

pip install pybind11
pip install rils-rols

Minimal working example

from sklearn.model_selection import train_test_split
from sklearn.datasets import load_diabetes, load_breast_cancer
from rils_rols.rils_rols import RILSROLSRegressor, RILSROLSBinaryClassifier
from random import seed, randint
from math import sin, log

''' RILSROLSRegressor/RILSROLSClassifier parameters:
    1. max_fit_calls=100000             -- maximal number of fitness function calls
    2. max_seconds=100                  -- maximal running time in seconds
    3. complexity_penalty=0.001         -- expression size penalty (used for FitnessType.PENALTY) -- larger value means size is more important
    4. max_complexity = 50              -- the maximal size of internal expression (without symplification)
    5. sample_size=1                    -- the size of the sample taken from the training part, takes value from [0, 1], where 0 activates automatic sample size selection
    6. verbose=False                    -- if True, the output during the program execution contains more details
    7. random_state=0                   -- random seed -- when 0 (default), the algorithm might produce different results in different runs
'''

random_state = 12345
samples = 200
train_size = 0.75
seed(random_state)

# toy regression dataset with known ground-truth 
X = list(zip([randint(1, 100) for _ in range(samples)], [randint(1, 100) for _ in range(samples)]))
y = [sin(x1)-78.8*log(x2)+4*x1+3.31*x2 for x1, x2 in X]
X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=train_size, test_size=1-train_size, random_state=random_state)

# RILSROLSRegressor inherit BaseEstimator (sklearn), so we have fit, predict and score methods, where the score method is R2
regressor = RILSROLSRegressor(sample_size=1,random_state=random_state)
regressor.fit(X_train, y_train)
# this prints out the learned simplified model
print(f'Final model is:\t{regressor.model_string()}')
print(f'Training R2 score:\t{regressor.score(X_train, y_train)}')
print(f'Testing R2 score:\t{regressor.score(X_test, y_test)}')
# this prints some additional information as well, uncomment it to show it
#print(f'Other info:\t{regressor.fit_report_string()}')
print('--------------------------------------------------------------------------------------------------------------')

# now regression on the dataset without known ground-truth -- diabetes
X, y = load_diabetes(return_X_y=True)
X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=train_size, test_size=1-train_size, random_state=random_state)
regressor = RILSROLSRegressor(sample_size=1, max_complexity=20, random_state=random_state)
regressor.fit(X_train, y_train)
print(f'Final model is:\t{regressor.model_string()}')
print(f'Training R2 score:\t{regressor.score(X_train, y_train)}')
print(f'Testing R2 score:\t{regressor.score(X_test, y_test)}')
#print(f'Other info:\t{regressor.fit_report_string()}')
print('--------------------------------------------------------------------------------------------------------------')

# finally, binary classification on the sklearn toy dataset -- breast_cancer
X, y = load_breast_cancer(return_X_y=True)
X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=train_size, test_size=1-train_size, random_state=random_state)
regressor = RILSROLSBinaryClassifier(sample_size=1, max_complexity=20, random_state=random_state)
regressor.fit(X_train, y_train)
print(f'Final model is:\t{regressor.model_string()}')
print(f'Training accuracy score:\t{regressor.score(X_train, y_train)}')
print(f'Testing accuracy score:\t{regressor.score(X_test, y_test)}')
#print(f'Other info:\t{regressor.fit_report_string()}')
print('--------------------------------------------------------------------------------------------------------------')

Citation

@article{kartelj2023rilsrols,
  title={RILS-ROLS: Robust Symbolic Regression via Iterated Local Search and Ordinary Least Squares},
  author={Kartelj, Aleksandar and Djukanovi{\'c}, Marko},
  journal={Journal of Big Data},
  volume={10},
  number={71},
  year={2023},
  publisher={Springer}, 
  doi = {10.1186/s40537-023-00743-2},
}