biogeme.optimization

Examples of use of several functions.

This is designed for programmers who need examples of use of the functions of the module. The examples are designed to illustrate the syntax. They do not correspond to any meaningful model.

Michel Bierlaire Sun Jun 29 2025, 18:10:12

from IPython.core.display_functions import display

import biogeme.biogeme_logging as blog
from biogeme.biogeme import BIOGEME
from biogeme.data.swissmetro import (
    CAR_AV_SP,
    CAR_CO_SCALED,
    CAR_TT_SCALED,
    CHOICE,
    SM_AV,
    SM_COST_SCALED,
    SM_TT_SCALED,
    TRAIN_AV_SP,
    TRAIN_COST_SCALED,
    TRAIN_TT_SCALED,
    read_data,
)
from biogeme.expressions import Beta
from biogeme.models import loglogit
from biogeme.results_processing import get_pandas_estimated_parameters
from biogeme.version import get_text

Version of Biogeme.

print(get_text())

The logger sets the verbosity of Biogeme. By default, Biogeme is quite silent and generates only warnings. To have more information about what it happening behind the scene, the level should be set to blog.INFO.

logger = blog.get_screen_logger(level=blog.INFO)

Read the data file

the_data = read_data()

Parameters to be estimated: alternative specific constants

asc_car = Beta('asc_car', 0, None, None, 0)
asc_train = Beta('asc_train', 0, None, None, 0)

The constant associated with Swissmetro is normalized to zero. It does not need to be defined at all. Here, we illustrate the fact that setting the last argument of the Beta function to 1 fixes the parameter to its default value (here, 0).

asc_sm = Beta('asc_sm', 0, None, None, 1)

Coefficients of the attributes

b_time = Beta('b_time', 0, None, None, 0)
b_cost = Beta('b_cost', 0, None, None, 0)

Definition of the utility functions.

v_train = asc_train + b_time * TRAIN_TT_SCALED + b_cost * TRAIN_COST_SCALED
v_sm = asc_sm + b_time * SM_TT_SCALED + b_cost * SM_COST_SCALED
v_car = asc_car + b_time * CAR_TT_SCALED + b_cost * CAR_CO_SCALED

Associate utility functions with the numbering of alternatives.

v = {1: v_train, 2: v_sm, 3: v_car}

Associate the availability conditions with the alternatives.

av = {1: TRAIN_AV_SP, 2: SM_AV, 3: CAR_AV_SP}

Definition of the model. This is the contribution of each observation to the log likelihood function.

log_probability = loglogit(v, av, CHOICE)

scipy: this is the optimization algorithm from scipy.

my_biogeme_scipy = BIOGEME(
    the_data,
    log_probability,
    save_iterations=False,
    generate_html=False,
    generate_yaml=False,
    optimization_algorithm='scipy',
)
my_biogeme_scipy.model_name = 'simple_example_scipy'
print(my_biogeme_scipy)
results_scipy = my_biogeme_scipy.estimate(
    starting_values={'asc_train': 0, 'b_time': 0, 'b_cost': 0, 'asc_car': 0}
)
pandas_parameters_scipy = get_pandas_estimated_parameters(
    estimation_results=results_scipy
)
display(pandas_parameters_scipy)

Here are the messages generated by the optimization algorithm

for k, v in results_scipy.optimization_messages.items():
    print(f'{k}:\t{v}')

Newton with trust region

my_biogeme_tr_newton = BIOGEME(
    the_data,
    log_probability,
    save_iterations=False,
    generate_html=False,
    generate_yaml=False,
    optimization_algorithm='TR-newton',
)
my_biogeme_tr_newton.model_name = 'simple_example_tr_newton'
print(my_biogeme_tr_newton)
results_tr_newton = my_biogeme_tr_newton.estimate(
    starting_values={'asc_train': 0, 'b_time': 0, 'b_cost': 0, 'asc_car': 0}
)
pandas_parameters_tr_newton = get_pandas_estimated_parameters(
    estimation_results=results_tr_newton
)
display(pandas_parameters_tr_newton)

Here are the messages generated by the optimization algorithm

for k, v in results_tr_newton.optimization_messages.items():
    print(f'{k}:\t{v}')

Newton/BFGS with trust region for simple bounds

This is the default algorithm used by Biogeme. It is the implementation of the algorithm proposed by Conn et al. (1988).

my_biogeme_simple_bounds = BIOGEME(
    the_data,
    log_probability,
    save_iterations=False,
    generate_html=False,
    generate_yaml=False,
    optimization_algorithm='automatic',
)
my_biogeme_simple_bounds.model_name = 'simple_example_simple_bounds'
print(my_biogeme_simple_bounds)
results_simple_bounds = my_biogeme_simple_bounds.estimate(
    starting_values={'asc_train': 0, 'b_time': 0, 'b_cost': 0, 'asc_car': 0}
)
pandas_parameters_simple_bounds = get_pandas_estimated_parameters(
    estimation_results=results_simple_bounds
)
display(pandas_parameters_simple_bounds)

Here are the messages generated by the optimization algorithm

for k, v in results_simple_bounds.optimization_messages.items():
    print(f'{k}:\t{v}')

When the second derivatives are too computationally expensive to calculate, it is possible to avoid calculating them at each successful iteration. The parameter second_derivatives allows to control that.

my_biogeme_simple_bounds_no_hessian = BIOGEME(
    the_data,
    log_probability,
    save_iterations=False,
    generate_html=False,
    generate_yaml=False,
    optimization_algorithm='simple_bounds',
    second_derivatives=0,
)
my_biogeme_simple_bounds_no_hessian.model_name = (
    'simple_example_simple_bounds_no_hessian'
)
print(my_biogeme_simple_bounds_no_hessian)
results_simple_bounds_no_hessian = my_biogeme_simple_bounds_no_hessian.estimate(
    starting_values={'asc_train': 0, 'b_time': 0, 'b_cost': 0, 'asc_car': 0}
)
pandas_parameters_simple_bounds_no_hessian = get_pandas_estimated_parameters(
    estimation_results=results_simple_bounds_no_hessian
)
display(pandas_parameters_simple_bounds_no_hessian)

Here are the messages generated by the optimization algorithm

for k, v in results_simple_bounds_no_hessian.optimization_messages.items():
    print(f'{k}:\t{v}')