General

RILS-ROLS is metaheuristic-based framework to deal with problems of symbolic regression.

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 Djukanovic. This paper is currently under review in the Journal of Big Data, Springer.

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

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:

pip install rils-rols

Minimal working example

from rils_rols.rils_rols import RILSROLSRegressor
from rils_rols.rils_rols_ensemble import RILSROLSEnsembleRegressor
from math import sin, log


''' RILSROLSRegressor parameters:
    1. max_fit_calls=100000             -- maximal number of fitness function calls
    2. max_seconds=100                  -- maximal running time in seconds
    3. fitness_type=FitnessType.PENALTY -- function that guides the search process, other possibilities are: FitnessType.BIC and FitnessType.SRM
    4. complexity_penalty=0.001         -- expression size penalty (used for FitnessType.PENALTY) -- larger value means size is more important
    5. initial_sample_size=0.01         -- the size of the sample taken from the training part (initially)
    6. random_perturbations_order=False -- if True, perturbations are checked in a random order, otherwise, according to R^2 of perturbation 
    7. verbose=False                    -- if True, the output during the program execution contains more details
    8. random_state=0                   -- random seed -- when 0 (default), the algorithm might produce different results in different runs
'''

''' RILSROLSEnsembleRegressor parameters:
    1. max_fit_calls=100000             -- maximal number of fitness function calls
    2. max_seconds=100                  -- maximal running time in seconds
    3. fitness_type=FitnessType.PENALTY -- function that guides the search process, other possibilities are: FitnessType.BIC and FitnessType.SRM
    4. complexity_penalty=0.001         -- expression size penalty (used for FitnessType.PENALTY) -- larger value means size is more important
    5. initial_sample_size=0.01         -- the size of the sample taken from the training part (initially)
    6. parallelism=8                    -- determines the number of RILS-ROLS regressors used in the ensemble
    7. verbose=False                    -- if True, the output during the program execution contains more details
    8. random_state=0                   -- random seed -- when 0 (default), the algorithm might produce different results in different runs
'''

regressors = [RILSROLSRegressor(), RILSROLSEnsembleRegressor()]

# toy dataset 
X = [[3, 4], [1, 2], [-10, 20], [10, 10], [100, 100], [22, 23]]
y = [sin(x1)+2.3*log(x2) for x1, x2 in X]

# RILSROLSRegressor and RILSROLSEnsembleRegressor inherit BaseEstimator (sklearn), so we have well-known fit method
for regressor in regressors:
    regressor.fit(X, y)

    # this prints out the learned simplified model
    print("Final model is:\t"+str(regressor.model_simp))

    # this prints some additional information as well
    output_string = regressor.fit_report_string(X, y)
    print("Detailed output:\t"+output_string)

    # applies the model to a list of input vectors, also well-known predict method
    X_test = [[4, 4], [3, 3]]
    y_test = regressor.predict(X_test)
    print(y_test)

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},
}